Elastic actuator device and system

Abstract

In some aspects, disclosed is an elastic actuator including an output shaft, at least one output rotor comprising at least one slot arranged in an arc formation on the output rotor, wherein the at least one output rotor is coaxially and rigidly mounted on the output shaft, an input member interfaced with the at least one output rotor comprising at least one spring chamber, wherein the input member is configured to rotate relative to the at least one output shaft, at least one compression spring positioned at least partially within the at least one slot of the at least one output rotor and the at least one spring chamber of the input member. Further disclosed is an exoskeleton including at least one disclosed elastic actuator, or an orthosis including at least one disclosed elastic actuator.

Description

[0001] Attorney Docket No.: 206572-0008-00WO

[0002] ELASTIC ACTUATOR DEVICE AND SYSTEM

[0003] CROSS-REFERENCE TO RELATED APPLICATIONS

[0004] This application claims priority to U.S. Provisional Application No. 63 / 687,983 filed on August 28, 2024, incorporated herein by reference in its entirety.

[0005] STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0006] This invention was made with government support under Award No. CMMI1944203 awarded by the National Science Foundation and Award No. W81XWH- 22-1-0193 awarded by the Department of Defense and Congressionally Directed Medical Research Programs (CDMRP). The U.S. government has certain rights in the invention.

[0007] BACKGROUND OF THE INVENTION

[0008] Series Elastic Actuators (SEAs) are commonly used in robots designed for physical Human-Robot Interactions (pHRI) including humanoid robots, service robots, and those developed for assistive and rehabilitation purposes. Key advantages of integrating an elastic element in series with the actuation system include precise control of interaction forces, backdrivability, and improved operational safety by decoupling the end effector from the motor inertia. Indeed, the elastic element enables direct measurement of the applied load by measuring the spring deflection, while the intrinsic compliance of the SEA’s elastic element ensures low system impedance across the frequency spectrum, as the closed-loop impedance of the system reduces to the passive impedance of the spring when the frequencies of the external disturbances exceed the controller bandwidth. Another advantage of SEAs is their ability to store and release energy. Prior work has demonstrated through numerical simulations and experiments that the SEA elastic element can store energy and deliver peak powers greater than the power limit of the SEA motor by a factor of 1.4. In addition, by selecting an appropriate spring rate, the energy that an actuator can deliver can be quadrupled. These properties are utilized in the design of running and bopping robots, allowing them to function with minimal energy input form the control system. On the other hand, major drawbacks of Attorney Docket No.: 206572-0008-00WO series elasticity include a reduction in force bandwidth compared to rigid actuation, and an upper boundary to the maximum stiffness that can be achieved, which is limited by the physical surfaces of the elastic element, unless advanced control methods are applied.

[0009] The elastic element is a useful component of a SEA, as it determines its range of actuation and torque resolution and affects its closed-loop bandwidth. A compliant element allows for accurate torque feedback from displacement measurements. However, higher compliance necessitates larger spring deformations to achieve large torques, such as those required in rehabilitation and assistive robots. Therefore, designing an elastic element requires a trade-off between compliance and deformation range and designing compact and lightweight SEA with high torque capabilities remains a challenge.

[0010] The elastic elements in rotary SEA designs can be classified into two broad categories: those with linear springs and those having torsional springs. The first category employs arrangements of compression springs or tension springs. Linear compression springs are often arranged tangentially around a circular frame. This configuration allows for a reduced factor but limits the deformation range of the spring element and results in a non-linear stiffness response. In contrast, designs that implement linear tension springs achieve a good linearity response at the expense of a reduced torque capacity (e.g., 8 Nm in one design and 11.3 Nm for another design, despite their high stiffness values of 72.4 Nm / rad and 64.2 Nm / rad respectively). Importantly, a small deformation range implies a low torque capacity per unit of passive stiffness, i .e., for the amount of maximum stiffness it can offer, the SEA elastic element cannot generate much torque. Linear stiffness responses can also be achieved using an agnostic-antagonistic configuration of linear compression springs connected to an actuator disk by a table loop. In this design, the deformation range and passive stiffness of the elastic element can be controlled with a proper selection of actuator disk diameter, maximum spring compression, and spring stiffness. However, this arrangement often leads to bulky designs that are hardly suitable for space-constrained applications, such as wearable robots.

