Advanced haptic actuators and systems

Abstract

This invention discloses a haptic actuator and associated haptic systems. The haptic actuator comprises a ‎miniaturized electromechanical structure that, when interfacing with a skin of a subject through an energy-recovering mechanism, supports bistable, self-sensing modes of deformation, for delivering dynamic and / or static stimuli of indentation, torsion, and / or vibration to the skin.

Description

[0001] ADVANCED HAPTIC ACTUATORS AND SYSTEMS

[0002] CROSS-REFERENCE TO RELATED PATENT APPLICATION

[0003] This application claims priority to and the benefit of U.S. Provisional Application No. 63 / 713,733, filed October 30, 2024, which is incorporated herein in its entirety by reference.

[0004] FIELD OF THE INVENTION

[0005] The invention relates generally to biosensors, and more particularly to advanced haptic actuators and systems.

[0006] BACKGROUND OF THE INVENTION

[0007] The background description provided herein is for the purpose of generally presenting the context of the invention. The subject matter discussed in the background of the invention section should not be assumed to be prior art merely as a result of its mention in the background of the invention section. Similarly, a problem mentioned in the background of the invention section or associated with the subject matter of the background of the invention section should not be assumed to have been previously recognized in the prior art. The subject matter in the background of the invention section merely represents different approaches, which in and of themselves may also be inventions. Work of the presently named inventors, to the extent it is described in the background of the invention section, as well as aspects of the description that may not otherwise qualify as prior art at the time of filing, are neither expressly nor impliedly admitted as prior art against the invention.

[0008] Human skin possesses a rich composition of afferent neurons. During physical interaction with the skin, cutaneous mechanoreceptors elicit activity in these neurons and serve as the basis for identification and localization of objects. An exciting recent direction in bioelectronics involves the development of systems that can engage these afferents in a fast, programmable manner.

[0009] In contrast with other peripheral nerves, somatosensory afferents can be selectively and noninvasively activated through direct interaction with the surface of the skin. As suggested by the emergence of systems for virtual and augmented reality, capabilities for fast, programmable manipulation of human sensory perception have wide-ranging applications in social media, gaming, and entertainment. Particularly compelling opportunities also exist in therapeutic biomedical systems that apply these somatosensory interfaces towards substituting and augmenting missing sensory capabilities.

[0010] Reaching the full potential of these applications will require engagement of both rapidly and slowly adapting (RA and SA) mechanoreceptors. These specialized cells, by coordinating with each other and with natural mechanical structures distributed throughout the skin, mediate the perceptual and emotional qualities of touch.

[0011] The rich set of mechanoreceptors found in human skin offers a versatile engineering interface for transmitting information and eliciting perceptions, potentially serving a broad range of applications in patient care and other important industries. Targeted multisensory engagement of these afferent units, however, faces persistent challenges, especially for wearable, programmable systems that need to operate adaptively across the body.

[0012] Therefore, a heretofore unaddressed need exists in the art to address the aforementioned deficiencies and inadequacies.

[0013] SUMMARY OF THE INVENTION

[0014] In one aspect, the invention relates to a haptic actuator comprising a miniaturized electromechanical structure that, when interfacing with a skin of a subject through an energyrecovering mechanism, supports bistable, self-sensing modes of deformation, for delivering dynamic and / or static stimuli of indentation, torsion, and / or vibration to the skin.

[0015] In one embodiment, the miniaturized electromechanical structure is a transducer and comprises a core and an armature coupled with one another, upon mechanical coupling with the skin, to form a bistable mechanism for operably storing and releasing mechanical energy in the skin between a compressed state and a relaxed state.

[0016] In one embodiment, the miniaturized electromechanical structure further includes a diaphragm that improves stability of states and enhances vibration.

[0017] In one embodiment, the core comprises an electromagnetic coil embedded in a soft ferromagnetic cylinder for focusing magnetic fields along its central longitudinal axis and reducing interference between closely spaced units.

[0018] In one embodiment, the core comprises an inner core; a cylindrical encasement; a bobbin placed between the inner core and the cylindrical encasement; and an electromagnetic coil wrapping on the bobbing from the bottom surface of the inner core to the opposing face of the bobbin, wherein the inner core and the cylindrical encasement are formed of a soft ferromagnetic material.

[0019] In one embodiment, the soft (low-coercivity) ferromagnetic material comprises iron or other iron-containing alloys, including iron-cobalt, permalloy, and / or stainless steel.

[0020] In one embodiment, the armature comprises a cap formed of a permanent magnetic material; a cylindrical ring formed of a nonmagnetic material (e.g., titanium, plastic, wood, nonmagnetic stainless steel) and / or the soft ferromagnetic material on the permanent magnetic cap; and a rigid rod having a first end being attached to the permanent magnetic cap through the cylindrical ring, and an opposite, second end interfacing with the skin as a linear shaft that translates through the core.

[0021] In one embodiment, the permanent magnetic material comprises a rare earth magnetic material (e.g., neodymium, Samarium-cobalt), and / or iron alloys with high-coercivity (e.g., alnico, ferrite).

[0022] In one embodiment, the diaphragm formed of an elastomeric material is configured to enclose a top of the miniaturized electromechanical structure.

[0023] In one embodiment, the elastomeric material comprises a composite of silicone-based elastomer (e.g., polydimethylsiloxane, PDM, dragonskin, ecoflex, silbione) and magnetic particles (e.g., iron oxide micro- and nano-particles). Such composites include PDMS-MNP described herein.

[0024] In one embodiment, the miniaturized electromechanical structure couples to the skin through an elastomeric substrate (adhesive layer) with a rigid, twist-locking harness whose height are adjustable to change an effective indentation depth of the armature.

[0025] In one embodiment, the harness is provided with a spacer for changing the effective indentation depth.

[0026] In one embodiment, the harness is configured to lock the vertical translation of the miniaturized electromechanical structure upon rotation, wherein a base of the harness adheres to the elastomeric substrate, which, in turn, adheres to the skin of the subject.

[0027] In one embodiment, the base of the harness is reinforced with a fiberglass mesh as a composite within the elastomeric substrate, so as to reduce mechanical mismatch between the harness and the elastomeric substrate.

[0028] In one embodiment, the elastomeric substrate is formed of a silicone-based elastomer.

[0029] In one embodiment, mechanical integration of the skin and bistable operation of the transducer requires that local energetic minima exist at the compressed and relaxed states, and polarization of the coil transiently induces transitions between the compressed state and the relaxed state.

[0030] In one embodiment, in the compressed state, the magnetic field imposed by the permanent magnet, channeled through the armature, magnetizes the soft ferromagnetic core, wherein the strong attraction induced between these elements exceeds the reactive force imposed by the skin, thereby maintaining compression without current applied at the coil, wherein from the compressed state, driving the coil with opposite polarity to the permanent magnet substantially weakens its effect on the core, thereby allowing the skin to push the armature into the relaxed state.

[0031] In one embodiment, in the relaxed state, the elasticity of the skin, along with a slight attraction to the paramagnetic / elastomeric diaphragm, prevents the armature from reverting without applied current, wherein from the relaxed state, driving the coil in alignment with the permanent magnet polarizes the armature and core, overcomes the compressive force of the skin, and drives the armature to transition back into the compressed state.

[0032] In one embodiment, the haptic actuator is operated with an inductance- or resonancebased self-sensing mechanism that operably tailors input power on demand.

[0033] In one embodiment, the haptic actuator is operated with a spring-mass mechanism that serves as the basis for delivering vibrotactile feedback.

[0034] In one embodiment, applying an alternating current at sub-transition amplitude vibrates the armature, creating a small perturbation around the initial state of the transducer, whereby the transducer can bias its modes of vibration to the static position of either the relaxed or compressed states depending on its history.

[0035] In one embodiment, the miniaturized electromechanical structure further comprises an elastomeric disk sandwiched between the armature and the core.

[0036] In one embodiment, in the relaxed state, the spring arises from the elasticities of the skin and the elastomeric / paramagnetic diaphragm, which interact with the armature on opposing ends, and in the compressed state, the spring arises from the elasticities of the elastomeric disk sandwiched between the armature and the core.

[0037] In one embodiment, the transducer further comprises a transmission structure that accommodates the miniaturized electromechanical structure within its internal volume and transmits the normal-directed force of the armature into tangential forces applied parallel to the surface of the skin. In one embodiment, the transmission structure comprises a Kresling pattern-inspired structure formed from patterning, bonding, and creasing of stiff plastic panels into a thin-walled hexagonal tube, wherein, upon linear compression, the hexagonal tube twist-buckles into a truss of supporting beams.

[0038] In one embodiment, the transmission structure comprises at least one tier, wherein as with normal-force operation, the transducer maintains two stable states balanced by the elastic force of the skin and the holding force of the permanent magnet.

[0039] In one embodiment, the transmission structure comprises two counter-rotating tiers with opposite chiralities having a top platform, a bottom platform and a middle platform disposed therebetween, which allows low-friction rotational coupling between two contacting elements adhered to the skin.

[0040] In one embodiment, the bottom platform couples to the skin as a ring positioned concentrically around the armature, the middle platform is affixed to a flat surface of the core, and the top platform is fixed to the shaft of the armature and couples to the skin through its adhesion with the permanent magnet of the armature.

[0041] In one embodiment, in operation, the permanent magnet within the armature, one of the adhering elements, pulls the core of the transducer towards it under its permanent magnetic field, and a longitudinal motion of the middle platform drives the top and bottom platforms to rotate in opposite directions, whereby operation of the transducer renders twisting motions in the armature and ring in opposite directions.

[0042] In one embodiment, electrostatic mechanisms give rise to bistability in the system. In such configuration, an electrostatic actuator is used instead of an electromagnetic coil, and an electret material is used instead of a permanent magnet.

[0043] In one embodiment, the electrostatic actuator is a HASEL (hydraulically amplified, self- healing, electrostatic) actuator. The HASEL actuator is a class of soft actuators that feature direct electrical activation via Maxwell stress, electrical self-healing, and fast actuation. In one embodiment, the actuation of the HASEL actuator uses high voltage current to create hydraulic pressure in soft structures that contain dielectric fluids.

[0044] In another aspect, the invention relates to a haptic actuating system comprising a plurality of haptic actuators arranged in an array, each actuator being disclosed above; and a controller for operating the plurality of haptic actuators.

[0045] In one embodiment, the controller is integrated with a System-on-Chip (SoC) and a built- in antenna.

[0046] In one embodiment, the SoC comprises at least one of a near-field communication (NFC) interface, a Bluetooth® interface, and a Wi-Fi® interface.

[0047] In one embodiment, the haptic actuating system further comprises driving electronics and sensing electronics electrically coupled between the plurality of haptic actuators and the controller; and flexible interconnects electrically connecting to the plurality of haptic actuators and the controller.

[0048] In one embodiment, the flexible interconnects comprise at least one of serpentine interconnects and zigzag interconnects.

[0049] In one embodiment, the haptic actuating system further comprises a power module for supplying power to the entire system.

[0050] In one embodiment, the power module comprises a battery; and a power management unit comprising a boost converter for driving the plurality of haptic actuators, and a low-dropout regulator for logic-level power.

[0051] In one embodiment, the driving electronics comprises an H-bridge for driving each haptic actuator with the power module, and a multiplexer for multiplexing the driving signals from the controller into the H-bridge.

[0052] In one embodiment, the driving electronics further comprises a supercapacitor for buffering the output of the boost converter.

[0053] In one embodiment, the sensing electronics comprises an inductance measurement unit; and a demultiplexer for demultiplexing the input from each haptic actuator into the inductance measurement unit.

[0054] In one embodiment, each haptic actuator itself serves as a sensor for the longitudinal position of its armature, and the inductance measurement unit captures the resonance frequency of each haptic actuator and reports to the controller whether it exists in the relaxed state or the compressed state.

[0055] In one embodiment, each haptic actuator is configured as a modular unit that is incorporated into a hexagonal tiling of self-similar units, wherein each unit is independently addressed from exposed contacts on the exterior tiles of the hexagonal grid.

[0056] In one embodiment, the flexible interconnects for each unit are configured so that traversing signals reach the correct units by soldering each identical unit at prescribed rotations of 120°, so as to route the driving signals to interior units of the array individually. In one embodiment, each haptic actuator is pitched at about 1.3 cm, which is within a spatial acuity of the skin.

[0057] In one embodiment, the haptic actuating system further comprises an outer encapsulation layer formed of a silicone-based elastomer encapsulating the haptic actuating system.

[0058] In one embodiment, the haptic actuating system is a wireless, skin-conformable haptic interface, which serves as a high-density channel capable of rendering input from a smart device comprising a 3D scanner and inertial measurement unit (IMU) sensors, which operably track the position and orientation of the subject and environment.

[0059] In one embodiment, the wireless, skin-conformable haptic interface has a flexible reconfiguration of the array while tolerating repeated mechanical bending and stretching.

[0060] In one embodiment, the wireless, skin-conformable haptic interface is usable for sensory substitution, wherein smart device based sensory cues derived from 3D scanning and inertial measurements yield perceptions that improve performance in models of visual, vestibular, and proprioceptive sensory substitution tasks.

[0061] In one embodiment, the haptic actuating system operably receives the sensory information over wireless communications from the smart device and renders feedback to the subject as replacement or augmentation of their sensory abilities.

[0062] In one embodiment, the wireless, skin-conformable haptic interface is operated to provide an intuitive frame of reference for virtual objects that follow the orientation of the body, as so to help individuals detect obstacles in their path without vision being necessary.

[0063] In one embodiment, the wireless, skin-conformable haptic interface is operated to provide feedback during standing balance as a means of enhancing postural stability.

[0064] In one embodiment, the wireless, skin-conformable haptic interface is operated to guide foot orientation in individuals with impaired proprioceptive control.

[0065] In one embodiment, the wireless, skin-conformable haptic interface is operated to guide a user’s hand towards target objects without vision being necessary.

[0066] In one aspect, the invention relates to a wearable haptic feedback system comprising plurality of bistable electromechanical transducers, each transducer being configured to be mechanically coupled to a user’s skin and including a ferromagnetic core, a movable armature having a permanent magnet, and an elastomeric diaphragm configured to deform the skin, wherein each transducer and the skin collectively form a bistable mechanical system having compressed and relaxed states defined by stored elastic energy of the skin; a control circuit configured to drive the transducer between the bistable states by transient current pulses and to detect its state via inductance-based self-sensing; and a wireless interface configured to receive sensory or positional input and to command corresponding tactile feedback patterns through the array of transducers.

[0067] In one embodiment, the bistable states are maintained without continuous power consumption.

[0068] In one embodiment, each transducer transitions between states using opposite polarity drive currents.

[0069] In one embodiment, the inductance-based sensing circuit measures resonance frequency to determine transducer position.

[0070] In one embodiment, the elastomeric diaphragm comprises a composite of polydimethylsiloxane (PDMS) and magnetic nanopowder.

[0071] In one embodiment, the armature includes a titanium shaft that directly couples mechanical displacement into the skin.

[0072] In one embodiment, the haptic feedback system further comprises a kirigami transmission structure configured to convert linear motion of the armature into tangential shear deformation of the skin.

[0073] In one embodiment, the kirigami structure comprises counter-rotating tiers arranged in opposite chiralities.

[0074] In one embodiment, each transducer is arranged in a modular, hexagonal array with flexible serpentine interconnects.

[0075] In one embodiment, the control circuit includes a Bluetooth low-energy controller and a rechargeable power source.

[0076] In one embodiment, the wireless interface receives sensory data from a smart device, including LiDAR-based 3D scanning or inertial measurements.

[0077] In one embodiment, the transducer delivers both static indentation and dynamic vibration stimuli.

[0078] In one embodiment, the vibration and indentation are independently controllable to engage distinct classes of mechanoreceptors.

[0079] In one embodiment, the transducer array provides sensory substitution feedback corresponding to spatial or balance cues.

[0080] In one embodiment, the feedback assists a user in detecting environmental obstacles or maintaining postural stability.

[0081] In one embodiment, the bistable structure employs skin elasticity to recover mechanical energy upon state transition.

[0082] In one embodiment, the transducer housing and harness are configured for adjustable indentation depth.

[0083] In one embodiment, the bistable haptic unit provides multimodal feedback including indentation, torsion, and vibration for sensory substitution.

[0084] These and other aspects of the invention will become apparent from the following description of the preferred embodiment taken in conjunction with the following drawings, although variations and modifications therein may be affected without departing from the spirit and scope of the novel concepts of the disclosure.

[0085] BRIEF DESCRIPTION OF THE DRAWINGS

[0086] The accompanying drawings illustrate one or more embodiments of the invention and together with the written description, serve to explain the principles of the invention. Wherever possible, the same reference numbers are used throughout the drawings to refer to the same or like elements of an embodiment.

[0087] FIG. 1 shows schematically multisensory feedback with a battery-powered array of biointegrated, bistable transducers. Panel a: Diagram of skin mechanoreceptors and their frequency responses. Panel b: Modes of haptic actuation, illustrating targeted mechanoreceptors. Panel c: Disassembled view of the bistable transducer, featuring skin as an integral mechanical component. The inset shows a photograph of the original transducer (left) next to a miniaturized design (relaxed and compressed states shown respectively in the middle and right). Panel d: Photograph of the transducer array mounted on the shoulder. Panel e: Photograph of the encapsulated interface mounted on the neck. Panel f: An example of sensory substitution, with a system incorporating an array of transducers, accelerometers, and 3D scanning (smartphone). Each of these components are connected to each other using the Bluetooth low-energy (BLE) protocol. Panel g: An example of sensory augmentation, with a system applied to detect objects outside the field of vision of the user.

[0088] FIG. 2 shows schematically mechanical features of the transducer and the role of skin in maintaining bistability. Panel a: Disassembled view of the bistable transducer, illustrating key mechanical components. Panel b: Schematic illustrations, free body diagrams, and potential energy associated with each state and transition (Fskin, the reactive force of skin; Fhoia, the holding force from the permanent magnet; Fcontact, the force of contact between the armature and opposing surfaces; Fcoii, the force applied by driving the coil with current; AEskin, energy stored as skin compression). The solid and faded traces correspond to operations with negative and positive (or zero) currents respectively. The potential energy is calculated from simulations as the integral of force over the indentation depth. Panel c: The minimum applied current required to overcome the energy barrier between each state plotted against the total indentation depth for a range of Young’s moduli, E. The shaded regions correspond to the boundaries of bistability, outside of which only one state is attainable (monostable, compressed or relaxed). The symbols correspond to experimental evaluation of the threshold on skin phantoms (bars show min-max; n = 4). Panel d: Phase diagram for Foil — > co showing regions across the parameter space of skin modulus and indentation depth for successful bistability. These regions are plotted for different layer thicknesses, h. The points correspond to experimental results from skin phantoms, where transitions are observed for Foil < 500 mA. Panel e: Mechanical bistability evaluation on three skin locations in n = 6 healthy individuals (three males, three females, ages 20-36; locations pictured below horizontal axis). The indentation depth was adjusted using three harness variants.

[0089] FIG. 3 shows schematically vibrotactile and shear force operation of the transducer. Panel a: Schematic illustration of the transducer in three modes of vibration. Panel b: Steady-state and quasi static behavior of the system during scanning of coil current (E = 43 kPa phantom), giving rise to hysteresis. Panel c: Temporal profile of deformation measured with digital image correlation (DIC) during vibration in each state ( oii-pk = 250 mA; / = 50 Hz; E = 43 kPa phantom). Panel d: Frequency profile of vibrotactile deformations (DIC and spring-mass simulation), e Vibration current amplitudes of perception thresholds (n = 12, 6 males, 6 females, ages 20-36). Panel f: State diagram showing the transition energies and continuous power consumptions associated with each state. Panel e: Energy cost to transmit information to the skin as a function of information rate, given different subsets of states (see Methods). Panel h: Schematic illustration of the torsion modality of the transducer (Fskin, skin reactive force; Ftorsion, applied tangential force; FnOrmai, applied normal force; 0tn, angle of torsion). Panel i: Photograph of the integrated kirigami structure. Panel j : Assembly of the planar pattern into a 3D kirigami structure (a, b, c, and a are key design parameters). Panel k: Finite element analysis of stress driven by creasing within the kirigami structure (PET yield stress, 80 MPa). Panel 1: DIC inplane strain on a skin phantom (E = 31 kPa; arrows, direction and magnitude of in-plane deformation). Panel m: Perceptual intensity reported by human participants for contacting elements matching that of the integrated transducer and deformations matching DIC results (« = 14, 8 males, 6 females, ages 23-31; p < 0.0001, Kruskal-Wallis test; whiskers, 5-95 percentile; boxes, interquartile; horizontal lines, medians; open circles, means; square markers, 5-95 percentile outliers).

[0090] FIG. 4 shows schematically system level implementation of an array of bistable transducers. Panel a: State diagram illustrating closed-loop control system and Bluetooth communication. Panel b: Photograph of transducer array integrated with driving electronics and closed-loop control system. Panel c: Inductance measurement of the transducer as a function of armature position (1 kHz; n = 4). Panel d: Resonant frequency measurements of 19 transducers using the integrated controller. The Horizontal line indicates the threshold chosen to discriminate between the relaxed and compressed states. Panel e: Photograph illustrating scene reconstruction mediated by LiDAR in a smartphone. Panel f: Diagram illustrating experimental setup and stimuli pattern (wave of indentation) for visual sensory substitution task. Panel g: Diagram illustrating experimental setup and stimuli pattern (vibration) for balance sensory substitution task. Panel h: Diagram illustrating experimental setup and stimuli pattern (vibration and indentation) for foot strike sensory substitution task. Panel i: Confusion matrix of participant performance on visual task, with the colormap indicating the frequency of occurrence (n = 7, four males, three females, ages 19-37; p = 0.0178, Wilcoxon signed-rank test, null hypothesis of random selection between six choices). Panel j : Participant balance duration in Sharpened Romberg task, comparing averages of repeat measures for each participant with and without feedback ( / ? = 10, five males, five female, ages 20-36; p = 0.00103, repeated measures ANOVA, testing the null hypothesis that that no differences exist in group means). Panel k: Foot strike vectors for four surfaces presented with variations in pitch and yaw (55-60 repeat measures; n = 3, two males, one female, ages 21-37; p < 0.001 within each subject, Wilcoxon signed-rank test, null hypothesis of equal mean to control). The legend lists angle combinations of (pitch, yaw) for the target surface. The solid arrows and transparent cones correspond to the mean and standard deviations of the foot unit normal vectors respectively. The broken arrows indicate unit normal vectors of the target surfaces.

[0091] FIG. 5 shows schematically transducer design and fabrication. Panel a: Fabrication of the core on a motorized stage. Each coil was wound to 8 layers along the 2.75 mm shaft of the bobbin to reach -63% fill density. The resistance of each coil was measured to verify consistency, and all transducers described in this article lie within 13-14 (7?COii = 13.39 ± 0.384 Q; n = 18). Panel b: Assembled transducer. Panel c: Disassembled view of the transducer with key mechanical components labelled. Panel d: Scale illustration of bistable transducer components and the variable harness system. Panel e: 3D illustration of the three harness variants employed in this study.

[0092] FIG. 6 shows schematically transducer array design and mechanical testing. Panel a: Schematic illustration of the mesh-reinforced regions of the adhesive layer. Panel b: Integration of the array with skin using the adhesive layer. Panel c: Layer-by-layer fabrication of the adhesive coupling, schematic illustrations and photographs. The adhesive layer started with a copper-clad fiberglass disk. On top of this substrate, we spin-coated (2000 rpm for 2 minutes; WS-650-23 Spin Coater, Laurell) a thin (90 pm) layer of silicone-based elastomer (Dragon Skin 10 Slow, Smooth-On). Before this layer was allowed to cure, fiberglass mesh (Fiberglass Warehouse) was layered into the thin layer of silicone. After curing this layer, the silicone-mesh composite was patterned by CO2 laser (VLS3.50DT) into a hexagonal tiling. Then, another layer of silicone (Dragon Skin 10 Slow, Smooth-On) was spin-coated onto the substrate at the full thickness of 140 pm (1000 rpm for 2 minutes). After curing at 75 °C for 3 hours, a 260 pm adhesive layer of silicone gel (Silbione RT Gel 4717, Elkem) was spun onto the substrate (1000 rpm for 30 seconds). This was cured at room temperature for 24 hours, and then the pattern was removed by laser cutting the outer shape. The elastomeric adhesive was then transferred onto a laminate backing, and the harnesses were bonded to the non-adhesive surface by dip-coating it with single-component silicone (RTV 3140, Dow Coming). Panel d: Photograph of two transducer units positioned inside the controller module and schematic illustrations demonstrating how each modular interconnect layer routes signals through the hexagonal array. The serpentine interconnects are two-layer flexible printed circuit boards (fPCBs) manufactured from 35 pm copper traces with a total thickness of 130 pm (PCBWay). During assembly, the internal contacts fold into the core where they can be soldered to the coil. Panels e-k: For numerical simulations, three-node and four-node composite shell elements were used for the polyimide (PI) thin film and copper traces respectively, and eight-node solid elements were used for the electronic components and adhesion layer respectively. Panel e: Model geometry for mechanical simulation of strain under a unit actuator during skin bending (50 mm radius). Panel f: Simulated strain using a substrate without mesh. Panel g: Simulated strain with a mesh- reinforced substrate. Panel h: Photograph of the haptic array under 20% lateral stretching. Panel i: Numerical simulation of strain within the dragonskin / mesh adhesive layer, polyimide interconnects (fracture strain, > 7%) , and copper traces (fracture strain, > 1%)6of the array during 20% lateral stretching. Panel j : Photograph of the haptic array under 50 mm bending radius. Panel k: Numerical simulation of strain within the dragonskin / mesh adhesive layer, polyimide interconnects, and copper traces of the array during bending (50 mm radius).

[0093] FIG. 7 shows schematically finite element modeling of electromagnetic and solid mechanical processes. Panel a: Demagnetization curve of an N48 neodymium magnet. Arnold Magnetics N48 from the Ansys material library was used for the permanent magnet part of armature with a modification of Brto 1 T in its B-H curve. Panel b: B-H curve of iron-cobalt (Vacoflux 50 Solid) and PDMS-MNP. The PDMS-MNP diaphragm used a self-defined material with a relative permeability of 1.04 and a bulk conductivity of 4 S / m. Panel c: Example quasimagnetostatic simulation showing the magnetic field strength and direction as a colormap and quiver plot ( / coil = 400 mA) for the compressed and relaxed states (* | \B\ | = 7.4 mT, stray magnetic field at 6.6 mm radial distance from central axis). A cylinder was built to represent the solenoid copper coil with 200 turns stranded current excitation. Magnetic force was driven with different currents and separation distance between the solenoidal core and armature. An adaptive mesh (tetrahedron elements) was adopted to ensure computation accuracy. Panel d: Axisymmetric model geometry and boundary conditions used in solid mechanical numerical modeling. Four- node bilinear reduced integration elements (CAX4R) and three-node linear elements (CAX3) were applied to different parts according to their geometric complexities. The mesh was highly refined in the indentation area, and convergence was guaranteed for all cases. Rigid body constraints were applied to all metal parts due to their large moduli relative to the skin phantom. A downward displacement was applied to the armature, and the corresponding reaction forces from the skin phantoms were evaluated. Panel e: Example simulations showing strain distribution within a skin phantom (45: 1, E = 43 kPa) for the relaxed and compressed states (2 mm effective indentation). Panel f: Schematic of the mass-spring-damper vibration model for the transducer and the periodic loading force applied to it. Panel g: Stress distribution within the kirigami structure in the relaxed state (PET yield stress, 80 MPa). The simulation includes two steps, starting from the fully unfolded state of the two kirigami modules, transitioning to the relaxed state (4.4 mm linear displacement from unfolded), and then transitioning to the compressed state (2 mm translation of the middle platform). The mesh of the skin phantom was refined in the area where it contacts the kirigami, and convergence was guaranteed for all cases. A tie constraint was applied to connect the bottom panel of the upper kirigami structure to the lower kirigami structure, and another tie constraint was applied between the top panel of the upper kirigami structure and the top surface of the armature. The contacting elements were firmly attached to the surface of the skin phantoms using cohesive elements. Panel h: Stress distribution within the kirigami structure in the compressed state. Panel i: In-plane strain of the skin phantom in the compressed state. A stiff skin phantom was employed here to evaluate the upper bound of stress in the structure (E = 5.1 MPa). Panel j : In-plane deformation of the skin phantom in the compressed state.

[0094] FIG. 8 shows schematically mechanical characterization of transducers, skin phantoms, and human skin. Panel a: Mechanical bistability evaluation in healthy individuals. Measurements were performed in five skin locations (depicted on left). The absolute value of current required to transition the armature between relaxed and compressed states was measured for n = 6 participants (three male, three female, ages 20-36). The indentation depth was adjusted by performing experiments with harnesses of varying heights. Panels b-i: Characterization of force as a function of extension was performed using a motorized stage (EDM303, Mark-10) and a force gauge (M5-2, Mark-10) with a 10 N capacity. Panel b: Experimental and simulated forces measured as a function of the longitudinal position of the armature for several applied current values (excluding PDMS-MNP diaphragm and skin compressive force). We defined the origin as where the base of the armature and the core are in contact, and we determined this using the force meter. For experimental results, the solid lines and shaded areas correspond to the means and standard deviations respectively (n = 8). The square markers correspond to the maximum recorded force for each current, averaged across all transducers. The inset shows the experimental setup. Panel c: Forces measured as a function of the longitudinal position of the armature rod (excluding force from core) for 40: 1, 45: 1, 50: 1, and 55:1 skin phantoms with thicknesses of d= 2 mm (inset shows experimental setup). Panel d: Forces measured as a function of the longitudinal position of the armature rod for 35: 1, 40: 1, 45:1, 50: 1, and 55: 1 skin phantoms with thicknesses of d= 5 mm. Panel e: Skin reactive forces measured as a function of the longitudinal position of the armature rod (excluding force from core) for the ventral aspect of the forearm for n = 6 subjects (three male, three female, ages 20-36; experimental setup shown in inset). Panel f: Skin reactive forces measured for the dorsal aspect of the palm above the adductor pollicis for n = 6 subjects (three male, three female, ages 20-36; location indicated in inset). Panel g: Skin reactive forces measured for the dorsal aspect of the palm above metacarpal III for n = 6 subjects (three male, three female, ages 20-36; location indicated in inset). Panel h: Tensile peeling force measurements of the harness attached to the silicone-mesh composite adhesive mounted on the forearm of n = 4 subjects (two male, two female, ages 26- 32). The horizontal line shows the holding force of the indentation actuator. Panel i: Tensile peeling force for a 07 mm disk pre-rotated to 30° and mounted on the forearm of n = 4 subjects (two male, two female, ages 26-32) with 3M 9699 double-sided adhesive. The horizontal line shows the holding force of the torsion actuator.

[0095] FIG. 9 shows schematically 3D Digital image correlation evaluation of vibrotactile deformation. The 3D digital image correlation (DIC) experiments utilized two high-speed cameras (2048 x 1088 pixel resolution; HT-2000M, Emergent) with 35 mm imaging lenses (Fl.4 manual focus; Kowa), operated at 500 Hz. To minimize errors associated with optical paths and camera distortions, both extrinsic and intrinsic camera parameters were optimized including f- number, illumination, focal length, light sensitivity, and gain systems. The 3D imaging acquisition hardware and the transducer system were externally synchronized to allow rapid, automated collection of data for various input powers and operating frequencies. Panel a: Photograph of experimental setup. Panel b: Representative photograph of image sequence showing speckle pattern. The phantom skin was uniformly coated with black dots (-50-200 pm) using a spray -painting technique. Then, a thin layer of white-pigmented PDMS of identical crosslinker ratio to the phantom was spin-coated on top (500 rpm, 2 minutes) to provide contrast. Panel c: 3D-reconstructed points vs true points. The investigation volume was 20 x 20 x 20 mm3, and RMSE between true calibration and 3D reconstructed points was on the order of 10 pm. The median values of difference between 66 true calibration points and 3D reconstructed points were -1.6, 5.2, and 0.1 pm for x, y, and z coordinates, respectively. To achieve high resolution and accuracy, the DIC subset radius and spacing were set as 10 and 4 pixels, resolving over 1950 grids. Data points with high correlation coefficients (>1.0 max correlation coefficient) were filtered out to minimize errors during the 3D reconstruction process. Filtered data sets were grid-interpolated into 20 x 20 grid points to generate consistent data points and grid locations across all sets of experiments. Panel d: Normal deformation of skin phantoms measured in the relaxed and compressed states with DIC. Panel e: Temporal profiles of skin phantom indentation (45:1 PDMS phantom, E = 43 kPa; Coii-pk = 250 mA) measured at the center of the contacting rod of the transducer with DIC during square wave perturbation of the coil (relaxed- state perturbation). Panel f: Temporal profile of compressed-state perturbation. Panel g: Temporal profile of full-transition vibration. Panel h: Frequency domain transformation of the temporal profile for relaxed-state perturbation. Panel i: Frequency domain transformation of the temporal profile for compressed-state perturbation. Panel j : Frequency domain transformation of the temporal profile for full-transition vibration.

[0096] FIG. 10 shows schematically design and fabrication of the kirigami transmission structure. Panel a: Basic split-crease unit cell design and fully folded Kresling pattern-inspired kirigami structure. Folding of the kirigami structure is feasible when the angle a exceeds 90°. To increase the height of the kirigami structure while keeping the base edge length constant, angle a should approach 90°, with angle P remaining relatively small. To meet these criteria, angles a and p were set to 100° and 30°, respectively. We chose the base edge length of the unit cell to be 6 mm, which achieves relatively small outer dimensions for the kirigami while providing sufficient internal space for the transducer. Panel b: Design of variant cell that uses a combination of straight and curved creases. The modification of the crease from a straight line to a curve further increases the internal space. Panel c: Curved crease design using the Bezier Curve method. We initially drew two equally long straight creases on the diagonal of the unit cell. We used five control points for generating the curve: the vertices of the two straight creases (Pl and P5), the midpoint of the top border of the unit cell (P2), the left comer point (P3), and the midpoint of the left border (P4). The curve generated using these rules closely followed the left border of the unit cell, which was not feasible for fabrication. Therefore, we shifted P4 vertically along the normal direction of the drawn curve to P4". Using the new set of control points (Pl, P2, P3, P4", P5), the left-curved crease was created. Panel d: Kirigami structure with only straight valley creases in the folded state (h = 6.75 mm). Choosing the crease length is a tradeoff between the resistance to deformation of the structure and the clearance between the panels and the internal transducer. Panel e: Variant kirigami structure with 2 mm straight crease length (h = 6.75 mm; folded state). This design avoids collision, and we ultimately used it in our study. Panel f: Crease length, 4 mm. Panel g: Two-tiered kirigami structure illustrating switchable motion states. Panel h: Bottom view of the contacting elements (ring and disk). Panel i: 2D patterns of the lower and upper tier kirigami modules for fabrication. Panel j : The panels used to make the kirigami structure, including one layer of PET plastic sheet and two layers of PU thin- film tape. Panel k: Photograph of the flat kirigami panel used for fabricating the 3D structure. Panel 1: Photograph of the assembled lower and upper tier kirigami modules.

[0097] FIG. 11. Perceptual intensity of vibration and torsion. Panels a-b: Vibration current amplitudes of perception thresholds (n = 12, 6 males, 6 females, ages 20-36). Panel a: Compressed state vibration. Panel b: Relaxed state vibration. Panel c: Relative perception of vibration in the transducer with respect to a commercial linear resonance actuator (LRA; dotted line, equivalent perception; n = 12, 6 males, 6 females, ages 20-36). Panels d-g: Perceptual intensity evaluated according to its definition in the Methods section for n = 14 human participants (8 males, 6 females, ages 23-31) under variations in indentation and torsion of the ring and disk structures. The left column shows mean values reported by each subject (w = 5 repeat measurements; bars, standard deviation), and the right column reflects all subjects (n = 14; bars, 1.5 interquartile range; shaded box, range between 25th and 75th percentiles; horizontal line, median; x, mean;

[0098] ♦ , outliers from 1.5 interquartile range). Panel d: Outcomes reported for Module 1, in which the ring was rotated to angles of 0.33°, 0.66°, and 1° with a static indentation of 0.2 mm. A statistically significant difference can be seen in these groups (p < 0.0001, Kruskal-Wallis test), and there was a moderate positive correlation between ratings and rotation angles (Spearman correlation, p = 0.580) which was highly statistically significant (p < 0.0001). Panel e: Outcomes reported for Module 2.1, in which the disk was rotated to angles of 5°, 10°, and 15° with a static indentation of 0 mm. According to the Kruskal-Wallis test, a statistically significant difference can be seen in these groups (p < 0.0001), and there was a moderate positive correlation between ratings and rotation angles (Spearman correlation, p = 0.596) which was highly statistically significant (p < 0.0001). Panel f: Outcomes reported for Module 2.2, in which the disk was rotated to angles of 5°, 10°, and 15° with a static indentation of -0.4 mm. A statistically significant difference can be seen in these groups (p < 0.0001, Kruskal-Wallis test), and there was a moderate positive correlation between ratings and rotation angles (Spearman correlation, / ? = 0.649) which was highly statistically significant (p < 0.0001). Panel g: Outcomes reported for Module 3, in which the ring and disk were rotated to angles of (0.33°, 5°), (0.66°, 10°), and (1°, 15°) with a static indentation of (0.2 mm, -0.4 mm). A statistically significant difference can be seen in these groups (p < 0.0001, Kruskal-Wallis test), and there was a moderate positive correlation between ratings and rotation angles (Spearman correlation, p = 0.599) which was highly statistically significant (p < 0.0001). Panels h-j : Torsion and indentation array discrimination experiments. Panel h: Illustration and photograph of the apparatus setup, which includes three torsion actuators (A, D, and E) and two indentation actuators (B and C). Panel i: Discrimination between indentation and torsion, combined results for 15 healthy participants (7 males, 8 females, ages 23-31 years). The mean perceived accuracy was 97.3% (0.053% SD) for torsion, 97.7% (0.037% SD) for indentation, and 97.5% (0.060% SD) across both torsion and indentation. Accuracy was averaged over 15 subjects with 10 repeated trials (n = 150). Panel j : Discrimination between patterns of torsion, combined results for 12 healthy participants (7 males, 5 females, ages 23-31). The overall mean accuracy of all patterns was 80.6%. Accuracy was averaged over 12 subjects with 10 repeated trials (n = 120).

[0099] FIG. 12 shows schematically miniaturization of indentation and torsional transducers. Panels a-e: Miniaturization of the indentation structure. The coil was wound to 12 Q. Panel a: Photograph of the original and miniaturized transducers. Panel b: Scale illustration of the miniaturized transducer. Panel c: Experimental and simulated forces measured as a function of the longitudinal position of the armature for several applied current values. Measurements were performed using a motorized stage (EDM303, Mark- 10) and a force gauge (M5-2, Mark- 10) with a 10 N capacity. Panel d: Simulated phase diagram for Tcoii showing regions across the parameter space of skin modulus and indentation depth for successful bistability. The shaded regions correspond to the boundaries of bistability, outside of which only one state is attainable (monostable, compressed or relaxed). Panel e: The minimum applied current required to overcome the energy barrier between each state plotted against the total indentation depth for a range of Young’s moduli, E (simulated). Panels f-k: Miniaturization of the torsion structure. Panel f: Photograph of the single-tiered kirigami structure. Panel g: Scale illustration of the onetiered kirigami structure. Panel h: Volumetric illustration of freely moving mechanical elements of the one-tiered structure. Panel i: Photograph of a haptic array incorporating units for both indentation and torsion. Panel j: Finite element analysis of stress driven by creasing within the kirigami structure (PET yield stress, 80 MPa; E = 31 kPa, skin). Panel k: DIC out-of-plane (left) and in-plane (right) strains on a skin phantom during the compressed state of the single-tier transducer (E = 31 kPa; arrows, direction and magnitude of in-plane deformation). The inner disk rotated 7.5° and translated 0.25 mm vertically relative to the outer ring.