[0011] The second category of SEA elastic elements includes commercial torsional springs and custom torsional springs. Commercial torsional springs usually Attorney Docket No.: 206572-0008-00WO feature low stiffness, low torque capacity and large deformation range. In these designs, the torsional elastic element is typically fitted between the output shaft of a geared motor and the SEA interaction port or, less often, in between a non-backdrivable and a backdrivable geared transmission. The latter solution results in a more compact and more compliant spring of a maximum interaction torque and allows for more precise control of the generated torques. Custom torsional springs can be monolithic or two-element planar springs. Monolithic designs are machined from solid stock and feature one or more spiral arms with both ends fully constrained (i.e., fixed-fixed geometry) which favors high stiffness and low deflection. However, monolithic design prevents the spiral arms from undergoing ideal bending under load. This restricts their useful deflection range, limiting the energy capacity of the spring. Several monolithic designs have also been proposed over the last fifteen years. In one instance, a custom-made double winding elastic element was introduced, based on two previous designs. This design exhibits a higher linear loaddeflection curve, nearly zero-backlash, and good fatigue life (0.14 million cycles). The main advantage of the double winding pattern is to cancel out radial forces acting on the center of the spring during loading and unloading, thereby reducing the radial load on the SEA’s output shaft. Double winding designs often result in a nearly linear response during loading, until the windings come into contact. However, significant hysteresis is generated during the unloading phase. Additionally, modeling the load-deflection response in these designs remains a challenge, as highlighted by the significant difference between expected and measured stiffness values. Another double spiral spring with linear response was presented in a different work. In this design, the spiral arms feature cutouts to reduce the spring’s weight. However, the deformation range is still limited (10 deg.).

[0012] A triple spiral pattern was introduced previously, featuring cross-parallel connected springs with opposing spiral directions. This configuration enables higher maximum torques and a symmetric load-deflection profile. However, the stiffness varies depending upon the load. A custom spiral spring presented previously was designed to drive the actuator in a single direction. Although this unidirectional design is not suited for applications that require compliance in both directions, it is beneficial for legged robots as it offers compliance in the direction of ground impact loading and precision in returning direction. Other designs of monolithic springs emphasize linearity and torque Attorney Docket No.: 206572-0008-00WO resolution but often exhibit significant mechanical backlash and a deformation range limited to 10 degrees or less.

[0013] Two-element planar springs are targeted towards more energy efficient applications. The planar spring features one or more arms connecting a central bore to an outer rim with a ftxed-free / hinged geometry. The fixed-free boundary conditions allow for greater deflection, usually trading some of the stiffness that can be achieved with a fixed-fixed boundary condition. For example, a cantilever-based design was introduced prior, building upon a previous prototype. This design used equally spaced cantilever beams, with one end allowed to rotate at the interface with a camshaft, and the other fixed to a rim. Although this design allows for a larger deformation range (approximately 12 deg), it results in different stiffness values depending on the load direction. Its designers also reported appreciable hysteresis, possibly due to the sliding contact between the cantilever arms and the camshaft resulting in energy loss.

[0014] Thus, there is a need in the art for compact and lightweight SEA with high torque capabilities and large deformation range that minimize mechanical backlash and hysteresis. The present invention meets this need.

[0015] SUMMARY OF THE INVENTION

[0016] In some aspects, an elastic actuator includes an output shaft, at least one output rotor comprising at least one slot arranged in an arc formation on the output rotor, wherein the at least one output rotor is coaxially and rigidly mounted on the output shaft, an input member interfaced with the at least one output rotor comprising at least one spring chamber, wherein the input member is configured to rotate relative to the at least one output shaft, at least one compression spring positioned at least partially within the at least one slot of the at least one output rotor and the at least one spring chamber of the input member.

[0017] In some embodiments, the input member is an input rotor, or an input shaft. In some embodiments, the at least one output rotor comprises a number of output rotors ranging between 1 and 5. In some embodiments, the at least one compression spring comprises a number of compression springs ranging between 1 and 10. In some Attorney Docket No.: 206572-0008-00WO embodiments, the at least one spring chamber comprises a number of spring chambers ranging between 1 and 10.

[0018] In some embodiments, each slot of the at least one slot in the at least one output rotor is spaced equally in the arc formation. In some embodiments, the arc formation of the at least one slot is arranged symmetrically, or asymmetrically, on the at least one output rotor. In some embodiments, the at least one compression spring protrudes laterally from at least one side of the at least one output rotor. In some embodiments, the at least one compression spring protrudes laterally from both sides of the at least one output rotor.

[0019] In some embodiments, the at least one spring chamber comprises at least one cut out region configured as a relief for the at least one compression spring. In some embodiments, the at least one compression spring is positioned within at least one of the slot and the at least one spring chamber with preload on the spring. In some embodiments, the at least one slot and the at least one spring chamber retain the at least one compression spring when the at least one compression spring is undergoing deformation. In some embodiments, the at least one compression spring compresses to a first end or a second end of the at least one spring chamber when the input member is rotated.

[0020] In some embodiments, the at least one output rotor comprises two output rotors, wherein the input member comprises a middle portion and two lateral portions, and the at least one spring chamber is formed by aligned cut out regions in the middle and lateral portions. In some embodiments, each output rotor comprises 5 equally spaced slots and 5 compression springs. In some embodiments, the at least one compression spring comprises least one type of spring selected from the group consisting of: straight coil springs, convex springs, concave springs, linear springs, non-linear springs, variable rates springs, and progressive springs. In some embodiments, the elastic actuator includes at least one bearing with an extending inner ring positioned between at least one output shaft and at least one input member.

[0021] In some aspects, a wearable system includes at least one disclosed elastic actuator attached to an exoskeleton or orthosis, and an actuation unit connected to the at least one actuator, wherein the actuation unit rotates the input member. Attorney Docket No.: 206572-0008-00WO

[0022] In some embodiments, the actuation unit rotates the input member with one or more cables. In some embodiments, the actuation unit rotates the input member with one or more motors. In some embodiments, each output rotor comprises 5 equally spaced slots and 5 compression springs. In some embodiments, the exoskeleton or orthosis comprises one or more weights configured to generate a perturbation in the movement or gait of the subject. In some embodiments, the orthosis is an ankle-foot orthosis.

[0023] In some aspects, an exoskeleton including at least one disclosed elastic actuator. In some aspects, an orthosis including at least one disclosed elastic actuator.

[0024] BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The following detailed description of embodiments of the invention will be better understood when read in conjunction with the appended drawings. It should be understood, however, that the invention is not limited to the precise arrangements and instrumentalities of the embodiments shown in the drawings.

[0026] Figs. 1A-1E are images depicting views of an exemplary actuator (in some examples referred to as “Elastic Spinners”). Fig. 1A depicts an assembled view of an exemplary actuator, illustrating the driver cable loop terminating at the cable grip pad. Fig. IB depicts an exploded view of an exemplary actuator, showing the main components. Fig. 1C depicts a side view (left) and an enlarge view (right) of an exemplary actuator. Fig ID depicts a side view (left) front view (middle) and enlarged view (right) of an exemplary output rotor for an actuator comprising compression springs positioned in slots on the output rotor. Fig. IE is a series of images showing the actuation of an exemplary actuator with a compression spring being compressed within a spring chamber.

[0027] Fig. 2 is an image depicting front (left) and back (right) views of a prototype of an exemplary portable system (e.g., exoskeleton, referred to in some examples as “Strider”), developed to assist walking exercises in individuals with lower- limb impairments.

[0028] Fig. 3A is an image depicting a perspective view of the exemplary system (e.g., exoskeleton in some examples referred to as “Strider” or “Strider Ankle Unit”). Red Attorney Docket No.: 206572-0008-00WO parts indicate personalized components. Fig. 3B is an image depicting a side view (left) and front view (right) of an exemplary bracket and actuator for the disclosed system.

[0029] Figs. 4A & 4B are images depicting views of an exemplary actuation unit for the disclosed exoskeleton (i.e., Strider). Fig. 4A shows two rear perspective views of the actuation unit. Fig. 4B shows a front perspective view of the actuation unit.

[0030] Fig. 5 is an image showing two ankle weights (1 kg each, orange box) attached to the distal end of the exoskeleton’s shank bracket to generate a perturbation.

[0031] Fig. 6 depicts an exemplary computer architecture for a computer for practicing the various embodiments of the invention.

[0032] Fig. 7 is an image depicting a front view of an exemplary actuator, referred to in some examples as “Elastic Spinners”, featuring a small (82 mm external diameter, 18.5 mm thickness) and lightweight (0.217 kg) form factor.

[0033] Figs. 8A & 8B are images depicting a Finite Element Analysis model. Fig. 8A depicts loads applied at the output rotors. Magenta arrows indicate circumferential forces at the contact locations between each spring and the output rotors. The yellow arrow indicates the bearing load between the output shaft and the output rotor (second bearing load not shown). Fig. 8B depicts computed von Mises stress distribution on the output rotors and shaft. Locations of the computed maximum von Mises stress and maximum alternating stress amplitude (Sa) are indicated.

[0034] Fig. 9 is an image depicting a testing rig used for passive response characterization of the disclosed actuator (i.e., Elastic Spinners). The input rotor assembly was fixed to a stationary frame, and a torque sensor was connected between the output shaft of Elastic Spinners and a torque handle, which was used to manually apply a quasi-periodic load.