[0100] FIG. 13 shows schematically visual and balance sensory substitution tasks. Panels a-h: Visual sensory substitution task. Confusion matrix of participant performance on object identification task ( / / = 7), with the colormap indicating the frequency of occurrence. The p-value was p = 0.0178, testing the null hypothesis that selections were made at random between six possible choices (Wilcoxon signed-rank test; n = 7). The effect size was large, r = 0.896, according to rank-biserial correlation. Panel a: Experimental setup of the visual sensory substitution task. Panel b: Subject 1, female, age 21. Panel c: Subject 2, female, age 23. Panel d: Subject 3, female, age 19. Panel e: Subject 4, male, age 37. Panel f: Subject 5, male, age 32. Panel g: Subject 6, male, age 30. Panel h: Subject 7, male, age 31. Panels i-s: Balance sensory substitution task. Participant performance on Sharpened Romberg task, measured as the time duration before losing balance. The p-value across repeated trials and subjects was p = 0.00103, testing the null hypothesis that that no differences exist in group means. The vertical bars indicate standard deviation, shaded boxes indicate the interquartile range, the horizontal lines above each box indicate medians, and filled circles symbols correspond to the means. Panel i: Stimulation patterns superimposed on smartphone display during rotation around the forward axis for the balance sensory substitution task. The virtual mesh highlights the LiDAR- reconstructed surface. Panel j: Subject 1, female, age 35. Panel k: Subject 2, female, age 35. Panel 1: Subject 3, female, age 20. Panel m: Subject 4, female, age 29. Panel n: Subject 5, female, age 32. Panel o: Subject 6, male, age 36. Panel p: Subject 7, male, age 20. Panel q: Subject 8, male, age 34. Panel r: Subject 9, male, age 33. Panel s: Subject 10, male, age 24.

[0101] FIG. 14 shows schematically foot strike sensory substitution task. Evaluation of the foot strike sensory substitution system. Panel a: Experimental setup depicting reference axes. As part of the task, four separate surfaces were presented at orientations ( r, (p) E {(0°, 0°), (15°, 60°), (15°, -60°), (30°, 0°)}. Panel b: Stimulation patterns superimposed on smartphone display during rotation around the forward axis. The virtual mesh highlights the LiDAR-reconstructed surface. Panels c-e: Unit normal vectors of foot and variable surface centered on common origin during task with feedback. The significance of the results for each individual was evaluated using the Wilcoxon signed-rank test over repeat trials (across all three phases), given the null hypothesis that this data arose from a distribution with identical mean to the matching control condition. Effect size was characterized according to rank-biserial correlation. Panel c: Subject 1, male, age 37 (n = 57, p < 0.0001, r = -0.59). Panel d: Subject 2, female, age 35 (n = 55, p < 0.0001, r = - 0.75). Panel e: Subject 3, male, age 21 (n = 60, p = 0.00027, r = -0.47). Panels f-h: Unit normal vectors of foot and variable surface centered on common origin during task without feedback (control). Panel f: Subject 1, male, age 37. Panel g: Subject 2, female, age 35. Panel h: Subject 3, male, age 21.

[0102] FIG. 15 shows schematically bistability measurements on skin phantoms. Panel a: Experimental setup for bistability evaluation, indicating skin phantoms (5 mm), harness variants, and a transducer. Panel b: Evaluation of bistability on skin phantoms with varying currents and crosslinker ratios for phantom thickness d= 5 mm. The heatmap shades correspond to the number of transducers (out of n = 4) that successfully transitioned under the given condition. The red column corresponds to the transition from relaxed to compressed, and the blue column corresponds to transition from compressed to relaxed. Each row corresponds to effective indentation (adjusted with harness variants), c Evaluation of bistability on skin phantoms with varying currents and crosslinker ratios for phantom thickness d= 2 mm (n = 3).

[0103] FIG. 16 shows schematically bistability measurements on human subjects. Evaluation of bistability for n = 6 subjects on the dorsal aspect of the neck near the C6 and C7 vertebrae (NK), dorsal aspect of upper arm (UA), ventral forearm (FA), dorsal palm on adductor pollicis (BS), and dorsal palm on metacarpal III (BR) with 1.5 mm and 2 mm effective indentations (Subject 1, male, age 36; Subject 2, male, age 30; Subject 3, male, age 23; Subject 4, female, age 20; Subject 5, female, age 20; Subject 6, female, age 24). The red column corresponds to the transition from relaxed to compressed, and the blue column corresponds to transition from compressed to relaxed.

[0104] FIG. 17 shows schematically current amplitudes from which vibration perception threshold were derived for Subjects 1-4. Each block plotted above represents one trial of the adaptive staircase, where red and blue indicate “yes” and “no” respectively for each given current (7coii-pk). The height of each block corresponds to the step size for each trial. Iterations alternate between ascending (starting below threshold and increasing until receiving “yes”) and descending (starting above threshold and decreasing until received “no”). Columns labelled “Start ascending” indicate that Iteration 1 and other odd-numbered iterations in that column are ascending. Columns labelled “Start descending” indicate that Iteration 1 and other odd-numbered iterations in that column are descending. For each combination of state and frequency, trials would start with the first trial in Iteration 1 (“Start ascending” column) and, immediately after, the first trial of Iteration 1 (“Start descending” column). The trials would then alternate back and forth (interleaved) between these columns in the order dictated by the direction (ascending or descending) of each subsequent iteration (Iterations 1-8). Participants: Subject 1, male, age 36; Subject 2, female, age 23; Subject 3, male, age 25; and Subject 4, female, age 28.

[0105] FIG. 18 shows schematically current amplitudes from which vibration perception threshold were derived for Subjects 5-8. Each block plotted above represents one trial of the adaptive staircase, where red and blue indicate “yes” and “no” respectively for each given current (7Coii-Pk). The height of each block corresponds to the step size for each trial. Iterations alternate between ascending (starting below threshold and increasing until receiving “yes”) and descending (starting above threshold and decreasing until received “no”). Columns labelled “Start ascending” indicate that Iteration 1 and other odd-numbered iterations in that column are ascending. Columns labelled “Start descending” indicate that Iteration 1 and other odd-numbered iterations in that column are descending. For each combination of state and frequency, trials would start with the first trial in Iteration 1 (“Start ascending” column) and, immediately after, the first trial of Iteration 1 (“Start descending” column). The trials would then alternate back and forth (interleaved) between these columns in the order dictated by the direction (ascending or descending) of each subsequent iteration (Iterations 1-8). Participants: Subject 5, female, age 20; Subject 6, female, age 20; Subject 7, male, age 29; and Subject 8, female, age 35.

[0106] FIG. 19 shows schematically current amplitudes from which vibration perception threshold were derived for Subjects 9-12. Each block plotted above represents one trial of the adaptive staircase, where red and blue indicate “yes” and “no” respectively for each given current (7coii-pk). The height of each block corresponds to the step size for each trial. Iterations alternate between ascending (starting below threshold and increasing until receiving “yes”) and descending (starting above threshold and decreasing until received “no”). Columns labelled “Start ascending” indicate that Iteration 1 and other odd-numbered iterations in that column are ascending. Columns labelled “Start descending” indicate that Iteration 1 and other odd-numbered iterations in that column are descending. For each combination of state and frequency, trials would start with the first trial in Iteration 1 (“Start ascending” column) and, immediately after, the first trial of Iteration 1 (“Start descending” column). The trials would then alternate back and forth (interleaved) between these columns in the order dictated by the direction (ascending or descending) of each subsequent iteration (Iterations 1-8). Participants: Subject 9, male, age 24; Subject 10, male, age 26; Subject 11, female, age 29; and Subject 12, male, age 33.

[0107] FIG. 20 shows schematically individual outcomes for perceptual intensity of torsional structures. Perceptual intensity evaluated according to its definition in the Methods section for n = 14 human participants (8 males, 6 females, ages 23-31) under variations in indentation and torsion of the ring and disk structures (bars, mean values over 5 repeat measures; whiskers, standard deviation). Panel a: Outcomes reported for Module 1, in which the ring was rotated to angles of 0.33°, 0.66°, and 1° with a static indentation of 0.2 mm. A statistically significant difference can be seen in these groups (p < 0.0001, Kruskal-Wallis test). Panel b: Outcomes reported for Module 2.1, in which the disk was rotated to angles of 5°, 10°, and 15° with a static indentation of 0 mm. According to the Kruskal-Wallis test, a statistically significant difference can be seen in these groups (p < 0.0001). Panel c: Outcomes reported for Module 2.2, in which the disk was rotated to angles of 5°, 10°, and 15° with a static indentation of -0.4 mm. A statistically significant difference can be seen in these groups (p < 0.0001, Kruskal-Wallis test). Panel d: Outcomes reported for Module 3, in which the ring and disk were rotated to angles of (0.33°, 5°), (0.66°, 10°), and (1°, 15°) with a static indentation of (0.2 mm, -0.4 mm). A statistically significant difference can be seen in these groups (p < 0.0001, Kruskal-Wallis test).

[0108] FIG. 21 shows schematically individual outcomes for torsion pattern discrimination. Accuracy was averaged over 10 repeated measures for each subject (7 males, 5 females, ages 23-31). Notable individual differences in tactile perception were observed.

[0109] FIG. 22 shows schematically a HASEL (hydraulically amplified, self-healing, electrostatic) actuator.

[0110] DETAILED DESCRIPTION OF THE INVENTION

[0111] The invention will now be described more fully hereinafter with reference to the accompanying drawings, in which exemplary embodiments of the invention are shown. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this invention will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. Like reference numerals refer to like elements throughout.

[0112] The terms used in this specification generally have their ordinary meanings in the art, within the context of the invention, and in the specific context where each term is used. Certain terms that are used to describe the invention are discussed below, or elsewhere in the specification, to provide additional guidance to the practitioner regarding the description of the invention. For convenience, certain terms may be highlighted, for example using italics and / or quotation marks. The use of highlighting has no influence on the scope and meaning of a term; the scope and meaning of a term is the same, in the same context, whether or not it is highlighted. It will be appreciated that same thing can be said in more than one way. Consequently, alternative language and synonyms may be used for any one or more of the terms discussed herein, nor is any special significance to be placed upon whether or not a term is elaborated or discussed herein. Synonyms for certain terms are provided. A recital of one or more synonyms does not exclude the use of other synonyms. The use of examples anywhere in this specification including examples of any terms discussed herein is illustrative only, and in no way limits the scope and meaning of the invention or of any exemplified term. Likewise, the invention is not limited to various embodiments given in this specification.

[0113] One of ordinary skill in the art will appreciate that starting materials, biological materials, reagents, synthetic methods, purification methods, analytical methods, assay methods, and biological methods other than those specifically exemplified can be employed in the practice of the invention without resort to undue experimentation. All art-known functional equivalents, of any such materials and methods are intended to be included in this invention. The terms and expressions which have been employed are used as terms of description and not of limitation, and there is no intention that in the use of such terms and expressions of excluding any equivalents of the features shown and described or portions thereof, but it is recognized that various modifications are possible within the scope of the invention claimed. Thus, it should be understood that although the invention has been specifically disclosed by preferred embodiments and optional features, modification and variation of the concepts herein disclosed may be resorted to by those skilled in the art, and that such modifications and variations are considered to be within the scope of this invention as defined by the appended claims.

[0114] Whenever a range is given in the specification, for example, a temperature range, a time range, or a composition or concentration range, all intermediate ranges and subranges, as well as all individual values included in the ranges given are intended to be included in the invention. It will be understood that any subranges or individual values in a range or subrange that are included in the description herein can be excluded from the claims herein.

[0115] It will be understood that, as used in the description herein and throughout the claims that follow, the meaning of “a”, “an”, and “the” includes plural reference unless the context clearly dictates otherwise. Thus, for example, reference to “a cell” includes a plurality of such cells and equivalents thereof known to those skilled in the art. As well, the terms “a” (or “an”), “one or more” and “at least one” can be used interchangeably herein. It is also to be noted that the terms “comprising”, “including”, and “having” can be used interchangeably.

[0116] It will be understood that when an element is referred to as being “on”, “attached” to, “connected” to, “coupled” with, “contacting”, etc., another element, it can be directly on, attached to, connected to, coupled with or contacting the other element or intervening elements may also be present. In contrast, when an element is referred to as being, for example, “directly on”, “directly attached” to, “directly connected” to, “directly coupled” with or “directly contacting” another element, there are no intervening elements present. It will also be appreciated by those of skill in the art that references to a structure or feature that is disposed “adjacent” another feature may have portions that overlap or underlie the adjacent feature.

[0117] It will be understood that, although the terms first, second, third etc. may be used herein to describe various elements, components, regions, layers and / or sections, these elements, components, regions, layers and / or sections should not be limited by these terms. These terms are only used to distinguish one element, component, region, layer or section from another element, component, region, layer or section. Thus, a first element, component, region, layer or section discussed below could be termed a second element, component, region, layer or section without departing from the teachings of the invention.

[0118] Furthermore, relative terms, such as “lower” or “bottom” and “upper” or “top,” may be used herein to describe one element’s relationship to another element as illustrated in the figures. It will be understood that relative terms are intended to encompass different orientations of the device in addition to the orientation depicted in the figures. For example, if the device in one of the figures is turned over, elements described as being on the “lower” side of other elements would then be oriented on “upper” sides of the other elements. The exemplary term “lower”, can therefore, encompasses both an orientation of “lower” and “upper,” depending of the particular orientation of the figure. Similarly, if the device in one of the figures is turned over, elements described as “below” or “beneath” other elements would then be oriented “above” the other elements. The exemplary terms “below” or “beneath” can, therefore, encompass both an orientation of above and below.

[0119] It will be further understood that the terms “comprises” and / or “comprising”, or “includes” and / or “including”, or “has” and / or “having”, or “carry” and / or “carrying”, or “contain” and / or “containing”, or “involve” and / or “involving”, “characterized by”, and the like are to be open-ended, i.e., to mean including but not limited to. When used in this disclosure, they specify the presence of stated features, regions, integers, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, regions, integers, steps, operations, elements, components, and / or groups thereof.

[0120] Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and the invention, and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.

[0121] As used in the disclosure, “around”, “about”, “approximately” or “substantially” shall generally mean within 20 percent, preferably within 10 percent, and more preferably within 5 percent of a given value or range. Numerical quantities given herein are approximate, meaning that the term “around”, “about”, “approximately” or “substantially” can be inferred if not expressly stated.

[0122] As used in the disclosure, the phrase “at least one of A, B, and C” should be construed to mean a logical (A or B or C), using a non-exclusive logical OR. As used herein, the term “and / or” includes any and all combinations of one or more of the associated listed items.

[0123] The term “flexibility” or “bendability”, as used in the disclosure, refers to the ability of a material, structure, device or device component to be deformed into a curved or bent shape without undergoing a transformation that introduces significant strain, such as strain characterizing the failure point of a material, structure, device or device component. In an exemplary embodiment, a flexible material, structure, device or device component may be deformed into a curved shape without introducing strain larger than or equal to 5%, for some applications larger than or equal to 1 %, and for yet other applications larger than or equal to 0.5% in strain-sensitive regions. A used herein, some, but not necessarily all, flexible structures are also stretchable. A variety of properties provide flexible structures (e.g., device components) of the invention, including materials properties such as a low modulus, bending stiffness and flexural rigidity; physical dimensions such as small average thickness (e.g., less than 100 microns, optionally less than 10 microns and optionally less than 1 micron) and device geometries such as thin film and open or mesh geometries.

[0124] The term “bending stiffness” refers to a mechanical property of a material, device or layer describing the resistance of the material, device or layer to an applied bending moment. Generally, bending stiffness is defined as the product of the modulus and area moment of inertia of the material, device or layer. A material having an inhomogeneous bending stiffness may optionally be described in terms of a “bulk” or “average” bending stiffness for the entire layer of material.

[0125] The term “elastomer”, as used in the disclosure, refers to a polymeric material which can be stretched or deformed and return to its original shape without substantial permanent deformation. Elastomers commonly undergo substantially elastic deformations. Useful elastomers include those comprising polymers, copolymers, composite materials or mixtures of polymers and copolymers. Elastomeric layer refers to a layer comprising at least one elastomer. Elastomeric layers may also include dopants and other non-elastomeric materials. Useful elastomers useful include, but are not limited to, thermoplastic elastomers, styrenic materials, olefenic materials, polyolefin, polyurethane thermoplastic elastomers, polyamides, synthetic rubbers, PDMS, polybutadiene, polyisobutylene, poly(styrene-butadiene-styrene), polyurethanes, polychloroprene and silicones. Exemplary elastomers include, but are not limited to, silicon containing polymers such as polysiloxanes including poly(dimethyl siloxane) (i.e., PDMS and h- PDMS), poly(methyl siloxane), partially alkylated poly(methyl siloxane), poly(alkyl methyl siloxane) and poly(phenyl methyl siloxane), silicon modified elastomers, thermoplastic elastomers, styrenic materials, olefenic materials, polyolefin, polyurethane thermoplastic elastomers, polyamides, synthetic rubbers, poly isobutylene, poly(styrene-butadiene-styrene), polyurethanes, polychloroprene and silicones. In one embodiment, a flexible polymer is a flexible elastomer.

[0126] The term “encapsulate” or “encapsulation”, as used in the disclosure, refers to the orientation of one structure such that it is at least partially, and in some cases completely, surrounded by one or more other structures. “Partially encapsulated” refers to the orientation of one structure such that it is partially surrounded by one or more other structures. “Completely encapsulated” refers to the orientation of one structure such that it is completely surrounded by one or more other structures. The invention includes devices having partially or completely encapsulated electronic devices, device components and / or inorganic semiconductor components.

[0127] Embodiments of the invention are illustrated in detail hereinafter with reference to accompanying drawings. The description below is merely illustrative in nature and is in no way intended to limit the invention, its application, or uses. The broad teachings of the invention can be implemented in a variety of forms. Therefore, while this invention includes particular examples, the true scope of the invention should not be so limited since other modifications will become apparent upon a study of the drawings, the specification, and the following claims. For purposes of clarity, the same reference numbers will be used in the drawings to identify similar elements. It should be understood that one or more steps within a method may be executed in different order (or concurrently) without altering the principles of the invention.

[0128] The rich set of mechanoreceptors found in human skin offers a versatile engineering interface for transmitting information and eliciting perceptions, potentially serving a broad range of applications in patient care and other important industries. Targeted multisensory engagement of these afferent units, however, faces persistent challenges, especially for wearable, programmable systems that need to operate adaptively across the body.

[0129] This invention introduces a miniaturized electromechanical structure - a bistable, selfsensing electromechanical transducer - and associated haptic system that integrates human skin as an elastic, energy -recovering element. Unlike conventional electrostatic, electromagnetic, or pneumatic haptic systems that continuously consume energy to maintain actuation, the system exploits the intrinsic elasticity of skin to achieve energy recovery and bistability - requiring power only during state transitions. The miniaturized electromechanical structure that, when combined with skin as an elastic, energy storing element, supports bistable, self-sensing modes of deformation. In this architecture, the skin’s inherent elasticity is utilized to form a bistable mechanical system in combination with the miniaturized electromagnetic transducer. Targeting specific classes of mechanoreceptors as the basis for distinct, programmed sensory responses, this haptic unit can deliver both dynamic and static stimuli, directed as either normal or shear forces. Systematic experimental and theoretical studies establish foundational principles and practical criteria for low-energy operation across natural anatomical variations in the mechanical properties of human skin. A wireless, skin-conformable haptic interface, integrating an array of these bistable transducers, serves as a high-density channel capable of rendering input from smartphone-based 3D scanning and inertial sensors. Demonstrations of this system include sensory substitution designed to improve the quality of life for patients with visual and proprioceptive impairments.

[0130] The invention includes the key novel features, but are not limited to: Bioelastic bistable actuation: the transducer mechanically couples with skin, forming a dual-state mechanism (compressed and relaxed) sustained by skin’s stored elastic energy; Inductance-based selfsensing control: built-in inductance measurement enables real-time detection of state and closed- loop power optimization; Kirigami-based shear transmission: a foldable structure converts linear motion into rotational or tangential skin deformation, enabling directional (shear) haptic feedback; Multimodal feedback in a skin-conformable array: combines static indentation, vibration, and shear actuation in a thin, wireless, battery-powered array; and Integration with smartphone sensors: real-time sensory substitution using LiDAR and IMU data for visual, vestibular, and proprioceptive assistance.