[0035] Figs. 10A & 10B are plots showing results for the passive stiffness response of the disclosed actuator. Fig. 10A shows the applied deflection on the spring element - periodic deflection (gray) and corresponding measured torque (blue). Fig. 10B shows the linear response (stiffness: 0.765 Nm / deg, or 43.8 Nm / rad) over a useful deformation range of ±24 deg. Attorney Docket No.: 206572-0008-00WO

[0036] Fig. 11 is an image depicting a testing rig used for dynamic response characterization of the disclosed Elastic Spinners. The elastic element was driven by a BLDC motor through a cable loop connecting a threaded motor spool to the input rotor.

[0037] Fig. 12 is a diagram depicting an exemplary cascaded torque-velocity controller.

[0038] Figs. 13A-13C are plots showing results of the closed-loop response of the disclosed actuator (e.g., SEA). Fig. 13A shows transient response to 6 Nm, 9 Nm and 12 Nm step inputs. Fig. 13B shows torque tracking of a 6 Nm sinusoidal commanded torque with frequency of 0.5 Hz and 2 Hz. Fig. 13C shows torque tracking of a 12 Nm sinusoidal commanded torque at the same two frequencies.

[0039] Figs. 14A & 14B are plots showing results for the closed-loop dynamic response of the disclosed Elastic Spinners within SEA configuration with locked output shaft. Fig. 14A shows the commanded torque Td (chirp signal, 12 Nm amplitude, 0-20 Hz frequency) and measured response Tm. Fig. 14B shows corresponding Bode plots derived by fitting experimental data to LTI transfer functions (4 poles, 2 zeros).

[0040] Figs. 15A-15C are plots showing the results for virtual stiffness rendering. Fig. 15A shows the virtual spring with null stiffness (zero impedance test). Fig. 15B shows the virtual spring with one-third of Elastic Spinners’ passive stiffness (14.33 Nm / rad). Fig. 15C shows the virtual spring with two-thirds of Elastic Spinners’ passive stiffness (28.67 Nm / rad, left of dashed vertical line) and full stiffness (43.8 Nm / rad, right of vertical dashed line).

[0041] Fig. 16 is a plot showing a comparison of deformation ranges (i.e., torque capacity per unit of passive stiffness) between Elastic Spinners and state-of-the-art devices. Blue circles represent monolithic designs, blue-green circles represent two- element planar springs, blue-red circles represent elastic elements that use linear springs, and the red circle indicates Elastic Spinners.

[0042] Fig. 17 is a flowchart illustrating the proposed design workflow to generate personalized Ankle Units.

[0043] Fig. 18A is an image depicting a side view of an exemplary SEA elastic module. Fig. 18B is a plot showing the results for the characterization of SEA passive stiffness. Attorney Docket No.: 206572-0008-00WO

[0044] Fig. 19 is a diagram depicting an exemplary torque-velocity cascaded PI controller.

[0045] Figs. 20A & 20B are plots showing the results from a torque-tracking performance test of the disclosed exoskeleton. The exoskeleton’s ankle joint was manually moved to track a sinusoidal trajectory (Fig. 20 A), and the commanded torque Td (Fig. 20B, blue line) was generated by a virtual torsional spring. The measured torque (Fig. 20B, red line) largely matched the commanded torque, indicating good tracking performances (RMSE = 0.40 Nm).

[0046] Fig. 21 is an image of a subject walking on a treadmill, with the Strider exoskeleton fitted to his left leg.

[0047] Fig. 22 is a plot showing interaction torque measured at the ankle joint during zero impedance treadmill walking at 1.3 m / s.

[0048] Fig. 23 is an image showing an exemplary Strider exoskeleton [Eraky et al., 2024] fitted on a study participant.

[0049] Fig. 24 is a diagram depicting an exemplary Strider control architecture.

[0050] Fig. 25 is a diagram depicting an experimental protocol.

[0051] Fig. 26 is a plot showing results for stride-by-stride velocity SV(i) and RL-AAN assistance level K(i) for a representative subject. Blue horizontal lines indicate average values within each walking bout.

[0052] Figs. 27A & 27B are plots showing results for a training session. Fig. 27A shows group averages of velocity errors csv across the walking bouts for fixed-K (light shades) and RL-AAN (dark shades) controllers. Fig. 27B shows group averages of assistance level K, as modulated by the RL-AAN controller, during the training sessions.

[0053] DETAILED DESCRIPTION

[0054] The following discussion omits or only briefly describes conventional features of actuator (e.g., elastic actuator, series elastic actuator) devices, systems and methods that are apparent to those skilled in the art. Those of ordinary skill in the pertinent arts may thus recognize that other elements may be desirable and / or necessary to implement the devices, systems, and / or methods described herein. It is noted that various embodiments are described in detail with reference to the drawings. Reference to Attorney Docket No.: 206572-0008-00WO these various embodiments does not limit the scope of the claims attached hereto. Additionally, any embodiments set forth in this specification are intended to be nonlimiting and merely set forth some of the many possible implementations for the appended claims. Further, particular features described herein can be used in combination with other described features in each of the various possible combinations and permutations. As such, it is understood that this detailed description is exemplary and explanatory only and is not restrictive of the broad inventive concepts upon which the embodiments disclosed herein are based.

[0055] Unless otherwise specifically defined herein, all terms are to be given their broadest reasonable interpretation. This includes meanings implied from the specification as well as meanings understood by those skilled in the art and / or as defined in dictionaries, treatises, etc.

[0056] It is noted that, as used in this specification and the appended claims, the singular forms “a,” “an,” and “the” include plural referents unless otherwise specified. The term “includes” and / or “including,” when used in this specification, specify the presence of stated features, elements, and / or components, but do not preclude the presence or addition of one or more other features, steps, operations, elements, components, and / or groups thereof.

[0057] Relative terms such as “horizontal,” “vertical,” “up,” “down,” “top,” and “bottom” as well as derivatives thereof (e.g., “horizontally,” “downwardly,” “upwardly,” etc.) should be construed to refer to the orientation as then-described or as shown in the drawing figure under discussion. These relative terms are for convenience of description and normally are not intended to require a particular orientation in actuality. Terms including “inwardly” versus “outwardly,” “longitudinal” versus “lateral,” and the like are to be interpreted relative to one another or relative to an axis of elongation, or an axis or center of rotation, as appropriate. Terms concerning attachments, coupling and the like, such as “connected” and “interconnected,” refer to a relationship wherein structures are secured or attached to one another either directly or indirectly through intervening structures, as well as both movable or rigid attachments or relationships, unless expressly described otherwise. The phrases “operatively” or “operably connected” indicates such Attorney Docket No.: 206572-0008-00WO an attachment, coupling, or connection that allows the pertinent structures to operate as intended by virtue of that relationship.

[0058] Reference throughout the specification to “one embodiment,” “an embodiment,” or “some embodiments” means that a particular feature, structure, or characteristic described in connection with at least one embodiment of the subject matter is included in at least one embodiment of the subject matter disclosed. Thus, the appearance of the phrases “in one embodiment,” “in an embodiment,” or “in some embodiments” in various places throughout the specification is not necessarily referring to the same embodiment. Further, the particular features, structures, or characteristics of “one embodiment,” “an embodiment,” or “some embodiments” may be combined in any suitable manner with each other to form additional embodiments of such combinations. It is intended that embodiments of the disclosed subject matter cover modifications and variations thereof. Terms such as “first,” “second,” “third,” etc., merely identify one of a number of portions, components, steps, operations, functions, and / or points of reference as disclosed herein, and likewise to not necessarily limit embodiments of the present disclosure to any particular configuration or orientation.

[0059] Moreover, throughout this disclosure, various aspects can be presented in a range format. It should be understood that the description in range format is merely for convenience and brevity and should not be construed as an inflexible limitation on the scope of the disclosure. Accordingly, the description of a range should be considered to have specifically disclosed all the possible subranges as well as individual numerical values within that range. For example, description of a range such as from 1 to 6 should be considered to have specifically disclosed subranges such as from 1 to 3, from 1 to 4, from 1 to 5, from 2 to 4, from 2 to 6, from 3 to 6, etc., as well as individual numbers within that range, for example, 1, 2, 2.7, 3, 4, 5, 5.3, 6, and any whole and partial increments therebetween. This applies regardless of the breadth of the range. As used herein, the term “about” in reference to a measurable value, such as an amount, a temporal duration, and the like, is meant to encompass the specified value or variations of plus or minus 20%, plus or minus 10%, plus or minus 5%, plus or minus 1%, and plus or minus 0.1% of the specified value, as such variations are appropriate and fit within the confines of a functional system. Attorney Docket No.: 206572-0008-00WO

[0060] The terms “proximal,” “distal,” “anterior,” “posterior,” “medial,” “lateral,” “superior,” and “inferior” are defined by their standard usage indicating a directional term of reference. For example, “proximal” refers to a position that is situated nearer to the center of a body or point of attachment or interest. In another example, “anterior” refers to the front of a body or structure, while “posterior” refers to the rear of a body or structure, in relation to a relative viewpoint. In another example, “medial” refers to the direction towards the midline of a body or structure, and “lateral” refers to the direction away from the midline of a body or structure. In some examples, “lateral” or “laterally” may refer to any sideways direction. In another example, “superior” refers to the top of a body or structure, while “inferior” refers to the bottom of a body or structure. It should be understood, however, that the directional term of reference may be interpreted within the context of a specific body or structure, such that a directional term referring to a location in the context of the reference body or structure may remain consistent as the orientation of the body or structure changes.