[0131] The inventive step of the invention resides in the synergistic combination of biological mechanics and electromechanical bistability. Using skin as a functional mechanical spring is non-obvious and departs from conventional actuator design. The energy-recovery principle achieves large displacement (>2 mm) and force (>1.4 N) with minimal power (~58 mJ per transition). The kirigami conversion of normal to tangential forces provides torsional tactile feedback in a compact form factor, which is an improvement over complex multi-motor designs. The self-sensing closed loop ensures adaptive control across anatomical variations, which is not achieved by existing fixed-parameter haptic devices. Integration into a modular, flexible, wireless array provides real-time feedback synchronized with 3D spatial cues from smartphones, enabling true sensory substitution.

[0132] The invention provides, among other things, the following advantages and beneficial effects: low power consumption and energy-efficient bistable actuation suitable for continuous wearable use; compact and conformable architecture enabling dense, flexible arrays attachable to various skin regions; multisensory realism through combined indentation, vibration, and torsion stimuli targeting both RA and SA mechanoreceptors; wireless and adaptive operation with smartphone integration for sensory substitution and rehabilitation; demonstrated enhancement of mobility, balance, and spatial awareness in users with visual and proprioceptive deficits; and manufacturable and modular system design suitable for scalable production and customizable applications (VR / AR, prosthetic feedback, medical assistive devices).

[0133] Without intent to limit the scope of the invention, exemplary embodiments of the invention are given below.

[0134] In some embodiments, the haptic actuator comprises a miniaturized electromechanical structure that, when interfacing with a skin of a subject through an energy-recovering mechanism, supports bistable, self-sensing modes of deformation, for delivering dynamic and / or static stimuli of indentation, torsion, and / or vibration to the skin.

[0135] In some embodiments, the miniaturized electromechanical structure is a transducer and comprises a core; and an armature coupled with one another, upon mechanical coupling with the skin, to form a bistable mechanism for operably storing and releasing mechanical energy in the skin between a compressed state and a relaxed state.

[0136] In some embodiments, the miniaturized electromechanical structure further includes a diaphragm that improves stability of states and enhances vibration.

[0137] In some embodiments, the core comprises an electromagnetic coil embedded in a soft ferromagnetic cylinder for focusing magnetic fields along its central longitudinal axis and reducing interference between closely spaced units.

[0138] In some embodiments, the core comprises an inner core; a cylindrical encasement; a bobbin placed between the inner core and the cylindrical encasement; and an electromagnetic coil wrapping on the bobbing from the bottom surface of the inner core to the opposing face of the bobbin, wherein the inner core and the cylindrical encasement are formed of a soft ferromagnetic material.

[0139] In some embodiments, the soft (low-coercivity) ferromagnetic material comprises iron or other iron-containing alloys, including iron-cobalt, permalloy, and / or stainless steel.

[0140] In some embodiments, the armature comprises a cap formed of a permanent magnetic material; a cylindrical ring formed of a nonmagnetic material (e.g., titanium, plastic, wood, nonmagnetic stainless steel) and / or the soft ferromagnetic material on the permanent magnetic cap; and a rigid rod having a first end being attached to the permanent magnetic cap through the cylindrical ring, and an opposite, second end interfacing with the skin as a linear shaft that translates through the core.

[0141] In some embodiments, the permanent magnetic material comprises a rare earth magnetic material (e.g., neodymium, Samarium-cobalt), and / or iron alloys with high-coercivity (e g., alnico, ferrite).

[0142] In some embodiments, the diaphragm formed of an elastomeric material is configured to enclose a top of the miniaturized electromechanical structure.

[0143] In some embodiments, the elastomeric material comprises a composite of silicone-based elastomer (e.g., polydimethylsiloxane, PDM, dragonskin, ecoflex, silbione) and magnetic particles (e.g., iron oxide micro- and nano-particles). Such composites include PDMS-MNP described herein..

[0144] In some embodiments, the miniaturized electromechanical structure couples to the skin through an elastomeric substrate (adhesive layer) with a rigid, twist-locking harness whose height are adjustable to change an effective indentation depth of the armature.

[0145] In some embodiments, the harness is provided with a spacer for changing the effective indentation depth.

[0146] In some embodiments, the harness is configured to lock the vertical translation of the miniaturized electromechanical structure upon rotation, wherein a base of the harness adheres to the elastomeric substrate, which, in turn, adheres to the skin of the subject.

[0147] In some embodiments, the base of the harness is reinforced with a fiberglass mesh as a composite within the elastomeric substrate, so as to reduce mechanical mismatch between the harness and the elastomeric substrate.

[0148] In some embodiments, the elastomeric substrate is formed of a silicone-based elastomer.

[0149] In some embodiments, mechanical integration of the skin and bistable operation of the transducer requires that local energetic minima exist at the compressed and relaxed states, and polarization of the coil transiently induces transitions between the compressed state and the relaxed state.

[0150] In some embodiments, in the compressed state, the magnetic field imposed by the permanent magnet, channeled through the armature, magnetizes the soft ferromagnetic core, wherein the strong attraction induced between these elements exceeds the reactive force imposed by the skin, thereby maintaining compression without current applied at the coil, wherein from the compressed state, driving the coil with opposite polarity to the permanent magnet substantially weakens its effect on the core, thereby allowing the skin to push the armature into the relaxed state.

[0151] In some embodiments, in the relaxed state, the elasticity of the skin, along with a slight attraction to the paramagnetic / elastomeric diaphragm, prevents the armature from reverting without applied current, wherein from the relaxed state, driving the coil in alignment with the permanent magnet polarizes the armature and core, overcomes the compressive force of the skin, and drives the armature to transition back into the compressed state.

[0152] In some embodiments, the haptic actuator is operated with an inductance- or resonancebased self-sensing mechanism that operably tailors input power on demand.

[0153] In some embodiments, the haptic actuator is operated with a spring-mass mechanism that serves as the basis for delivering vibrotactile feedback.

[0154] In some embodiments, applying an alternating current at sub-transition amplitude vibrates the armature, creating a small perturbation around the initial state of the transducer, whereby the transducer can bias its modes of vibration to the static position of either the relaxed or compressed states depending on its history.

[0155] In some embodiments, the miniaturized electromechanical structure further comprises an elastomeric disk sandwiched between the armature and the core.

[0156] In some embodiments, in the relaxed state, the spring arises from the elasticities of the skin and the paramagnetic / elastomeric diaphragm, which interact with the armature on opposing ends, and in the compressed state, the spring arises from the elasticities of the elastomeric disk sandwiched between the armature and the core.

[0157] In some embodiments, the transducer further comprises a transmission structure that accommodates the miniaturized electromechanical structure within its internal volume and transmits the normal-directed force of the armature into tangential forces applied parallel to the surface of the skin.

[0158] In some embodiments, the transmission structure comprises a Kresling pattern-inspired structure formed from patterning, bonding, and creasing of stiff plastic panels into a thin-walled hexagonal tube, wherein, upon linear compression, the hexagonal tube twist-buckles into a truss of supporting beams.

[0159] In some embodiments, the transmission structure comprises at least one tier, wherein as with normal-force operation, the transducer maintains two stable states balanced by the elastic force of the skin and the holding force of the permanent magnet.

[0160] In some embodiments, the transmission structure comprises two counter-rotating tiers with opposite chiralities having a top platform, a bottom platform and a middle platform disposed therebetween, which allows low-friction rotational coupling between two contacting elements adhered to the skin.

[0161] In some embodiments, the bottom platform couples to the skin as a ring positioned concentrically around the armature, the middle platform is affixed to a flat surface of the core, and the top platform is fixed to the shaft of the armature and couples to the skin through its adhesion with the permanent magnet of the armature.

[0162] In some embodiments, in operation, the permanent magnet within the armature, one of the adhering elements, pulls the core of the transducer towards it under its permanent magnetic field, and a longitudinal motion of the middle platform drives the top and bottom platforms to rotate in opposite directions, whereby operation of the transducer renders twisting motions in the armature and ring in opposite directions.

[0163] In some embodiments, electrostatic mechanisms give rise to bistability in the system. In such configuration, an electrostatic actuator is used instead of an electromagnetic coil, and an electret material is used instead of a permanent magnet.

[0164] In some embodiments, the electrostatic actuator is a HASEL (hydraulically amplified, self-healing, electrostatic) actuator. The HASEL actuator is a class of soft actuators that feature direct electrical activation via Maxwell stress, electrical self-healing, and fast actuation. In some embodiments, the actuation of the HASEL actuator uses high voltage current to create hydraulic pressure in soft structures that contain dielectric fluids.

[0165] In some embodiments, the haptic actuating system comprises a plurality of haptic actuators arranged in an array, each actuator being disclosed above; and a controller for operating the plurality of haptic actuators.

[0166] In some embodiments, the controller is integrated with a System-on-Chip (SoC) and a built-in antenna.

[0167] In some embodiments, the SoC comprises at least one of a near-field communication (NFC) interface, a Bluetooth® interface, and a Wi-Fi® interface.

[0168] In some embodiments, the haptic actuating system further comprises driving electronics and sensing electronics electrically coupled between the plurality of haptic actuators and the controller; and flexible interconnects electrically connecting to the plurality of haptic actuators and the controller.

[0169] In some embodiments, the flexible interconnects comprise at least one of serpentine interconnects and zigzag interconnects.

[0170] In some embodiments, the haptic actuating system further comprises a power module for supplying power to the entire system.

[0171] In some embodiments, the power module comprises a battery; and a power management unit comprising a boost converter for driving the plurality of haptic actuators, and a low-dropout regulator for logic-level power.

[0172] In some embodiments, the driving electronics comprises an H-bridge for driving each haptic actuator with the power module, and a multiplexer for multiplexing the driving signals from the controller into the H-bridge.

[0173] In some embodiments, the driving electronics further comprises a supercapacitor for buffering the output of the boost converter.

[0174] In some embodiments, the sensing electronics comprises an inductance measurement unit; and a demultiplexer for demultiplexing the input from each haptic actuator into the inductance measurement unit.

[0175] In some embodiments, each haptic actuator itself serves as a sensor for the longitudinal position of its armature, and the inductance measurement unit captures the resonance frequency of each haptic actuator and reports to the controller whether it exists in the relaxed state or the compressed state.

[0176] In some embodiments, each haptic actuator is configured as a modular unit that is incorporated into a hexagonal tiling of self-similar units, wherein each unit is independently addressed from exposed contacts on the exterior tiles of the hexagonal grid.

[0177] In some embodiments, the flexible interconnects for each unit are configured so that traversing signals reach the correct units by soldering each identical unit at prescribed rotations of 120°, so as to route the driving signals to interior units of the array individually.

[0178] In some embodiments, each haptic actuator is pitched at about 1.3 cm, which is within a spatial acuity of the skin.

[0179] In some embodiments, the haptic actuating system further comprises an outer encapsulation layer formed of a silicone-based elastomer encapsulating the haptic actuating system.

[0180] In some embodiments, the haptic actuating system is a wireless, skin-conformable haptic interface, which serves as a high-density channel capable of rendering input from a smart device comprising a 3D scanner and inertial measurement unit (IMU) sensors, which operably track the position and orientation of the subject and environment.

[0181] In some embodiments, the wireless, skin-conformable haptic interface has a flexible reconfiguration of the array while tolerating repeated mechanical bending and stretching.

[0182] In some embodiments, the wireless, skin-conformable haptic interface is usable for sensory substitution, wherein smart device based sensory cues derived from 3D scanning and inertial measurements yield perceptions that improve performance in models of visual, vestibular, and proprioceptive sensory substitution tasks.

[0183] In some embodiments, the haptic actuating system operably receives the sensory information over wireless communications from the smart device and renders feedback to the subject as replacement or augmentation of their sensory abilities.

[0184] In some embodiments, the wireless, skin-conformable haptic interface is operated to provide an intuitive frame of reference for virtual objects that follow the orientation of the body, as so to help individuals detect obstacles in their path without vision being necessary.

[0185] In some embodiments, the wireless, skin-conformable haptic interface is operated to provide feedback during standing balance as a means of enhancing postural stability.

[0186] In some embodiments, the wireless, skin-conformable haptic interface is operated to guide foot orientation in individuals with impaired proprioceptive control.

[0187] In some embodiments, the wireless, skin-conformable haptic interface is operated to guide a user’s hand towards target objects without vision being necessary. In one aspect, the invention relates to a wearable haptic feedback system comprising plurality of bistable electromechanical transducers, each transducer being configured to be mechanically coupled to a user’s skin and including a ferromagnetic core, a movable armature having a permanent magnet, and an elastomeric diaphragm configured to deform the skin, wherein each transducer and the skin collectively form a bistable mechanical system having compressed and relaxed states defined by stored elastic energy of the skin; a control circuit configured to drive the transducer between the bistable states by transient current pulses and to detect its state via inductance-based self-sensing; and a wireless interface configured to receive sensory or positional input and to command corresponding tactile feedback patterns through the array of transducers.

[0188] In some embodiments, the bistable states are maintained without continuous power consumption.

[0189] In some embodiments, each transducer transitions between states using opposite polarity drive currents.

[0190] In some embodiments, the inductance-based sensing circuit measures resonance frequency to determine transducer position.

[0191] In some embodiments, the elastomeric diaphragm comprises a composite of polydimethylsiloxane (PDMS) and magnetic nanopowder.

[0192] In some embodiments, the armature includes a titanium shaft that directly couples mechanical displacement into the skin.

[0193] In some embodiments, the haptic feedback system further comprises a kirigami transmission structure configured to convert linear motion of the armature into tangential shear deformation of the skin.

[0194] In some embodiments, the kirigami structure comprises counter-rotating tiers arranged in opposite chiralities.

[0195] In some embodiments, each transducer is arranged in a modular, hexagonal array with flexible serpentine interconnects.

[0196] In some embodiments, the control circuit includes a Bluetooth low-energy controller and a rechargeable power source.

[0197] In some embodiments, the wireless interface receives sensory data from a smart device, including LiDAR-based 3D scanning or inertial measurements.

[0198] In some embodiments, the transducer delivers both static indentation and dynamic vibration stimuli.

[0199] In some embodiments, the vibration and indentation are independently controllable to engage distinct classes of mechanoreceptors.

[0200] In some embodiments, the transducer array provides sensory substitution feedback corresponding to spatial or balance cues.

[0201] In some embodiments, the feedback assists a user in detecting environmental obstacles or maintaining postural stability.

[0202] In some embodiments, the bistable structure employs skin elasticity to recover mechanical energy upon state transition.

[0203] In some embodiments, the transducer housing and harness are configured for adjustable indentation depth.

[0204] In some embodiments, the bistable haptic unit provides multimodal feedback including indentation, torsion, and vibration for sensory substitution.

[0205] Without intent to limit the scope of the invention, exemplary instruments, apparatus, methods and their related results according to the embodiments of the invention are given below. Note that titles or subtitles may be used in the examples for convenience of a reader, which in no way should limit the scope of the invention. Moreover, certain theories are proposed and disclosed herein; however, in no way they, whether they are right or wrong, should limit the scope of the invention so long as the invention is practiced according to the invention without regard for any particular theory or scheme of action.

[0206] EXAMPLE 1:

[0207] BIOELASTIC STATE RECOVERY FOR HAPTIC SENSORY SUBSTITUTION

[0208] In this example, we introduce concepts of engineering science that enable targeting of the mechanical response profiles associated with these receptors through a wireless, real-time interface. Panel b of FIG. 1 illustrates the transmission of indentation, shear, and vibrotactile stimuli through different contacting elements that include kirigami structures and cylindrical probes. The diversity in modes of engagement, density of power delivery, and efficiency in operation of our small-scale mechanical transducers represent key, enabling advances over alternative electrostatic, pneumatic, and electromagnetic approaches.

[0209] The foundational concept of this transducer, illustrated in panel c of FIG. 1, is the integration of skin as a central mechanical component, yielding a bistable mechanism that recovers energy stored under compressive loading. Detailed biomechanical studies establish principles for further miniaturization, as displayed in the inset to panel c of FIG. 1. Inductancebased self-sensing operations also lead to greater efficiency as part of a closed-loop control strategy. These features make it possible to assemble flexible, lightweight, interconnected arrays, as pictured in panels d-e of FIG. 1, with functional diversities that greatly exceed previous reports. In demonstrations of this untethered, skin-conformable array as a haptic interface for sensory substitution (examples shown in panels f-g of FIG. 1), smartphone-based sensory cues derived from 3D scanning and inertial measurements yield perceptions that improve performance in models of visual and proprioceptive sensory impairments.

[0210] Design principles, biomechanical integration, and bistable operation

[0211] The ability to store and release mechanical energy in skin arises from three mechanically distinct components — the core, armature, and diaphragm (panel a of FIG. 2 and FIG. 5). The core contains an electromagnetic coil embedded in a soft ferromagnetic (iron-cobalt) cylinder, which serves to focus magnetic fields along its central longitudinal axis and to reduce interference between closely spaced units (panel c of FIG. 7). Iron-cobalt also appears as part of the armature assembly, along with a neodymium permanent magnet and titanium rod. This rod interfaces with the skin as a linear shaft that translates through the core. An elastomeric diaphragm, a composite of polydimethylsiloxane and magnetic nanopowder (PDMS-MNP), encloses the top of the structure. Each transducer couples to the skin through an adhesive layer with rigid, twist-locking harnesses whose heights can be adjusted to change the effective indentation depth of the armature (FIGS. 5-6). To reduce mechanical mismatch between the rigid actuators and the soft, elastomeric adhesive layer, the bonding areas of the harnesses are reinforced with composites of patterned fiberglass mesh.

[0212] The core, armature, and diaphragm, upon mechanical coupling with the skin, form a bistable mechanism, in which energy stored by compressing the skin is returned upon transition to relaxed conditions. In the compressed state (illustrated in panel b of FIG. 2), the magnetic field imposed by the permanent magnet, channeled through the armature, magnetizes the soft ferromagnetic core. The strong attraction induced between these elements exceeds the reactive force imposed by the skin, thereby maintaining compression without current applied at the coil. From this state, driving the coil with opposite polarity to the permanent magnet substantially weakens its effect on the core, thus allowing the skin to push the armature into the relaxed state. In the relaxed state (illustrated in panel b of FIG. 2), the elasticity of the skin, along with a slight attraction to the PDMS-MNP diaphragm, prevents the armature from reverting without applied current. From the relaxed state, driving the coil in alignment with the permanent magnet polarizes the armature and core, overcomes the compressive force of the skin, and drives the armature to transition back into the compressed state. Using this bistable operation, the power unit dissipates energy to transition between each state but not to persistently remain in any state.

[0213] Mechanical integration of the skin and bistable operation of the transducer requires that: (1) local energetic minima exist at the compressed and relaxed states, and (2) polarization of the coil transiently induces transitions between these states (see potential energy graphs of panel b of FIG. 2). Across a range of mechanical properties and input parameters, systematically examined through numerical modeling (FIG. 7) and direct evaluation on skin phantoms (FIG. 15), the shaded regions in panels c-d of FIG. 2 bound conditions satisfying the first and second criteria respectively. Panel c of FIG. 2 shows that a successful transition from relaxed to compressed requires larger driving currents for stiffer skin, while the transition from compressed to relaxed follows the opposite trend. As shown in panel e of FIG. 2, the transducer operates successfully across three skin locations on six human subjects with applied currents of at most 400 mA (FIG. 8 and FIG. 16 for additional skin locations).

[0214] Panel e of FIG. 2 and Tables 1-2 show that each skin location recovers varying amounts of energy, consistent with the range of skin mechanical properties recorded in FIG. 8. Considering that the transducer requires 1.17 J of input work to transition to the relaxed state without skin being present, the transducer saves between 742-1169 mJ from the contribution of skin in the locations reported in Tables 1-2 for 2 mm indentations. To accommodate these variations, the transducers feature an inductance-based self-sensing mechanism, which, as subsequently described, tailors input power on demand. Requiring only 58 mJ on average for transitions (2 mm indentation; Tables 1-2), the transducers lead to linear displacements of greater than 2 mm and forces up to 1.4 N (panel b of FIG. 8). As outlined in Table 3, this device, while being compact and untethered, exceeds benchmark performances of alternatives based on electrostatic and electromagnetic schemes. These systematic investigations also yield principles for optimization — as shown in FIG. 12, mechanical characterization reveals that an optimized unit with 2.1 mm height (4.1 mm, relaxed state), operating over a narrower range of indentations, has performance matching the original design for 2 mm indentations. Table 1: Mechanical bistability evaluation in clinical samples of healthy individuals (Subject 1, male, age 36; Subject 2, male, age 30; Subject 3, male, 23). Measurements were performed in three skin locations. The absolute value of current and pulse duration required to transition the armature between indented and closed states was measured for n = 6 participants. The indentation depth was adjusted by performing experiments with harnesses of varying heights. The skin was preconditioned by indenting it for 30 s before each transition.