[0061] The terms “patient,” “subject,” “individual,” and the like are used interchangeably herein, and refer to any animal amenable to the systems, devices, and methods described herein. The patient, subject or individual may be a mammal, and in some instances, a human.

[0062] Disclosed herein are Elastic Spinners, a compact, bidirectional elastic element for rotary series elastic actuators (SEAs). The uniqueness of Elastic Spinners is due to the innovative layout featuring linear compression springs arranged in an arc formation on two coaxial, rigidly-connected rotors mounted on the SEA output shaft, which rotate relative to an input rotor. The input rotor features chambers that enclose the springs undergoing deformation. Unlike previous designs that use linear springs, Elastic Spinners achieve a wide deformation range (+ / - 0.42 radians or + / - 24 deg) while maintaining a high linear (R2= 0.998) response, generating 43.8 Nm / rad stiffness without appreciable mechanical backlash or hysteresis in bidirectional loading. Moreover, despite a compact (82 mm outer diameter) and lightweight (0.217 kg) design, Elastic Spinners provide a torque capacity of 18 Nm.

[0063] In some embodiments, Elastic Spinners feature a set of identical off-the- shelf linear compression springs arranged in an arc formation on rigidly connected, Attorney Docket No.: 206572-0008-00WO coaxial output rotor plates. This configuration results in a reaction torque that is linearly proportional to the deformation angle between the input and output rotors.

[0064] One distinctive feature of Elastic Spinners is the use of linear compression springs in a new arc formation, which enables a linear response within a wide passive deformation range, as well as low hysteresis, nearly null backlash, and relatively high torque capacity, in a compact and lightweight design. Indeed, the presented dual-rotor prototype can exert up to 18 Nm, offering a large passive deformation range of ±24 deg, and a small (external diameter 82 mm, thickness 18.5 mm) and lightweight (0.217 kg) form factor. The use of widely- available off-the-shelf linear compression springs help reduce the fabrication costs. Additional embodiments of Elastic Spinners are also disclosed herein with various configuration of the device offering support for a range of applications, sizes and outputs.

[0065] Referring now to Figs. 1A-1E, shown is an exemplary actuator 100 according to aspects of the present invention. In some embodiments, actuator 100 may be referred to herein as an SEA, an elastic actuator, an elastic element, a spring element, and / or "Elastic Spinners". Generally, actuator 100 comprises at least one output rotor 120 mounted on an output shaft 110 (e.g., SEA output shaft), and an input member 140 interfaced with the at least one output rotor 120, wherein the at least one output rotor 120 is configured to rotate relative to the input member 140. The bidirectional rotation and elastic actuation of actuator 100 is enabled by at least one compression spring 160 arranged in a curved or arc formation within actuator 100. For example, in some embodiments, a slot in output rotor 120 and a spring chamber input member 140 form a curved or arc formation for retaining the at least one compression spring 160. Referring to Figs. IB & 1C, in some embodiments, the compression spring 160 is retained by a slot 122 in output rotor 120 and a spring chamber 142 that is formed from cut-out regions or portions of input member 140. In some embodiments, compression spring 160 partially resides in slot 122 of output rotor 120, and spring chamber 142 of input member 140, each of which partially retain, and constrain the movement of compression spring 160. The input member 140 and output rotor 120 may rotate in either direction relative to one another, however the rotation is constrained in both directions from the compression spring 160 being compressed on either end of spring chamber 142. For example, when Attorney Docket No.: 206572-0008-00WO input member 140 is rotated clockwise relative to output rotor 120, compression spring 160 is compressed to a first end of spring chamber 142, and when rotated counterclockwise, compression spring 160 is compressed to a second end of spring chamber 142. A clockwise rotation of input member 140 relative to output rotor 120 is shown in Fig. IE. The at least one compression spring 160 may be loaded into slot 122 and / or spring chamber 142 with preload on the spring.

[0066] In some embodiments, input member 140 may comprise an input rotor and / or an input shaft. It should be appreciated that input member 140 may be driven by cables when in the form of an input rotor, and driven by a motor or other drivetrain when in the form of an input shaft. In some embodiments, input member 140 is driven with one or more cables 170 (e.g., a cable loop, or first and second cables). In some embodiment, input member 140 comprises one or more cable tracks 150 for at least partially retaining and / or guiding one or more cables 170. In some embodiments, one or more cables 170 are attached to input member 140 with an attachment point 172 (e.g., cable grip pad).

[0067] In some embodiments, input member 140 comprises an assembly or housing formed from one or more plates or portions. For example, in some embodiments, input member 140 comprises a middle plate or portion 140a, and one or more lateral plates or portions (e.g., cover plates). In some embodiments, the one or more lateral portions may comprise lateral portions 140b and 140c, as depicted in Fig. IB. In some embodiments, the at least one output rotor 120 comprises a first output rotor 120a and a second output rotor 120b. However, any number of output rotor 120 may be used with an input member 140 having any number of portions to form an actuator 100 with any number of slots, spring chambers and springs. In some embodiments, each output rotor 120 is connected by a crossmember 128 (e.g., a torque link) that extends out of actuator 100. In some embodiments, each crossmember 128 passes through a central opening 146 in middle portion 140a of input member 140. It should be appreciated that each portion of input member 140 (e.g., middle portion 140a, lateral portions 140b, 140c) may be fixedly attached via crossmembers, bolts, slots and pins, and the like. Further, input member 140 and output rotor 120 may comprise features for coaxial alignment such as slots, grooves, pins, tabs, tenon and mortise, and the like, the same features may be further used to constrain or limit the rotation of the input member relative to the output rotor 120, or vice Attorney Docket No.: 206572-0008-00WO versa. In some embodiments, actuator 100 comprises one or more sensors 180, such as a position sensor, or any of sensors 665 for computer 600 disclosed herein. In some embodiments, one or more sensors 180 are affixed to input member 140 via a sensor mount 182 and are configured to measure the position of the output shaft 110 (and output rotor 120) relative to the input member 140.

[0068] In some embodiments, the assembly of middle portion 140a and one or more lateral portions forms one or more spring chambers 142 that function to retain a compression spring 160. For example, a cut out portion 142a in middle portion 140a aligns with cut out portions 142b, 142c of one or more lateral portions 140b, 140c to form one or more spring chambers 142. In some embodiments, the one or more spring chambers 142 comprise cut out portions or slots 144 that serve as reliefs for compression springs 160. Referring again to Fig. IB, shown is an input member 140 comprising a middle portion 140a and lateral portions 140b and 140c. Each cutout portion 142a in middle portion 140a comprises an inner slot 144a that serves to separate springs positioned on either side of the spring chamber 142. The one or more lateral portions may also comprise cut out portions or slots, such as slot 144b and slot 144c that serve as reliefs for compression springs 160.

[0069] In some embodiments, actuator 100 comprises a single-rotor model (e.g., one output rotor 120), which does not require a middle portion 140a. In some embodiments, actuator 100 comprises a dual -rotor model (e.g., two output rotors 120), which incorporates a middle portion 140a. In some embodiments, actuator 100 comprise three output rotors 120, wherein an additional middle portion 140a is incorporated, that is, actuator 100 comprises first and second middle portions 140a, and in some embodiments, also comprises lateral portions 140b, 140c. In some embodiments, each output rotor 120 can accommodate up to five compression springs 160, with a minimum of one compression spring 160 fitted in each spring chamber 142. In some embodiments, if the diameter of output rotor 120 is increased, additional spring chambers 142 can be incorporated along the circumference, thereby allowing for more compression springs 160 to be fitted. It should be understood herein that the minimum number of compression springs 160 is one, which may be placed in at least one spring chamber 142, while the maximum number of compression springs 160 may correspond to the total number of Attorney Docket No.: 206572-0008-00WO available spring chamber 142 that may be fitted on output rotor 120 dependent on size and formation of the spring chamber 142.

[0070] The actuator 100 may comprise any number of output rotors 120. For example, in some embodiments, the number of output rotors 120 ranges between 1 and 10, or 1 and 20, or 1 and 30. The actuator 100 may comprise any number of compression springs 160. For example, in some embodiments, the number of compression springs 160 ranges between 1 and 10, or 1 and 20, or 1 and 30. The actuator 100 may comprise any number of spring chambers 142. It should be appreciated that the number of spring chambers 142 may be correlated to the number of compression springs 160. For example, in some embodiments, the number of spring chambers 142 ranges between 1 and 10, or 1 and 20, or 1 and 30. A preferred embodiment comprises 2 output rotors 120, each output rotor 120 configured to retain 5 compression springs 160 positioned in in arc formation around each output rotor 120. The spring chambers 142 and slots 122 may be formed in any suitable pattern, arrangement or formation for actuator 100. In some embodiments, the spring chambers 142 and / or slots 122 are formed in a concentric circle or arc formation on input member 140 and / or output rotor 120 as detailed herein. This configuration is shown to have particularly suitable characteristics for linear torquedeflection response with minimal hysteresis and backlash.