[0215] 2 mm indentation 1.5 mm indentation

[0216] Rel. Com. Com. Rel. Rel. Com. Com. Rel.

[0217] Subject 1 Forearm 200 mA 400 mA 100 mA 400 mA

[0218] 10 ms 20 ms 10 ms 60 ms

[0219] 5.36 mJ 4.28 mJ 1.34 mJ 129 mJ

[0220] Dorsal hand (Mill) 150 mA 400 mA 100 mA 400 mA

[0221] 20 ms 40 ms 10 ms 80 ms

[0222] 6.06 mJ 85.7 mJ 1.34 mJ 171 mJ

[0223] Dorsal hand (AP) 100 mA 400 mA 100 mA 400 mA

[0224] 10 ms 20 ms 10 ms 80 ms

[0225] 1.34 mJ 42.8 mJ 1.34 mJ 171 mJ

[0226] Subject 2 Forearm 150 mA 300 mA 100 mA 400 mA

[0227] 10 ms 20 ms 10 ms 80 ms

[0228] 3.01 mJ 24.1 mJ 1.34 mJ 171 mJ

[0229] Dorsal hand (Mill) X X 100 mA 400 mA

[0230] 10 ms 100 ms

[0231] 1.34 mJ 214 mJ

[0232] Dorsal hand (AP) 200 mA 400 mA 100 mA X

[0233] 10 ms 10 ms 10 ms

[0234] 5.36 mJ 21.4 mJ 1.34 mJ

[0235] Subject s Forearm 100 mA 400 mA 50 mA X

[0236] 40 ms 60 ms 10 ms

[0237] 5.36 mJ 129 mJ 0.335 mJ

[0238] Dorsal hand (Mill) 100 mA 400 mA 100 mA X

[0239] 40 ms 20 ms 10 ms

[0240] 5.36 mJ 4.28 mJ 1.34 mJ

[0241] Dorsal hand (AP) 100 mA 400 mA 50 mA 400 mA

[0242] 20 ms 60 ms 20 ms 400 ms

[0243] 2.68 mJ 129 mJ 0.670 mJ 857 mJ

[0244] Table 2: Mechanical bistability evaluation in clinical samples of healthy individuals (Subject 4, female, age 20; Subject 5, female, age 20; Subject 6, female, 24). Measurements were performed in three skin locations. The absolute value of current and pulse duration required to transition the armature between indented and closed states was measured for n = 6 participants. The indentation depth was adjusted by performing experiments with harnesses of varying heights. The skin was preconditioned by indenting it for 30 s before each transition.

[0245] _ 2 mm indentation _ 1.5 mm indentation

[0246] _ Rel. Com, Com, — » Rel. Rel. Com, Com, Rel.

[0247] Subject 4 Forearm _ 150 mA _ 400 mA _ 100 mA _ 400 mA 10 ms 200 ms 10 ms 200 ms

[0248] 3.01 mJ 428 mJ 1.34 mJ 428 mJ

[0249] Dorsal hand (Mill) 100 mA 350 mA 50 mA 400 mA

[0250] 20 ms 40 ms 10 ms 900 ms

[0251] 2.68 mJ 65.6 mJ 0.335 mJ 1930 mJ

[0252] Dorsal hand (AP) 100 mA 400 mA 50 mA 400 mA

[0253] 40 ms 100 ms 20 ms 300 ms

[0254] 5.36 mJ 214 mJ 0.670 mJ 643 mJ

[0255] Subject s Forearm 200 mA 400 mA 100 mA 400 mA

[0256] 20 ms 40 ms 10 ms 200 ms

[0257] 10.7 mJ 85.7 mJ 1.34 mJ 428 mJ

[0258] Dorsal hand (Mill) 200 mA 400 mA 100 mA 400 mA

[0259] 10 ms 40 ms 10 ms 200 ms

[0260] 5.36 mJ 85.7 mJ 1.34 mJ 428 mJ

[0261] Dorsal hand (AP) 100 mA 400 mA 100 mA 400 mA

[0262] 20 ms 40 ms 10 ms 300 ms

[0263] 2.68 mJ 85.7 mJ 1.34 mJ 643 mJ

[0264] Subject 6 Forearm 100 mA 400 mA 50 mA 400 mA

[0265] 20 ms 200 ms 10 ms 200 ms

[0266] 2.68 mJ 428 mJ 0.335 mJ 428 mJ

[0267] Dorsal hand (Mill) 250 mA 300 mA 50 mA 400 mA

[0268] 10 ms 10 ms 10 ms 100 ms

[0269] 8.37 mJ 12.1 mJ 0.335 mJ 214 mJ

[0270] Dorsal hand (AP) 100 mA 400 mA 100 mA 400 mA

[0271] 20 ms 20 ms 10 ms 200 ms

[0272] 2.68 mJ 42.8 mJ 1.34 mJ 428 mJ

[0273] Table 3: Performance comparisons between wearable indentation actuator arrays.

[0274] Ref. Tethered Mechanism Size* Blocking | Max Transition Continuous holding extension energy power force (N) (mm) (mJ) (mW)

[0275] This No Bioelastic / H 7 mm x 1.4 1 0.6 3 58 NA work Electro- D 7 mm magnetic (305 mm3)

[0276] This No Bioelastic / H 2.1 mm x 0.55 0.3 2 NR NA work Electro- D 8 mm

[0277] (scaled) magnetic (106 mm3)

[0278] 1 ,2 Yes — high- Electrostatic H O.S mm x 0.75 NA 0 5 NA 200 voltage (2 k V) D 10 mm instrument (63 mm3) Yes — Pneumatic H 0.14 mm x 2.5 pneumatic D 8 mm (7 mm3) pump in backpack *Based on dimensions without adhesive layers or supporting electronics. “Size of pneumatic pump

[0279] NA, not applicable. NR, not reported.

[0280] Bimodal vibrotactile actuation

[0281] The mechanical structure of skin, along with its role in the bistable operation of our transducers, helps define a spring-mass system that serves as the basis for delivering vibrotactile feedback (panel a of FIG. 3 and panel f of FIG. 7). In the relaxed state, this spring arises from the elasticities of the skin and PDMS-MNP diaphragm, which interact with the armature on opposing ends. To allow a similar effect in the compressed state, the transducer contains an elastomeric disk layered between the core and armature. As shown in panels a-c of FIG. 3, applying an alternating current at sub -transit! on amplitude vibrates the armature, creating a small perturbation around the initial state of the transducer. Following the hysteresis curve shown in panel b of FIG. 3, the transducer can bias its modes of vibration to the static position of either the relaxed or compressed states depending on its history.

[0282] As shown in panels c-d of FIG. 3, the spatiotemporal profiles of mechanical deformation, measured with three-dimensional digital image correlation (DIC) on skin phantoms (FIG. 9), clearly distinguish these two modes of vibration. For each frequency tested, human participants (n = 12) perceive vibrotactile stimulus in both the relaxed and compressed states with thresholds reported in panel e of FIG. 3and panels a-b of FIG. 11.

[0283] Our system aims to deliver static indentation and dynamic vibration as perceptually distinct channels of information. On this basis, panels f-g of FIG. 3 demonstrate how integrating these operations allows the transducer to deliver information at faster bitrates, given a fixed budget for power consumption. Panel g of FIG. 3 also indicates that bistable operation in the 0-2 bits / s regime offers superior power consumption with respect to purely vibrational modes. The independent and simultaneous control of indentation and vibration also raises the prospect for manipulation of a broader range of sensations that incorporate mixed input from slowly adapting (SA) and rapidly adapting (RA) mechanoreceptors.

[0284] Shear actuation with a kirigami transmission structure

[0285] Human tactile perception not only reflects the temporal pattern of mechanical stimuli but also the direction of applied forces. Generalizing the contact surface of the transducer beyond a simple indenting rod, panels h-i of FIG. 3 illustrate a kirigami structure that transmits the normal-directed force of the armature into tangential forces applied parallel to the surface of the skin. This Kresling pattern-inspired structure arises from the patterning, bonding, and creasing of stiff plastic panels into a thin-walled hexagonal tube (panel j of FIG. 3). As illustrated in FIG. 10, our split-crease design accommodates the transducer within the internal volume of the structure itself. Upon linear compression, as simulated in panel k of FIG. 3 and FIG. 7, the pattern twistbuckles into a truss of supporting beams.

[0286] Assembled into two counter-rotating tiers, our design shown in panels h-j of FIG. 3 allows low-friction rotational coupling between two contacting elements adhered to the skin. The neodymium magnet within the armature, one of the adhering elements, pulls the core of the transducer towards it under its permanent magnetic field. Since the two tiers have opposite chiralities, longitudinal motion of the middle platform drives the top and bottom platforms to rotate in opposite directions. The bottom platform couples to the skin as a ring positioned concentrically around the armature. The top platform, fixed to the shaft of the armature, couples to the skin through its adhesion with the neodymium magnet of the armature. Therefore, operation of the transducer renders twisting motions in the armature and ring in opposite directions. These principles similarly define the operation of a miniaturized, one-tiered structure described in FIG. 12. As with normal -force operation, these transducers maintain two stable states balanced by the elastic force of the skin and the holding force of the permanent magnet. As with normal-force operation, vibratory modes are possible in either of these two states.

[0287] With the compact, efficient design reported here, the kirigami transducer generates a total rotation of up to 14° between the disk and ring elements, as measured by 3D DIC on a skin phantom (E = 31 kPa). Furthermore, only 0.4 mm normal deformation is generated for this torsion angle. Panel 1 of FIG. 3 demonstrates that the maximal tangential strain, focused on the edges of the disk, reaches beyond 75%. The disk, having a smaller radius than the ring, accounts for the largest deformation. The one-tiered structure, meanwhile, yields a rotation of 7.5° and a normal deformation of 0.25 mm (FIG. 12). As shown in panel m of FIG. 3 and panels d-j of FIG. 11, human participants (n = 14) report a clear increase in perceptual intensity as the angle of torsion increases from 5° to 15°. Furthermore, panels h-j of FIG. 11 show that participants (n = 15) can clearly distinguish this torsional mode from indentation. Self-sensing from a wireless, battery-powered array

[0288] Both normal and shear modes of actuation rely critically on mechanical coupling to the skin to support bistable operation. Spatial and temporal variability in the mechanical behavior of skin, as documented in panel e of FIG. 2, motivate the use of the self-sensing control strategy summarized in panels a-b of FIG. 4. Through inductance-based measurements, the transducer itself can serve as a sensor for the longitudinal position of its armature (panel c of FIG. 4). The circuit elements outlined in panel b of FIG. 4capture the resonance frequency of each transducer and report to the controller whether it exists in the relaxed state or the compressed state (panel d of FIG. 4). As the basis for a closed-loop system, self-sensing allows the transducer to recover energy stored in skin deformations, which would otherwise dissipate under mismatched transition currents.

[0289] Integrated as part of the hexagonal array described in panels a-b of FIG. 4, a Bluetooth controller routes this sensor input, along with output from drivers, to 19 transducers through a layer of serpentine interconnects. The modular design of each identical transducer unit, illustrated in panel d of FIG. 6, enables flexible reconfiguration of the array while tolerating repeated mechanical bending and stretching (1000 cycles; panels h-k of FIG. 6). Each haptic unit is pitched at 1.3 cm, well within the reported spatial acuity of most skin areas, including the neck and forearm (5.5 mm and 2.4 mm by two-point discrimination population means, respectively). Considering these principles, panel i of FIG. 12 depicts an array with units for both torsion and indentation that can be employed as subpixels within these areas.

[0290] A small 500-mAhr lithium-ion battery, integrated within the controlling circuit, supplies power to the entire system. In system-level demonstrations — described in the following section — the battery regularly sustains operation over three-hour intervals without losing performance. Putting aside power losses from the controller, the 500 mAhr capacity of the battery would, in principle, allow the transducer to transition twice per second over 16 hours, given an average input energy of 58 ml across both transitions (derived from Tables 1-2). Without closed-loop control, each transition towards compressed and each transition towards relaxed would consume 6.36 mJ and 323 mJ more energy respectively (285% overall; average across six subjects, three skin locations) to accommodate the full range of input thresholds recorded in Tables 1-2. With output voltage buffered by a supercapacitor (panel b of FIG. 4), the controller can transition all 19 units simultaneously and at least 29 units / s on average given 58 mJ per transition. The peak array temperature remains under 40 °C during characteristic conditions for the system level demonstrations outlined in the following section.

[0291] Sensory substitution using inertial measurements and 3D scanning

[0292] Panel a of FIG. 4 illustrates the operation of a system that draws real-time information from an advanced suite of sensors offered in modem smartphones. With respect to an internal reconstruction of the surrounding environment, as visualized in panel e of FIG. 4, inertial measurement units (IMUs) and light detection and ranging (LiDAR) 3D scanners track the position and orientation of the user. Our haptic device receives this sensory information over a Bluetooth connection and renders feedback to the user as replacement or augmentation of their sensory abilities. In our demonstrations, the user wears the haptic device on the back of their neck (as displayed in panel e of FIG. 1), which provides an intuitive frame of reference for virtual objects that follow the orientation of the body. Panels f-h of FIG. 4 illustrate how this single configuration can address three separate sensory impairments using different profiles of indentation and vibration.

[0293] The first sensory substitution system, illustrated in panel f of FIG. 4, aims to help individuals with visual impairment detect obstacles in their path. As shown in panel f of FIG. 4, panel a of FIG. 13, a smartphone held by the subject anchors six virtual detection windows to the room using LiDAR at a variable distance (2.5 m in this example) from the user. Each window sends a pattern of skin indentation to the haptic device when a physical object crosses its respective boundary at the prescribed distance. In healthy, blindfolded participants (n = 7), this sensory substitution system yields an accuracy of 81.8% across all participants and cues (panel i of FIG. 4). As shown in FIG. 13, participants perform best when distinguishing the horizontal position of cues.

[0294] Another configuration of this system, illustrated in panel g of FIG. 4, provides feedback during standing balance as a means of enhancing postural stability. As shown in panel g of FIG. 4, a smartphone held against the body of the subject tracks its orientation using an IMU. This data serves feedback to the haptic device, which, analogous to spirit level, renders a line of vibration that follows the postural angle of the user (panel i of FIG. 13). In healthy participants (n = 10), this sensory substitution system improves performance on the standard Sharpened Romberg test. As shown in panel j of FIG. 4and FIG. 13, subjects maintain their balance 20- 313% longer on average under guidance from the haptic device.

[0295] Finally, panel h of FIG. 4illustrates an application that aims to guide foot orientation in individuals with impaired proprioceptive control. Adverse foot positioning is often an inciting event for ankle injury. As shown in panels a and h of FIG. 4, the user wears an external IMU in their shoe and holds a smartphone in their hand. The smartphone uses LiDAR to track the orientation of an adjacent surface and the external IMU to track foot orientation. The haptic device receives these streams of information and renders vibration in the direction of error between the foot and surface (panel b of FIG. 14). With their eyes closed, this sensory substitution system allows healthy participants (n = 3) to match their foot strike orientation to a target surface positioned at varying combinations of pitch and yaw. The magnitude of error for each participant, shown in panel k of FIG. 4 and FIG. 14, is 8.82° (mean; 5.33° SD; n = 172, three subjects). As demonstrated in FIG. 14, each participant produces consistent results, even with step intervals under 1 s, suggesting that this information can be used in real-time to help them adjust their motion.

[0296] Conclusions

[0297] Interfacing with the skin through an energy-recovering mechanism, the bistable, selfsensing transducer introduced here offers new operational modes and associated haptic sensations that significantly exceed the performance of other approaches. These concepts serve as the foundation for a programmable, skin-conformable array that receives and renders patterns of multimodal mechanical stimuli. Through its ability to deliver large forces and displacements, it can reproduce cutaneous sensations associated with both SA and RA classes of mechanoreceptors. It can also blend static and dynamic deformations, addressing sensations that require coordinated and simultaneous engagement between these classes. Finally, using a compact, efficient kirigami transmission structure, it can manipulate the direction of force. These mechanosensory pathways contribute to a broad range of important human sensory perceptions, including the origin, direction, and textural quality of skin contact made with its physical environment. Thus, the ability to simultaneously deliver indentation, torsion, and vibration offers a strong basis for immersive haptic realism and improved intuitiveness of its applications. This multisensory operation is especially well suited for biomedical applications that require integration of complex streams of somatosensory information, such as those examined herein. In demonstrations of a wireless, skin-conformable haptic interface, smartphone-based sensory cues derived from 3D scanning and inertial measurements yield perceptions that improve performance in models of visual, vestibular, and proprioceptive sensory substitution tasks. EXAMPLE 2:

[0298] TRANSDUCER FABRICATION

[0299] The architecture of one transducer is illustrated in FIG. 5. A soft (low-coercivity) ferromagnetic alloy (iron-cobalt 1 : 1; Vacoflux 50, Vacuumschmelze) was used for the inner core of the solenoid, the base of the armature, and the cylindrical encasement. Each of these parts was machined by CNC lathe and wire EDM. The magnetic components, together with a 3D- printed bobbin (Black v4 resin; Form 3B, Formlabs) and a flexible printed circuit board (fPCB) interconnect layer (PCBWay), were assembled on the stage of the coil-winder pictured in panel a of FIG. 5. The lead wires of the coil were then soldered to the fPCB interconnects, which wrapped from the bottom surface of the inner core to the opposing face of the bobbin. The armature was fabricated from an N48 nickel-plated neodymium magnet (Apex Magnets), a cylindrical ring of iron-cobalt, and a 1.57 mm diameter titanium pin. An elastomeric ring (Dragon Skin 10 Slow, Smooth-On) was sandwiched between the base of the armature and the inner core.

[0300] The diaphragms were fabricated as caps that could be fitted across the top surface of each bobbin assembly. The elastomeric caps were cured inside a two-part mold. The top surface of the cap was a composite of polydimethylsiloxane (PDMS) and magnetic nanopowder (MNP). Iron oxide (II, III) MNP (50-100 nm particle size; Sigma- Aldrich) and Part B of Sylgard 184 (Dow Corning) were mixed 15: 100 by mass using a planetary mixer (2000 rpm for 5 minutes under 0.2 kPa pressure; ARV-310P, Thinky) and were then allowed to return to room temperature. Part A of Sylgard 184 was then added in a 1 : 10 ratio by mass of Part B and mixed using a planetary mixer (2000 rpm for 30 seconds under 0.2 kPa pressure). The PDMS-MNP composite was reverse pipetted (12 pL) into the outer half of the mold and cured before filling the rest of the mold with unmodified PDMS (Parts A and B, 1 : 10 by mass). The diaphragms were cured at 75 °C for 3 hours.

[0301] EXAMPLE 3: MODULAR TWIST-LOCKING HARNESSES, CONSUMABLE ADHESIVE LAYER, AND ENCAPSULATION

[0302] The harness includes two parts that lock the vertical translation of the device upon rotation (FIG. 5). They were 3D printed with Black V4 resin (Form 3B, formlabs). As shown in panels d-e of FIG. 5, harnesses were fabricated with spacers so that the effective indentation depth could be set to 1 mm, 1.5 mm, or 2 mm.

[0303] The lower part of the harness adheres to the elastomeric substrate, which, in turn, adheres to the wearer’s skin. In order to reduce mechanical mismatch between the soft substrate and rigid harness, a hexagonal ring at the base of the harness was reinforced with a fiberglass mesh as a composite within the elastomeric substrate. Panel c of FIG. 6 shows an overview of the fabrication process. The adhesive layer started with a copper-clad fiberglass disk. On top of this substrate, we spin-coated (2000 rpm for 2 minutes; WS-650-23 Spin Coater, Laurell) a thin (90 pm) layer of silicone-based elastomer (Dragon Skin 10 Slow, Smooth-On). Before this layer was allowed to cure, fiberglass mesh (Fiberglass Warehouse) was layered into the thin layer of silicone. After curing this layer, the silicone-mesh composite was patterned by CO2 laser (VLS3.50DT) into a hexagonal tiling. Then, another layer of silicone (Dragon Skin 10 Slow, Smooth-On) was spin-coated onto the substrate at the full thickness of 140 pm (1000 rpm for 2 minutes). After curing at 75 °C for 3 hours, a 260 pm adhesive layer of silicone gel (Silbione RT Gel 4717, Elkem) was spun onto the substrate (1000 rpm for 30 seconds). This was cured at room temperature for 24 hours, and then the pattern was removed by laser cutting the outer shape. The elastomeric adhesive was then transferred onto a laminate backing, and the harnesses were bonded to the non-adhesive surface by dip-coating it with single-component silicone (RTV 3140, Dow Coming). Panel d of FIG. 4 shows a photograph of two transducer units positioned inside the controller module and schematic illustrations demonstrating how each modular interconnect layer routes signals through the hexagonal array. The serpentine interconnects are two-layer flexible printed circuit boards (fPCBs) manufactured from 35 pm copper traces with a total thickness of 130 pm (PCBWay). During assembly, the internal contacts fold into the core where they can be soldered to the coil.

[0304] The outer encapsulation (FIG. le) of the device was comprised of a silicone-based elastomer (Silbione RTV 4420, Elkem). The encapsulation was cured at 75 °C for 3 hours between a two-part mold milled from aluminum. The resulting encapsulation layer had a thickness of 0.3 mm.

[0305] EXAMPLE 4:

[0306] FINITE ELEMENT MODELING OF ELECTROMAGNETIC AND SOLID MECHANICAL PROCESSES The commercial software packages Ansys and ABAQUS were used for simulation of quasi-magnetostatic and solid mechanical processes respectively. Model geometries, boundary conditions, and numerical configurations for the unit transducer and array are detailed in panels a-f of FIG. 7 and panels h-k of FIG. 6 respectively. Elastic moduli (E) and Poisson’s ratios (v) were Edragon = 15 MPa and Vdragon = 0.48 for dragon skin; / Asin = 2000 MPa and Wesin = 0.35 for 3D printed parts; and Epi = 2.5 GPa and vpi = 0.34 for polyimide (PI). The fiberglass mesh composite was modeled as a transverse isotropic elastic material with E = E = 180 MPa, E3 = 0.162 MPa, 1’12 = 0.48, 1’13 = 1’23 = 0.37, G12 = 60.8 MPa and G13 = G23 = 102 MPa. Each skin phantom was modeled as a Mooney-Rivlin hyperelastic material with an initial modulus of 10- 400 kPa and a hardening coefficient of 2. Copper was modeled as elastoplastic (without hardening), with EAU= 119 GPa, VAU= 0.34, and a yield strain of 0.3%.

[0307] Panels g-i of FIG. 7 detail the model geometries, boundary conditions, and numerical configurations for simulation of the kirigami structure with a skin phantom. Specifically, panel g of FIG. 7 is a stress distribution within the kirigami structure in the relaxed state (PET yield stress, 80 MPa). The simulation consists of two steps, starting from the fully unfolded state of the two kirigami modules, transitioning to the relaxed state (4.4 mm linear displacement from unfolded), and then transitioning to the compressed state (2 mm translation of the middle platform). The mesh of the skin phantom was refined in the area where it contacts the kirigami, and convergence was guaranteed for all cases. A tie constraint was applied to connect the bottom panel of the upper kirigami structure to the lower kirigami structure, and another tie constraint was applied between the top panel of the upper kirigami structure and the top surface of the armature. The contacting elements were firmly attached to the surface of the skin phantoms using cohesive elements, panel h of FIG. 7 is a stress distribution within the kirigami structure in the compressed state. Panel i of FIG. 7 is a in-plane strain of the skin phantom in the compressed state. A stiff skin phantom was employed here to evaluate the upper bound of stress in the structure (E = 5.1 MPa).

[0308] The elastic modulus (E), Poisson's ratio (v), and mass density (0) were as follows: Eskin = 5.1 MPa, Vskin 0.48, and / kin 1.02 g / cm3for the skin phantom; Epet 4000 MPa, vPet 0.4, andPet = 1.54 g / cm3for PET plastic; and Epu= 7.84 MPa, vpu= 0.4, andpu= 1.25 g / cm3for polyurethane (PU) plastic.

[0309] EXAMPLE 5: PHANTOM SKIN MECHANICAL CHARACTERIZATION AND BISTABILITY MEASUREMENTS

[0310] The criteria for bistability and minimum transition currents were evaluated using skin phantoms with varying compressive moduli. Using the setup described in panels c-d of FIG. 8, the force-extension characteristics were determined and fitted to a theoretical indentation model, which accounts for the contact between a rigid cylinder with a flat end and an elastic half-space (35:1 PDMS mixing ratio, E = 85 kPa; 40: 1, E = 61 kPa; 45: 1, E = 43 kPa; 50: 1, E = 31 kPa; 55: 1, E = 24 kPa).

[0311] The experimental setup and results of the bistability experiments can be seen in FIG. 15. Prior to testing, the transducer was attached to a phantom skin and transitioned between compressed and relaxed modes once to eliminate any unintended friction that may have arisen during installation. A 2-second pulse was then applied to the transducer to discount viscous effects, and the minimum transition currents for both compressed and relaxed states were recorded. The study involved phantoms of thicknesses 2 mm and 5 mm with different moduli (PDMS mixing ratios with 35: 1, 40: 1, 45: 1, 50: 1, and 55: 1) and three effective indentations (2 mm, 1 .5 mm, and 1 mm) adjusted with variations in the harness spacer (0 mm, 0.5 mm, and 1 mm). Current-controlled stimuli were driven in the range of -450 to 450 mA (2602 System SourceMeter, Keithley). To account for performance variation, 3-4 different transducers were employed for each experimental condition.

[0312] EXAMPLE 6:

[0313] HUMAN SKIN MECHANICAL CHARACTERIZATION AND BISTABILITY MEASUREMENTS

[0314] Human subjects: All subject participation was fully voluntary with informed consent obtained before the experiments. Research protocols were approved by the Institutional Review Board at Northwestern University (STU00214800) and the Ethics Committee of Westlake University (2023073 IJHQ001).

[0315] As shown in panels e-g of FIG. 8, the compressive moduli of human skin were assessed at three distinct locations (dorsal palm on adductor pollicis, dorsal palm on metacarpals, and ventral forearm) in a cohort of six individuals (three males and three females, ages 20-36). The obtained experimental data was employed to calculate the skin moduli using a theoretical indentation model, which accounts for the contact between a rigid cylinder with a flat end and an elastic half-space.

[0316] As shown in panel e of FIG. 2, panel a of FIG. 8, and FIG. 16, the bistability and minimum transition current of the transducer were evaluated on five different locations of human skin: dorsal palm on adductor pollicis, dorsal palm on metacarpals, ventral forearm, dorsal aspect of upper arm, and dorsal aspect of the neck near the C6 and C7 vertebrae. A total of six human subjects (three males, three females, ages 20-36), participated in the study. Once attached to the skin, the transducer underwent a transition to the compressed and relaxed modes to eliminate any unintended friction between the armature and holder that may have occurred during installation. Following a 1 -minute break to allow for complete relaxation of the skin, the minimum currents required to induce the compressed and relaxed states of the transducer were measured using 500- millisecond pulses. Current-controlled stimuli were driven in the range of -450 to 450 mA in increments of 50 mA (2602 System SourceMeter, Keithley). Two different harness heights (0 mm and 0.5 mm) were employed during the testing process, providing effective indentations of 2.1 mm and 1.6 mm respectively.

[0317] Using a similar protocol, the minimum input energy for transitions was evaluated for a subset of skin locations on the same six subjects (dorsal palm on adductor pollicis, dorsal palm on metacarpals, and ventral forearm). To determine the upper bound for a given skin location, the skin was preconditioned by indenting it for 30 s before each transition. To determine minimum input energy, the current magnitude was scanned between -450 to 450 mA in increments of 50 mA. For each current, the pulse duration was sequentially incremented by 100 ms (starting with 50 ms) until the transducer transitioned or until pulse duration reached 2000 ms. The input work was calculated assuming Ohmic losses and Uii = 13.39 Q (mean; 0.384 Q SD; n = 18). Tables 1-2 report the current amplitude and pulse duration combinations that yielded the minimum input energy for each condition.

[0318] EXAMPLE 7:

[0319] SPRING-MASS MODEL OF TRANSDUCER VIBRATION

[0320] An analytical model was developed to study the vibration behavior of the transducer, based on the following: mx + kx + ex = F, (1) where m is the mass of the transducer (panel f of FIG. 7). Variables k and c are the skin (or skin phantom) stiffness and damping coefficient for relaxed-state vibration, respectively, x is the indentation depth. Fis the magnetic force acting on the plunger (panel f of FIG. 7). £ is derived based on the slope of indentation curve of skin phantom and F is derived from the corresponding magnetic force to the experimentally measured vibration displacement. Because of the small vibration amplitude, an average magnetic force was used, where Fi is the average force for positive currents and F2is the average force for negative currents. Therefore, the magnetic force can be expanded into a Fourier series: where co = 2itf, and / is the excitation frequency. The steady-state solution of x is , which is the effective damping ratio. In our simulations, m = 1.1 g, k = 570 N / m, Fi = 38 mN, F2 = -24 mN, and f = 0.5.

[0321] EXAMPLE 8:

[0322] HIGH-SPEED THREE-DIMENSIONAL DIGITAL IMAGE CORRELATION

[0323] Three-dimensional (3D) digital image correlation (DIC), was implemented to accurately quantify the indentation depth and deformation fields induced by the transducer on a skin phantom. FIG. 9 shows setup details.

[0324] 3D DIC was used to measure the spatiotemporal profiles of deformation during vibrotactile stimuli. On a 45:1 PDMS phantom (E = 43 kPa), the transducer was driven with fcoii-pk = 250 mA and frequencies, 50 Hz, 100 Hz, 150 Hz, and 200 Hz (square waveform). These waveforms were applied in both the relaxed and compressed states (panels c-d of FIG. 3 and FIG. 9). Panels g-j of FIG. 9 also shows an example of full-transition vibration, produced by applying Foii-Pk = 300 mA.

[0325] In addition, 3D DIC was used to evaluate the deformation of a skin phantom (50: 1, E = 31 kPa). The full height of the stacked Kresling modules was 13.6 mm, and the lower module started in the relaxed state at a height of 5 mm (translating 2 mm to the compressed state). Panel 1 of FIG. 3 shows the deformation field of the skin phantom when the transducer is in the compressed state. A current amplitude of 7coii = 500 mA was applied for transitions to and from the compressed state (2 s and 50 ms pulse durations, respectively).

[0326] EXAMPLE 9:

[0327] EVALUATING PERCEPTION THRESHOLDS OF VIBROTACTILE STIMULUS ON HUMAN SUBJECTS

[0328] The perception threshold for vibration was measured for n = 12 subjects (six male, six female, ages 20-36) using a transducer placed on the dorsal aspect of the palm of each subject, above the adductor pollicis. Both the relaxed and compressed states were tested for four different frequencies (50, 100, 150, or 200 Hz). Each subject was instructed to provide a yes or no judgement with no repeats (two-altemative forced choice). For each condition, an adaptive staircase was carried out in eight alternating ascending and descending sequences. While ascending, the staircase would reverse when the participant reported “yes,” and, while descending, the staircase would reverse when the participant reported “no.” Two interleaved staircases were carried out for each condition, one initially descending and the other initially ascending. Amplitude step sizes of 10 mA and 25 mA were used for the relaxed and compressed vibrations respectively. Each stimulus was played for a 1-second interval. The participants were not given any visual or auditory cues from the transducer. Raw data for the experiments can be found plotted in FIGS. 17-19. For the synthesized results shown in panel e of FIG. 3 and panels a-b of FIG. 11, the thresholds of the last four sequences for each staircase were averaged.

[0329] EXAMPLE 10:

[0330] COMMERCIAL COMPARISON OF VIBROTACTILE STIMULUS ON HUMAN SUBJECTS

[0331] Our methodology for evaluating transducers against benchmark stimuli is adapted from Ref. 39. The perceived vibration of our device was evaluated by comparing it with a commercially available linear resonance actuator (LRA; VG0840001D, Vybronics). The LRA allows independent control over amplitude and frequency, making it a comparable benchmark for the vibrotactile modes of our system. This specific unit has a comparable size to ours. The vibration of our transducer was generated in two modes: compressed and relaxed. Our transducer and the LRA were attached to the left and right hands respectively, above the dorsal aspect of the adductor pollicis. The LRA (23.2 Q) was driven with an amplitude of 76 mA and frequencies spanning 50-200 Hz. Our transducer (13.39 Q) was driven at currents ranging from 50-250 mA and frequencies matching the LRA. During 5-second vibration intervals, participants (n = 12, six males, six females, ages 20-36) reported whether the vibration felt stronger on their left or right hand. The participants were not given any visual or auditory cues from the transducer. The same stimulus was then repeated, and the participants were asked to rate the intensity of the weaker hand on a scale of 0 to 10, where 10 indicates that the intensities were the same, and 0 indicates they felt no sensation. If the participant reported that the sensation was stronger on the LRA hand, the relative perception of our transducer was calculated as a percentage of their perception of the LRA: (relative perception) = 10% x (reported intensity). Meanwhile, if the participant reported that they perceived the hand with our transducer more strongly, the score was calculated as (relative perception) = 10% x (20 - (reported intensity)) (i.e., 0 corresponded to 200% while 10 corresponded to 100%). Samples marked unstable (US) in Table 5 refer to cases where the device was monostable under the given conditions or where the given current was sufficient to generate a full transition.

[0332] The significance of these results was evaluated using the one-sample t-test with equal variance assumption, given the null hypothesis that the mean is zero. The results of this statistical analysis across n = 12 subjects are given in Tables 5-6.

[0333] Table 4: Performance comparisons between wearable vibration actuator arrays.

[0334] Ref. Tethered Mechanism SizeaMax Continuous Indentation Bimodal frequency power tested (mW)

[0335] This No Bioelastic / H 7 mm x 200 134 Yes Yes wor ElectroD 7 mm k magnetic (305 mm3)

[0336] 1,2 Yes — high- Electrostatic H O.S mm x 200 200 Yes No voltage (2 kV) D 10 mm instrument (63 mm3)

[0337] Yes No No No magnetic D 18 mm (voice coil) (610 mm3) 7,8 No Electro- H 1.45 mm x 750 14 No No magnetic D 5 mm

[0338] (voice coil) (28 mm3)

[0339] 9 No Electro- H 4.2 mm x 300 115 No No magnetic L 12 mm x W 12

[0340] (voice coil) mm (605 mm3)

[0341] 10 No Electro- H 2 mm x 130c158 No No magnetic D 7 mm

[0342] (eccentric (77mm3) rotating mass)

[0343] 11 No Electro- H 2.7 mm x 130c180 No No magnetic D 8 mm

[0344] (eccentric (136 mm3) rotating mass)

[0345] “Based on dimensions without adhesive layers or supporting electronics.bSize of pneumatic pump.

[0346] “Frequency is not independently controlled from amplitude.

[0347] NA, not applicable. NR, not reported.

[0348] Table 5: Individual participant responses as part of the vibrotactile perception experiments for relaxed-state vibration (Subject 1, male, age 36; Subject 2, male, age 30; Subject 3, male, age 23; Subject 4, female, age 20; Subject 5, female, age 20; Subject 6, female, age 24; Subject 7, male, age 23; Subject 8, male, age 25; Subject 9, female, age 25; Subject 10, female, age 29; Subject 11, male, age 24; Subject 12, female, age 31). The p-value shows the t-test given the null hypothesis that the mean is zero. e 7

[0349] 100 100 50 US 100 10 40 30 20 70 80 60 US 0.00034

[0350] 750 110 90 US US 120 100 120 50 70 100 80 US <0.0001

[0351] 200 140 120 US US 160 100 130 80 100 100 80 US <0.0001

[0352] 250 140 150 US US 180 130 150 140 100 120 US US <0.0001

[0353] 100 25 10 10 0 50 0 0 0 0 0 0 0 0 0.189

[0354] 50 50 10 90 110 0 40 10 30 20 0 0 30 0 00919

[0355] 100 110 10 1 10 130 30 80 20 80 90 90 110 80 <0.0001

[0356] 150 120 50 110 US 100 120 90 100 100 100 120 US <0.0001

[0357] 200 140 100 US US 170 140 150 140 100 100 130 US <0.0001

[0358] 250 170 150 US US 180 150 160 150 120 120 130 US <0.0001

[0359] 150 25 10 10 0 10 0 0 0 0 0 0 0 0 0.0819

[0360] 50 30 10 70 70 50 40 0 60 30 0 0 10 0.00232

[0361] 100 70 50 90 100 70 60 30 80 60 50 80 60 <0.0001

[0362] 150 90 1 10 100 1 10 80 90 100 90 90 100 110 100 <0.0001

[0363] 200 100 120 110 130 100 80 100 90 100 110 100 US <0.0001

[0364] 250 130 150 120 120 110 100 120 110 110 110 100 US <0.0001

[0365] 200 25 10 10 0 0 10 0 0 0 0 0 0 0 0 0819 50 10 10 20 0 30 10 0 50 10 0 10 0 0.014

[0366] 100 10 10 30 80 40 20 20 70 30 10 90 30 0.000865

[0367] 150 20 30 70 100 80 30 30 80 40 30 90 60 <0.0001

[0368] 200 40 100 90 90 60 40 30 80 40 100 80 60 <0.0001

[0369] 250 70 110 100 1 10 90 70 50 80 70 130 100 90 <0.0001

[0370] *US, mechanical system was unstable or monostable under the given conditions.

[0371] Table 6: Individual participant responses as part of the vibrotactile perception experiments for compressed-state vibration (Subject 1, male, age 36; Subject 2, male, age 30; Subject 3, male, age 23; Subject 4, female, age 20; Subject 5, female, age 20; Subject 6, female, age 24; Subject 7, male, age 23; Subject 8, male, age 25; Subject 9, female, age 25; Subject 10, female, age 29; Subject 11, male, age 24; Subject 12, female, age 31) . The p-value shows the t-test given the null hypothesis that the mean is zero. f oii pk SI S2 S3 S4 S5 S6 S7 S8 S9 S10 Sil S12 p-value

[0372] 100 0 0 10 0 0 0 0 20 10 10 0 0 0.0538

[0373] 150 0 0 40 0 0 0 10 30 20 10 0 0 0.0418

[0374] 200 10 10 30 10 0 0 20 70 20 20 0 0 0.018

[0375] 250 20 20 40 20 10 20 50 110 30 30 0 0 0.00553

[0376] 100 25 NR NR NR NR NR NR NR NR NR NR NR NR —

[0377] 50 0 0 0 0 0 0 0 10 0 0 0 0 0 339

[0378] 100 0 0 10 0 0 0 0 80 0 10 0 0 0 234

[0379] 150 0 10 30 0 0 0 0 80 20 10 0 10 0.0708

[0380] 200 10 10 50 0 10 10 10 90 60 30 0 10 0.0126

[0381] 250 20 10 60 10 10 20 10 100 70 100 0 10 0.00743

[0382] 150 25 0 0 0 0 0 0 0 0 0 0 0 0 —

[0383] 50 0 0 30 0 0 0 0 60 0 0 0 0 0 191

[0384] 100 0 0 50 0 0 0 0 90 0 10 0 10 0 128

[0385] 150 10 10 90 0 0 10 0 90 10 10 0 10 0 0598

[0386] 200 10 10 80 30 0 20 10 100 30 50 0 10 0.00918

[0387] 250 20 20 80 30 10 30 10 100 80 50 10 10 0.00198

[0388] 200 25 NR NR NR NR NR NR NR NR NR NR NR NR —

[0389] 50 0 0 0 0 0 0 0 20 0 0 0 0 0 339

[0390] 100 0 0 30 0 0 0 0 80 0 10 0 0 0 173

[0391] 150 0 0 60 0 0 0 0 70 0 10 0 10 0.11

[0392] 200 0 0 60 0 0 10 10 90 10 20 10 10 0.0439

[0393] 250 10 10 80 0 10 20 20 80 20 30 20 10 0.0061

[0394] *NR, not recorded. EXAMPLE 11:

[0395] INFORMATION-THEORETIC ANALYSIS

[0396] The transducer was characterized according to the amount of energy required to transmit a unit of information to the skin. Putting aside aspects such as frequency of vibration and spatial pattern, the transducer can deliver as many as four distinct symbols (illustrated in FIG. 3f). These symbols of information correspond to the compressed (C), relaxed (R), compressed vibration (CV), and relaxed vibration (RV) states. The transducer expends a finite amount of energy, Ex^y, to transition between the compressed and relaxed states, but it only requires a continuous dissipation of power, Py, when it arrives in the vibration states. In the case where we can approximate that the states arise with a uniform probability distribution, we can define the energy per bit of information as where tsis the time interval between symbols, and S is the set of available states. According to the definition of information rate,b, the interval can be calculated according to ts= log2|5| / fb. Since self-transitions do not require energy to establish, we assume Ez_,x= 0 for Vx. Also, there is no work associated with a direct transition to a vibration state, Ec^cv= 0 and ER^RV= 0, and the work associated with an indirect transition follows ER^CV= ER-Cand EC^RV= EC^R. Finally, as previously stated, the compressed and relaxed states do not require continuous dissipation of energy, Pc= 0 and PR= 0. Given these parameters, the average energy per bit of information for subsets of FIG. 3f can be calculated according to

[0397] The transition energies, ER^C= 4.59 mJ and EC^R= 111 mJ, were taken from the average values reported from human measurements in Tables 1-2. The power consumption of the vibration states is based on Ohmic losses for / COii-pk = 250 mA (Pcv= 515 mW) and / Coii-Pk = 100 mA (PRV= 134 mW) in the compressed and relaxed vibration states respectively, assuming a constant direct-current resistance of / Loii = 13.39 (mean; 0.384 SD; n = 18) in the transducer.

[0398] A typical commercial vibration can also be described by Eqn. 9. For the LRA used in our perception experiments (VG0840001D, Vybronics), only having on and off states, this calculation simplifies to Fb({0N, OFF}) = PLRA / (2 > )■ Since we determined that the perception of vibration was similar for most participants between the relaxed state of our transducer and the LRA at 100 Hz (FIG. 11c) and the same power consumption, the entry for S 6 {R, RV} in FIG. 3g also reflects the characteristics of the LRA (PLRA= 134 mW).

[0399] EXAMPLE 12:

[0400] FABRICATION OF THE KIRIGAMI STRUCTURE AND ITS INTEGRATION WITH THE BISTABLE TRANSDUCER

[0401] A Kresling-inspired kirigami structure, fabricated from a series of precisely engineered folds and configurations, can convert linear motion into torsional motion. During the folding process, the distance, A, and rotation angle, 0, between the top and bottom panels follow the relationship, where a is the side length of the unit cell and r is the radius of the circumscribed circle of the hexagonal panel. The challenge in integrating a Kresling structure with our bistable, linear actuator, is that the internal space undergoes significant compression during the folding process, leading to collision, panels a-f of FIG. 10 and their legends detail the process of accommodating the transducer within the kirigami structure using a split-crease design.

[0402] For a Kresling module to transmit the linear motion of the bistable transducer into rotation of the hexagonal panels, rotation between the core and armature needs to be coupled, panels f-k of FIG. 12 discuss how this can be achieved in a one-tiered structure using a physical limiter. Meanwhile, as depicted in panel g of FIG. 10, the two-tiered counter-rotating structure couples with rotation of the core and armature without the need for such a limiter. In this design, the middle panel is created by attaching the bottom panel of the upper module to the top panel of the lower module. The flat surface of the solenoidal core is affixed to the middle panel, and the upper surface of the armature is bonded to the top panel. In this structure, the permanent magnetic field of the armature was enhanced by adding a larger neodymium magnet (7 mm diameter, 1 mm thickness). Controlled by the transducer, this integrated device enables transition between the relaxed and compressed states. The contacting elements of the integrated device (as shown in panel h of FIG. 10) can be attached to the skin surface using double-sided tape (3M 55236).

[0403] The kirigami panels have a three-layer structure, as shown in panels i-j of FIG. 10. These layers include a central PET plastic sheet (0.2 mm thick) as well as upper and lower layers of PU thin-film adhesive tape (0.1 mm thick). A commercial cutting machine (Silhouette Cameo 4) was used to cut the PET plastic sheet according to the designated pattern. Subsequently, PU thin film adhesive tape was applied to the surfaces of the cut plastic units, obtaining the required flat kirigami panels for constructing the 3D kirigami structure, as illustrated in panel k of FIG. 10. Finally, oily glue was used to attach the taped panels to the hexagonal panels, completing the fabrication of the 3D kirigami structures, as shown in panel 1 of FIG. 10.

[0404] EXAMPLE 13:

[0405] EVALUATION OF THE PERCEPTION OF SKIN TORSION ON HUMAN SUBJECTS

[0406] In the exemplary study, a total of 14 participants (8 males, 6 females, ages 23-31) were recruited. The experimental setup featured an adjustable device capable of simultaneous and independent adjustment of both height and two nested angles. This apparatus was complemented by an arm support, a wrist support, and a laptop used for controlling the adjustable device. The ends of the double-layer stepper motor shafts of the adjustable device were affixed with a ring and a disk, both of which matched in sizes and materials with the bottom ring and disk of the integrated transducer. Throughout the experimental procedure, the ring and disk were securely attached to each participant’s forearm using double-sided adhesives (3M 55236). The participants were not given any visual or auditory cues from the transducer.

[0407] We executed this study in four experimental modules, with three sets of rotation angleindentation combination for each module. The ranges for all modules were based deformations evaluated from DIC results (panel i of FIG. 3). For Module 1, only the ring rotates (angles, 0.33°, 0.66°, and 1°) with a constant indentation depth of 0.2 mm. Module 2.1 involves the exclusive rotation of the disk at angles of 5°, 10°, and 15°, maintaining a constant indentation depth of 0 mm. For Module 2.2, the disk again rotates at angles of 5°, 10°, and 15°, along with a uniform - 0.4 mm indentation depth. For Module 3, simultaneous rotations of both the ring and the disk were driven in angle combinations of (0.33°, 5°), (0.66°, 10°), and (1°, 15°) with 0.2 mm and - 0.4 mm indentation depths for the ring and disk respectively. After experiencing each set of angle-indentation conditions five times, participants were asked to rate their perceived perceptual intensity on a 7-point scale, ranging from 1 to 7. Results are reported in panel m of FIG. 3, panels d-g of FIG. 11, FIG. 20, and Tables 7-10.

[0408] Table 7: Perceived intensities (as defined in Methods) under different rotation angles of the ring (indentation: 0.2 mm; Subject 1, male, age 27; Subject 2, male, age 29; Subject 3, male, age 29; Subject 4, male, age 29; Subject 5, male, age 27; Subject 6, female, age 29; Subject 7, male, age 24; Subject 8, male, age 23; Subject 9, male, age 31; Subject 10, female, age 23; Subject 11, female, age 27; Subject 12, female, age 23; Subject 13, female, age 27; Subject 14, female, age 25).

[0409] Module 1 (ring)

[0410] Table 8: Perceived intensities (as defined in Methods) under different rotation angles of the disk (indentation: 0 mm; Subject 1, male, age 27; Subject 2, male, age 29; Subject 3, male, age 29;

[0411] Subject 4, male, age 29; Subject 5, male, age 27; Subject 6, female, age 29; Subject 7, male, age 24; Subject 8, male, age 23; Subject 9, male, age 31; Subject 10, female, age 23; Subject 11, female, age 27; Subject 12, female, age 23; Subject 13, female, age 27; Subject 14, female, age 25).

[0412] Module 2.1 (disk)

[0413]

[0414] Table 9: Perceived intensities (as defined in Methods) under different rotation angles of the disk (indentation: -0.4 mm; Subject 1, male, age 27; Subject 2, male, age 29; Subject 3, male, age 29; Subject 4, male, age 29; Subject 5, male, age 27; Subject 6, female, age 29; Subject 7, male, age 24; Subject 8, male, age 23; Subject 9, male, age 31; Subject 10, female, age 23; Subject 11, female, age 27; Subject 12, female, age 23; Subject 13, female, age 27; Subject 14, female, age 25).

[0415] Module 2.2 (disk)

[0416] Table 10: Perceived intensities (as defined in Methods) under different rotation angles of the ring (indentation: 0.2 mm) and disk (indentation: -0.4 mm; Subject 1, male, age 27; Subject 2, male, age 29; Subject 3, male, age 29; Subject 4, male, age 29; Subject 5, male, age 27; Subject 6, female, age 29; Subject 7, male, age 24; Subject 8, male, age 23; Subject 9, male, age 31; Subject 10, female, age 23; Subject 11, female, age 27; Subject 12, female, age 23; Subject 13, female, age 27; Subject 14, female, age 25).

[0417] Module 3 (ring & disk)

[0418] A non-parametric analysis method, the Kruskal-Wallis Test was used to assess differences among the three groups within each module. The relevant test results are presented in Table 11. In addition, we conducted a post-hoc analysis among the same groups using the Dunn Test. This analysis method allowed us to determine which specific pairwise comparisons among the groups exhibited significant differences (see Table 11). Notably, the %2values obtained from the Dunn test align with the Kruskal-Wallis %2values, affirming the reliability of the Dunn test. To control the error rate, the p-values were adjusted using the Bonferroni method. To assess the difference in indentation at two distinct levels (0 mm and -0.4 mm) across three different rotation angles (5°, 10°, and 15°), a paired t-test was conducted to compare the means of Modules 2.1 and 2.2. The statistical results are detailed in Table 12. Finally, we adopted the Spearman rank correlation coefficient to evaluate monotonicity, with results summarized in Table 13.

[0419] Table 11: Extended statistical analysis of the torsion perception experiments using the Kruskal- Wallis Test and Dunn Test. Dunn Test (Bonferroni Correction)

[0420] Table 12: Statistical analysis of the torsion perception experiments using paired t-test.

[0421] Table 13: Results of the Spearman's rank correlation (p) coefficient analysis for torsion perception experiments.

[0422] EXAMPLE 14:

[0423] COMPARING THE PERCEPTION OF SKIN TORSION AND INDENTATION ON HUMAN SUBJECTS

[0424] In this exemplary study, a total of 15 healthy participants (7 males, 8 females, ages 23-31 years) were recruited. Two two-tiered torsion units (A and D) and two indentation actuators (B and C) were affixed to the left forearm of each participant (panels h-i of FIG. 11). To avoid perception based on actuator location, the indentation and torsion units were alternately positioned at close distances (1 cm). Each stimulus consisted of a single forward and reverse transition within 100 ms. The participants were not given any visual or auditory cues from the transducer. Stimuli from each of the four actuators (illustrated in panels h-i of FIG. 11) were presented randomly n = 10 times, and participants reported whether they perceived indentation or vibration. Raw data and results can be found in Table 14 and panel i of FIG. 11 respectively.

[0425] Table 14: Number of accurate discriminations between indentation and torsion, individual results for 15 healthy participants (10 repeated measures; Subject 1, female, age 26; Subject 2, female, age 27; Subject 3, female, age 27; Subject 4, female, age 25; Subject 5, male, age 31; Subject 6, male, age 27; Subject 7, male, age 29; Subject 8, male, age 29; Subject 9, female, age 23; Subject 10, male, age 26; Subject 11, female, age 23; Subject 12, male, age 29; Subject 13, male, age 24; Subject 14, female, age 25; Subject 15, female, age 29).

[0426] EXAMPLE 15: COMPARING THE PERCEPTION OF SKIN TORSION AT MULTIPLE LOCATIONS ON HUMAN SUBJECTS

[0427] This study involved 12 healthy participants (7 males, 5 females, ages 23-31). Three two- tiered torsion units were mounted on the left forearm of each participant, with locations labelled as A, D, and E in panels h-i of FIG. 11. Each stimulus consisted of a single forward and reverse transition within 100 ms. The participants were not given any visual or auditory cues from the transducer. Four patterns of simultaneous stimuli, illustrated in panels h-j of FIG. 11, were presented randomly n = 10 times, and participants reported which pattern they perceived. Individual results are shown in FIG. 21 and Table 15. Summarized results are reported in panel j of FIG. 11.

[0428] Table 15: Number of accurate discriminations between patterns of torsion, individual results for 12 healthy participants (10 repeated measures; Subject 1, female, age 27; Subject 2, male, age 31; Subject 3, male, age 27; Subject 4, male, age 29; Subject 5, male, age 29; Subject 6, female, age 23; Subject 7, male, age 26; Subject 8, female, age 23; Subject 9, male, age 29; Subject 10, male, age 24; Subject 11, female, age 25; Subject 12, female, age 29).

[0429] EXAMPLE 16:

[0430] ARRAY AND CONTROLLER FABRICATION

[0431] The driving electronics for the haptic device were mounted and soldered to a flexible printed circuit board (fPCB; PCBWay). The operation of the board was controlled with a Bluetooth 5.0 controller (ISP 1807, Insight SIP) integrated with the nRF52840 System-on-Chip (Nordic Semiconductor) and a built-in antenna. The device was powered by a rechargeable, 500- mAhr lithium-ion battery (LP802036JU, Jauch Quartz). The power management comprised a 5.1 V DC DC boost converter (TPS61235, Texas Instruments) for driving the transducers and a low- dropout regulator (TPS7A0231, Texas Instruments) for logic-level power. A 500-mF supercapacitor was used to buffer the output of the 5.1 V boost converter (EDLC371420, TDK). An independent H-bridge (DRV8837, Texas Instruments) was used to drive each transducer with the 5.1 V power supply. The logic input for each H-bridge was delivered from GPIO expanders (TCA9555, Texas Instruments) which, in turn, communicated with the controller with a serial two-wire interface (TWI) line. Inductance measurements were performed using a dedicated integrated circuit (LDC1101, Texas Instruments), which communicated with the controller with a serial peripheral interface (SPI) line. Analog demultiplexers (MAX4691EGE+, Analog Devices) were used to demultiplex the input from each transducer into the inductance measurement unit.

[0432] Each transducer was configured as a modular unit that could be incorporated into a hexagonal tiling of self-similar units. Each element was independently addressed from exposed contacts on the exterior tiles of the 19-element hexagonal grid. To route the driving signals to interior elements of the array, the embedded interconnects of each element were configured so that traversing signals would reach the correct elements by soldering each identical element at prescribed rotations of 120°. The orientation diagram is illustrated in panel d of FIG. 6.

[0433] EXAMPLE 17:

[0434] CYCLIC MECHANICAL TESTING OF THE HAPTIC ARRAY

[0435] An array of 19 actuators with 1-2 Q coils was affixed to an elastomeric substrate (Ecoflex). The substrate's two ends were secured to a motorized stretching machine. Device bending was induced by narrowing the gap between the clamps, calculating the bending radius from a side view of the device and substrate (panel h of FIG. 6). Stretching (18%) was achieved by widening the gap between the clamps, calculating relative stretching based on the distance between actuators (panel j of FIG. 6). Resistance measurements were performed to detect opencircuits from interconnect damage after 1000 cycles of bending and 1000 cycles of stretching.

[0436] EXAMPLE 18:

[0437] VISUAL SENSORY SUBSTITUTION SYSTEM AND TASK

[0438] For the visual sensory substitution system, as shown in FIG. 4f, FIG. 13a, the user has the haptic device mounted on the back of their neck, and they hold the smartphone (iPhone 12 Pro, Apple) in their hand. LiDAR and IMU sensors anchor six virtual detection windows to the room, which remain fixed in space at a distance defined by the user (2.5 m, for this task) even when the phone moves (top left, top middle, top right, bottom left, bottom middle, and bottom right). When an object crosses the boundary of the window, it sends a cue to the haptic device corresponding to the location of that window. The haptic cues render as a wave of indentation that travels between the bottom and top in the left, middle, or right columns of the haptic array. To indicate the bottom row, the wave starts at the top and ends at the bottom. To indicate the top row, the wave starts at the bottom and ends at the top.

[0439] We evaluated this task on healthy, normal individuals with blindfolds (n = 7, four males, three females, ages 19-37). In the experiment, each window was triggered manually by the investigator presenting a ball through the respective location. The task was carried out in three phases, with the first two being part of the training. The first part of the training, which lasted 5- 10 minutes, included an introduction to the system and a short period of exploration during which time the participant could direct cues. In the second phase of training, the participants were asked to indicate the location of perceived cues while closing their eyes (10-20 minutes). Four repeats of each cue were presented randomly. During this phase, the participants were given verbal feedback about the accuracy of their answers. In the last phase, in which we recorded answers as part of our experiment, we asked the participants to close their eyes and wear a blindfold. Along with the participants being blindfolded, they were given earplugs (SA-7-5, Lysian) and noise-cancelling headphones (WH-CH720N, Sony). The headphones continuously played pink noise during the experiments. The participants were given cues randomly in each of the six locations. Each of the locations was repeated six times in random order. The significance of the accuracy of each participant ( / ? = 7) was evaluated using the Wilcoxon signed-rank test, given the null hypothesis that selections were made at random between six choices (i.e., accuracy arose from a distribution with mean 16.7%). In addition, the effect size was characterized according to rank-biserial correlation, calculated from the z-statistic of the signed-rank test.

[0440] EXAMPLE 19:

[0441] BALANCE SENSORY SUBSTITUTION SYSTEM AND TASK

[0442] For the balance sensory substitution system, as illustrated in FIG. 4g, a smartphone (iPhone 12 Pro, Apple) held against the body of the subject tracks its orientation using an IMU. This data serves feedback to the haptic device, which, analogous to spirit level, renders a line of vibration that follows the postural angle of the user (panel i of FIG. 13 for feedback patterns). We evaluated this task on healthy, normal individuals (w = 10, five males, five females, ages 20-36). We used the Sharpened Romberg Test (eyes closed) to measure standing stability and postural control. As shown in panel g of FIG. 4, the participants were asked to remove their shoes and stand with two feet in a line (toe-to-heel). Their arms were crossed in front of the body, and their eyes were closed. Each patient would try to maintain their balance, and they were evaluated on the time they could stand without opening their eyes, shifting their feet, or moving their arms. After instruction on the task and devices, the participants would be allowed one trial with and without feedback. During the experiment, twenty repeated trials were recorded for each participant. To reduce fatigue, the participants were asked to sit and rest for two minutes between every four attempts. The sequence of attempts with feedback and without feedback were counterbalanced between rest intervals (see Table 16). Statistical significance for the outcomes of these experiments was evaluated by modeling the presence and absence of feedback as a factor in a repeated-measures ANOVA model (9 degrees of freedom). The balance duration, acting as the dependent variable, was transformed logarithmically to account for its right-skewed distribution. Ultimately, the p-value was determined under the null hypothesis that no differences exist in group means (FIG. 13).

[0443] Table 16: Participant balance durations as part of the Sharpened Romberg task (Subject 1, female, age 35; Subject 2, female, age 35; Subject 3, female, age 20; Subject 4, female, age 29; Subject 5, female, age 32; Subject 6, male, age 36; Subject 7, male, age 20; Subject 8, male, age 34; Subject 9, male, age 33; Subject 10, male, age 24).

[0444] SI S2 S3 S4 S5 S6 S7 S8 S9 S10 B 309.53 34.52 35.17 67.02 120.48 33.61 7.1 10.94 15.87

[0445] A 78.34 20.33 62.48 20.03 110.13 36 23.97 48.48 7 96 11.21

[0446] Rep. B 12.1 79.13 27.1 44.36 65.12 15.67 1 1.33 60.77 11.15 12.1

[0447] 4A 10.71 88.09 23.64 49.16 6.5 18.53 31.81 14.79 36.25 10.71

[0448] A 18.38 54.44 24.55 18.18 19.39 14.62 49 3 10.81 20.23 18.38

[0449] B 39.42 315.82 89.95 122.09 21.44 6.61 51.32 31.56 35.58 39.42

[0450] Relative 136.6% 77.1% 177.1% 142.9% 147.2% 234.3% -32.8% -22.8% 260.7%, -17.3% change

[0451] Rep. A 8.41 126.96 52.27 77.12 17.6 24.36 32.48 19.53 17.24 8.41

[0452] 3B 36.58 229.1 72.79 49.2 17.17 4.5 87 35.34 54.76 36.58

[0453] B 36.12 38.16 122.42 260.39 63.15 13.22 40 9 54.37 8 71 36.12

[0454] A 9.18 40.86 39.7 155.61 12.97 6.02 20.17 19.83 21.31 9.18

[0455] Relative 77.7% 313.3% 59.3% 112.3% 33% 162.7% -41.7%, 142.9% 127.9%, 64.6% change

[0456] *A indicates an attempt without feedback, and B indicates an attempt with feedback.

[0457] **Relative change in balance duration with feedback relative to balance duration without feedback. The quantity was calculated from the mean values from the two conditions in each repetition.

[0458] EXAMPLE 20:

[0459] FOOT STRIKE SENSORY SUBSTITUTION SYSTEM AND TASK

[0460] For the foot strike sensory substitution system, as illustrated in panel h of FIG. 4, the user wears an external IMU (AirPods, Apple) in their right shoe and holds a smartphone (iPhone 12 Pro, Apple) in their hand. The smartphone uses LiDAR to track the orientation of an adjacent surface and the external IMU to track foot orientation. The haptic device receives these streams of information and renders vibration in the direction of error between the foot and surface (panel a of FIG. 14).

[0461] The foot strike task was aimed at testing whether the system could be used to help a participant match their foot strike orientation without receiving any other external feedback. We tested the system on healthy normal individuals with their eyes closed (n = 3, two males, one female, ages 21-37). As shown in panel h of FIG. 4 and panel a of FIG. 14, a variable surface would be presented in front of the participant at fixed orientations of ( / , (p ) 6 {(0°, 0°), (15°, 60°), (15°, -60°), (30°, 0°)} where i > is the pitch of the surface and (p is the yaw (FIG. 14a for reference frame for pitch and yaw). During the experiment, the LiDAR modality on the smartphone was used to evaluate the orientation of the surface and send feedback to the haptic device. Feedback in the form of vibration would be provided to the haptic device, and the location of vibration would indicate where error exists between the orientations of the surface and foot (panel b of FIG. 14). Upon contact with the surface, the haptic device would deliver indentation in the pattern detected upon contact. The participants were trained on the system for 25-40 minutes, and then they were asked to match their foot to the presented surface by stepping forward onto the surface. Error was measured as the angle between the foot and the surface. The task was carried out in five phases, with the first two being part of the training. The first part of the training, which lasted 5-10 minutes, included an introduction to the system and a short period of exploration during which time the participant could direct cues. In the second phase of training, the participants were asked to match the location of perceived cues while closing their eyes (20-30 minutes). Repeats of each cue were presented randomly. During this phase, the participants were given feedback about the accuracy of their answers. In the last three phases, we recorded the error for each cue as part of 60 trials (20 trials per phase). In each experimental phase, the participant was presented with each of the fixed orientations randomly until they completed 5 trials for each surface. During each phase, the participant was asked to attempt to complete the motion within designated time intervals, 1.5 s, 1 s, and < 1 s progressively.

[0462] Control experiments without the haptic device were performed in subsequent sessions for each subject. The structure of these sessions, including training parameters, mirrored the feedback group. Control conditions were tested for 20 repeat trials, including 5 presentations of each surface orientation (see Table 18).

[0463] The actual step intervals are reported for each participant in Table 17. The significance of these results was evaluated for each participant using the Wilcoxon signed-rank test, given the null hypothesis that the feedback results arise from a distribution with the same mean as the control conditions, n = 3. The effect size was characterized according to rank-biserial correlation, calculated from the z-statistic of the signed-rank test. See panels c-e of FIG. 14 for individual statistical results.

[0464] Table 17: Participant error measured during the foot strike task with feedback. In Phases 1-3, Subject 1 (male, age 37) had step intervals 2.10 ± 1.04 s, 1.68 ± 0.481 s, and 1.07 ± 0.257 s respectively. In Phases 1-3, Subject 2 (female, age 35) had step intervals 1.72 ± 0.274 s, 1.44 ± 0.226 s, and 0.901 ± 0.127 s respectively. In Phases 1-3, Subject 3 (male, age 21) had step intervals 1.65 ± 0.459 s, 1.38 ± 0.321 s, and 0.964 ± 0.276 s respectively.

[0465] Subject Orientation Phase Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Mean Mean ±

[0466] 1 (15°, -60°) 1 5 50 5.01 7.03 6.45 — 5.99 8.09 ±

[0467] 2 2 54 3.79 7.58 8.91 — 5.71 3.95 3 13.39 1068 9.07 17.11 — 12.56

[0468] 3 679 8.33 9.51 4.69 4.45 6.75

[0469] 3 (15° -60°) 1 1295 489 520 395 630 666

[0470] (15°, 60°) 1 902 1735 3.97 3.38 7.98 8.34

[0471] 2 11.42 5.11 13.42 12.83 18.66 12.29 '' ■;,±

[0472] 3 17.90 1007 13.07 5.40 3.84 10.06

[0473] Table 18: Participant error measured during the foot strike task without feedback (control; Subject 1, male, age 37; Subject 2, female, age 35; Subject 3, male, age 21).

[0474] Subject Orientation (> ft ■,<[>) Trial 1 Trial! Trial 3 Trial 4 Trial 5 Mean±SD(°)

[0475] (°) (°) (°) (°) (°)

[0476] 1 (15°, -60°) 11.30 10.73 1012 14.81 18.23 13.04±307 The foregoing description of the exemplary embodiments of the invention has been presented only for the purposes of illustration and description and is not intended to be exhaustive or to limit the invention to the precise forms disclosed. Many modifications and variations are possible in light of the above teaching.

[0477] The embodiments were chosen and described in order to explain the principles of the invention and their practical application so as to enable others skilled in the art to utilize the invention and various embodiments and with various modifications as are suited to the particular use contemplated. Alternative embodiments will become apparent to those skilled in the art to which the invention pertains without departing from its spirit and scope. Accordingly, the scope of the invention is defined by the appended claims rather than the foregoing description and the exemplary embodiments described therein.

[0478] Some references, which may include patents, patent applications and various publications, are cited and discussed in the description of this invention. The citation and / or discussion of such references is provided merely to clarify the description of the invention and is not an admission that any such reference is “prior art” to the invention described herein. All references cited and discussed in this specification are incorporated herein by reference in their entireties and to the same extent as if each reference was individually incorporated by reference.

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Claims

CLAIMSWhat is claimed is:

1. A haptic actuator, comprising: a miniaturized electromechanical structure that, when interfacing with a skin of a subject through an energy-recovering mechanism, supports bistable, self-sensing modes of deformation, for delivering dynamic and / or static stimuli of indentation, torsion, and / or vibration to the skin.

2. The haptic actuator of claim 1, wherein the miniaturized electromechanical structure is a transducer and comprises a core and an armature coupled with one another, upon mechanical coupling with the skin, to form a bistable mechanism for operably storing and releasing mechanical energy in the skin between a compressed state and a relaxed state.

3. The haptic actuator of claim 2, wherein the miniaturized electromechanical structure further comprises a diaphragm that improves stability of states and enhances vibration.

4. The haptic actuator of claim 2, wherein the core comprises an electromagnetic coil embedded in a soft ferromagnetic cylinder for focusing magnetic fields along its central longitudinal axis and reducing interference between closely spaced units.

5. The haptic actuator of claim 4, wherein the core comprises an inner core; a cylindrical encasement; a bobbin placed between the inner core and the cylindrical encasement; and an electromagnetic coil wrapping on the bobbing from the bottom surface of the inner core to the opposing face of the bobbin, wherein the inner core and the cylindrical encasement are formed of a soft ferromagnetic material.

6. The haptic actuator of claim 5, wherein the soft (low-coercivity) ferromagnetic material comprises iron or other iron-containing alloys, including iron-cobalt, permalloy, and stainless steel.

7. The haptic actuator of claim 2, wherein the armature comprises a cap formed of apermanent magnetic material; a cylindrical ring formed of a nonmagnetic material including titanium, plastic, wood and / or non-magnetic stainless steel, or the soft ferromagnetic material on the permanent magnetic cap; and a rigid rod having a first end being attached to the permanent magnetic cap through the cylindrical ring, and an opposite, second end interfacing with the skin as a linear shaft that translates through the core.

8. The haptic actuator of claim 7, wherein the permanent magnetic material comprises a rare earth magnetic material including neodymium and / or Samarium-cobalt, iron alloys with high-coercivity including alnico and / or ferrite, and composites thereof.

9. The haptic actuator of claim 3, wherein the diaphragm formed of an elastomeric material is configured to enclose a top of the miniaturized electromechanical structure.

10. The haptic actuator of claim 9, wherein the elastomeric material comprises a composite of silicone-based elastomer including polydimethylsiloxane, dragonskin, ecoflex and / or silbione, and magnetic particles including iron oxide micro- particles and / or nanoparticles. Such composites include PDMS-MNP described herein.

11. The haptic actuator of claim 2, wherein the miniaturized electromechanical structure couples to the skin through an elastomeric substrate (adhesive layer) with a rigid, twistlocking harness whose height are adjustable to change an effective indentation depth of the armature.

12. The haptic actuator of claim 11, wherein the harness is provided with a spacer for changing the effective indentation depth.

13. The haptic actuator of claim 11, wherein the harness is configured to lock the vertical translation of the miniaturized electromechanical structure upon rotation, wherein a base of the harness adheres to the elastomeric substrate, which, in turn, adheres to the skin of the subject.

14. The haptic actuator of claim 13, wherein the base of the harness is reinforced with a fiberglass mesh as a composite within the elastomeric substrate, so as to reduce mechanical mismatch between the harness and the elastomeric substrate.

15. The haptic actuator of claim 11, wherein the elastomeric substrate is formed of a silicone- based elastomer.

16. The haptic actuator of any one of claims 1-15, wherein mechanical integration of the skin and bistable operation of the transducer requires that local energetic minima exist at the compressed and relaxed states, and polarization of the coil transiently induces transitions between the compressed state and the relaxed state.

17. The haptic actuator of claim 16, wherein in the compressed state, the magnetic field imposed by the permanent magnet, channeled through the armature, magnetizes the soft ferromagnetic core, wherein the strong attraction induced between these elements exceeds the reactive force imposed by the skin, thereby maintaining compression without current applied at the coil, wherein from the compressed state, driving the coil with opposite polarity to the permanent magnet substantially weakens its effect on the core, thereby allowing the skin to push the armature into the relaxed state.

18. The haptic actuator of claim 17, wherein in the relaxed state, the elasticity of the skin, along with a slight attraction to the paramagnetic / elastomeric diaphragm, prevents the armature from reverting without applied current, wherein from the relaxed state, driving the coil in alignment with the permanent magnet polarizes the armature and core, overcomes the compressive force of the skin, and drives the armature to transition back into the compressed state.

19. The haptic actuator of any one of claims 1-18, wherein the haptic actuator is operated with an inductance- and resonance-based self-sensing mechanism that operably tailors input power on demand.

20. The haptic actuator of any one of claims 1-18, wherein the haptic actuator is operatedwith a spring-mass mechanism that serves as the basis for delivering vibrotactile feedback.

21. The haptic actuator of claim 20, wherein applying an alternating current at sub-transition amplitude vibrates the armature, creating a small perturbation around the initial state of the transducer, whereby the transducer can bias its modes of vibration to the static position of either the relaxed or compressed states depending on its history.

22. The haptic actuator of claim 21, wherein the miniaturized electromechanical structure further comprises an elastomeric disk sandwiched between the armature and the core.

23. The haptic actuator of claim 22, wherein in the relaxed state, the spring arises from the elasticities of the skin and the paramagnetic / elastomeric diaphragm, which interact with the armature on opposing ends, and in the compressed state, the spring arises from the elasticities of the elastomeric disk sandwiched between the armature and the core.

24. The haptic actuator of any one of claims 1-23, wherein the transducer further comprises a transmission structure that accommodates the miniaturized electromechanical structure within its internal volume and transmits the normal-directed force of the armature into tangential forces applied parallel to the surface of the skin.

25. The haptic actuator of claim 24, wherein the transmission structure comprises a Kresling pattern-inspired structure formed from patterning, bonding, and creasing of stiff plastic panels into a thin-walled hexagonal tube, wherein, upon linear compression, the hexagonal tube twist-buckles into a truss of supporting beams.

26. The haptic actuator of claim 25, wherein the transmission structure comprises at least one tier, wherein as with normal-force operation, the transducer maintains two stable states balanced by the elastic force of the skin and the holding force of the permanent magnet.

27. The haptic actuator of claim 25, wherein the transmission structure comprises two counter-rotating tiers with opposite chiralities having a top platform, a bottom platformand a middle platform disposed therebetween, which allows low-friction rotational coupling between two contacting elements adhered to the skin.

28. The haptic actuator of claim 27, wherein the bottom platform couples to the skin as a ring positioned concentrically around the armature, the middle platform is affixed to a flat surface of the core, and the top platform is fixed to the shaft of the armature and couples to the skin through its adhesion with the permanent magnet of the armature.

29. The haptic actuator of claim 28, wherein in operation, the permanent magnet within the armature, one of the adhering elements, pulls the core of the transducer towards it under its permanent magnetic field, and a longitudinal motion of the middle platform drives the top and bottom platforms to rotate in opposite directions, whereby operation of the transducer renders twisting motions in the armature and ring in opposite directions.

30. A haptic actuating system, comprising: a plurality of haptic actuators arranged in an array, wherein each actuator is according to any one of claims 1-29; and a controller for operating the plurality of haptic actuators.

31. The haptic actuating system of claim 30, wherein the controller is integrated with a System-on-Chip (SoC) and a built-in antenna.

32. The haptic actuating system of claim 31, wherein the SoC comprises at least one of a near- field communication (NFC) interface, a Bluetooth® interface, and a Wi-Fi® interface.

33. The haptic actuating system of claim 30, further comprising: driving electronics and sensing electronics electrically coupled between the plurality of haptic actuators and the controller; and flexible interconnects electrically connecting to the plurality of haptic actuators and the controller.

34. The haptic actuating system of claim 33, wherein the flexible interconnects comprise at least one of serpentine interconnects and zigzag interconnects.

35. The haptic actuating system of claim 33, further comprising a power module for supplying power to the entire system.

36. The haptic actuating system of claim 35, wherein the power module comprises a battery; and a power management unit comprising a boost converter for driving the plurality of haptic actuators, and a low-dropout regulator for logic-level power.

37. The haptic actuating system of claim 36, wherein the driving electronics comprises an H- bridge for driving each haptic actuator with the power module, and a multiplexer for multiplexing the driving signals from the controller into the H-bridge.

38. The haptic actuating system of claim 37, wherein the driving electronics further comprises a supercapacitor for buffering the output of the boost converter.

39. The haptic actuating system of claim 33, wherein the sensing electronics comprises an inductance measurement unit; and a demultiplexer for demultiplexing the input from each haptic actuator into the inductance measurement unit.

40. The haptic actuating system of claim 39, wherein each haptic actuator itself serves as a sensor for the longitudinal position of its armature, and the inductance measurement unit captures the resonance frequency of each haptic actuator and reports to the controller whether it exists in the relaxed state or the compressed state.

41. The haptic actuating system of claim 33, wherein each haptic actuator is configured as a modular unit that is incorporated into a hexagonal tiling of self-similar units, wherein each unit is independently addressed from exposed contacts on the exterior tiles of the hexagonal grid.

42. The haptic actuating system of claim 40, wherein the flexible interconnects for each unitare configured so that traversing signals reach the correct units by soldering each identical unit at prescribed rotations of 120°, so as to route the driving signals to interior units of the array individually.

43. The haptic actuating system of claim 40, wherein each haptic actuator is pitched at about 1.3 cm, which is within a spatial acuity of the skin.

44. The haptic actuating system of any one of claims 30-43, further comprising an outer encapsulation layer formed of a silicone-based elastomer encapsulating the haptic actuating system.

45. The haptic actuating system of claim 44, being a wireless, skin-conformable haptic interface, which serves as a high-density channel capable of rendering input from a smart device comprising a 3D scanner including LiDAR and / or binocular cameras and inertial measurement unit (IMU) sensors, which operably track the position and orientation of the subject and environment.

46. The haptic actuating system of claim 45, wherein the wireless, skin-conformable haptic interface has a flexible reconfiguration of the array while tolerating repeated mechanical bending and stretching.

47. The haptic actuating system of claim 45, wherein the wireless, skin-conformable haptic interface is usable for sensory substitution, wherein smart device based sensory cues derived from 3D scanning and inertial measurements yield perceptions that improve performance in models of visual, vestibular, and proprioceptive sensory substitution tasks.

48. The haptic actuating system of claim 47, wherein the haptic actuating system operably receives the sensory information over wireless communications from the smart device and renders feedback to the subject as replacement or augmentation of their sensory abilities.

49. The haptic actuating system of claim 48, wherein the wireless, skin-conformable haptic interface is operated to provide an intuitive frame of reference for virtual objects that follow the orientation of the body, as so to help individuals detect obstacles in their path without vision being necessary.

50. The haptic actuating system of claim 48, wherein the wireless, skin-conformable haptic interface is operated to provide feedback during standing balance as a means of enhancing postural stability.

51. The haptic actuating system of claim 48, wherein the wireless, skin-conformable haptic interface is operated to guide foot orientation in individuals with impaired proprioceptive control.

52. The haptic actuating system of claim 48, wherein the wireless, skin-conformable haptic interface is operated to guide a user’s hand towards target objects without vision being necessary.

53. A wearable haptic feedback system, comprising:A plurality of bistable electromechanical transducers, each transducer being configured to be mechanically coupled to a user’s skin and including a ferromagnetic core, a movable armature having a permanent magnet, and an elastomeric diaphragm configured to deform the skin, wherein each transducer and the skin collectively form a bistable mechanical system having compressed and relaxed states defined by stored elastic energy of the skin; a control circuit configured to drive the transducer between the bistable states by transient current pulses and to detect its state via inductance-based self-sensing; and a wireless interface configured to receive sensory or positional input and to command corresponding tactile feedback patterns through the array of transducers.

54. The haptic feedback system of claim 53, wherein the bistable states are maintained without continuous power consumption.

55. The haptic feedback system of claim 53, wherein each transducer transitions between states using opposite polarity drive currents.

56. The haptic feedback system of claim 53, wherein the inductance-based sensing circuit measures resonance frequency to determine transducer position.

57. The haptic feedback system of claim 53, wherein the elastomeric diaphragm comprises a composite of poly dimethyl siloxane (PDMS) and magnetic nanopowder.

58. The haptic feedback system of claim 53, wherein the armature includes a titanium shaft that directly couples mechanical displacement into the skin.

59. The haptic feedback system of claim 53, further comprising a kirigami transmission structure configured to convert linear motion of the armature into tangential shear deformation of the skin.

60. The haptic feedback system of claim 59, wherein the kirigami structure comprises counter-rotating tiers arranged in opposite chiralities.

61. The haptic feedback system of claim 53, wherein each transducer is arranged in a modular, hexagonal array with flexible serpentine interconnects.

62. The haptic feedback system of claim 53, wherein the control circuit includes a Bluetooth low-energy controller and a rechargeable power source.

63. The haptic feedback system of claim 53, wherein the wireless interface receives sensory data from a smart device, including LiDAR-based 3D scanning or inertial measurements.

64. The haptic feedback system of claim 53, wherein the transducer delivers both static indentation and dynamic vibration stimuli.

65. The haptic feedback system of claim 64, wherein the vibration and indentation areindependently controllable to engage distinct classes of mechanoreceptors.

66. The haptic feedback system of claim 53, wherein the transducer array provides sensory substitution feedback corresponding to spatial or balance cues.

67. The haptic feedback system of claim 66, wherein the feedback assists a user in detecting environmental obstacles or maintaining postural stability.

68. The haptic feedback system of claim 53, wherein the bistable structure employs skin elasticity to recover mechanical energy upon state transition.

69. The haptic feedback system of claim 53, wherein the transducer housing and harness are configured for adjustable indentation depth.

70. The haptic feedback system of claim 53, wherein the bistable haptic unit provides multimodal feedback including indentation, torsion, and vibration for sensory substitution.

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