[0071] It should be appreciated that each compression spring 160 must at least partially protrude laterally from the respective slot 122 on the output rotor 120 such that a portion of spring 160 abuts or makes contact with portions of spring chamber 142. A preferred configuration is shown in the enlarged view of Fig. 1C, where spring 160 extends out laterally and equally from both sides of slot 122 of output rotor 120, and portions of spring 160 abut or make contact with faces 148a, 148b, the pair of faces formed on both the first and second ends of cut out portion 142a and cutout portion 142b. In some embodiments, slot 122 comprises a gap 124 (e.g., clearance gap) for providing clearance to at least one spring 160 (as shown in Fig. ID).

[0072] Compression spring 160 may be any suitable spring that will compress within slot 122 and spring chamber 142 when input member 140 is rotated relative to output rotor 120. For example, in some embodiments, compression spring 160 is selected Attorney Docket No.: 206572-0008-00WO from the group consisting of: straight coil springs, convex springs, concave springs, linear springs, non-linear springs, variable rates springs, and progressive springs.

[0073] Referring now to Fig. ID, shown are dimensions and arrangements for an exemplary output rotor 120. In some embodiments, slots 122 are arranged in an arc formation with a radius 190 ranging between 10 mm and 100 mm, 20 mm and 50 mm, or about 30 mm. In some embodiments, radius 190 is about 31 mm. In some embodiments, the radius 190 may be adjusted depending on the number of spring chambers 142 that can be accommodated within a single output rotor 120, wherein the radius 190 is configurable as a function of the number of spring chambers 142 accommodated along the output rotor 120 circumference, such that an increase in the number of spring chambers 142 corresponds to an increase in radius 190. In some embodiments, the output rotor 120 preferably has a radius 190 of at least about 10 mm, as smaller radii (e g., 5 mm) are not practical for accommodating the necessary bearings 126 and spring chambers 142. In some embodiments, each spring chamber 142 is configured to house a compression spring 160 having a minimum diameter of about 3 mm. In some embodiments, each slot 122 has an arc 192 ranging between 10° and 90°, 20° and 80°, 30° and 70, or about 50°. In some embodiments, arc 192 is about 52°. In some embodiments, the arc 192, or determining the length or degree of arc 192, is a function of the free length and solid length of the compression spring 160, as well as the desired spring preload. This preload is critical to maintaining each compression spring 160 in position on the output rotor 120 and to reducing backlash. In some embodiments, this relationship is expressed as Equation 5 of Example 1 below, where Sf and Si are the free length and solid length of the compression springs 160, respectively; R is radius 190, D is the compression spring diameter 196, AOmax is the maximum deflection angle of the elastic actuator 100, and £, is the preload. In some embodiments, the preload ) ranges between 1 mm and 20 mm, 1 mm and 10 mm, 1 mm and 5 mm, or 3 mm and 4 mm. In some embodiments, with the selected compression spring 160 and desired preload, the arc 192 is 52° (or about 50°). In some embodiments, a recommended range for the arc 192 is between 10° and 90°, although the exact value depends on the chosen compression spring 160 and the desired deflection angle AOmax. In some embodiments, AOmax is less than 360°, less than 290°, less than 180°, less than 90°, less than 45°, less than 30°, or less than 15°. In some Attorney Docket No.: 206572-0008-00WO embodiments, AOmax ranges between 10and 180°, 1 ° and 90°, 10and 45°, 10° and 45°, 20° and 40°, 20° and 30°, or 22° and 26°. In some embodiments, AOmax is about 1°, 2°, 3°, 4°, 5°, 6°, 7°, 8°, 9°, 10°, 11°, 12°, 13°, 14°, 15°, 16°, 17°, 18°, 19°, 20°, 21°, 22°, 23°, 24°, 25°, 26°, 27°, 28°, 29°, 30°, 31°, 32°, 33°, 34°, 35°, 36°, 37°, 38°, 39°, 40°, 41°, 42°, 43°, 44°, 45°, 46°, 47°, 48°, 49°, 50°, 51°, 52°, 53°, 54°, 55°, 56°, 57°, 58°, 59°, or about 60°.

[0074] It should be appreciated that spring chamber 142 may share the same configuration, pattern or formation on input member 140. In some embodiments, each chamber 142 and / or slot 122 is spaced equally along the arc or concentric formation. In some embodiments, each chamber 142 and / or slot 122 are arranged symmetrically, or asymmetrically along the arc or concentric formation. The output rotor 120 should be sufficiently thin (e.g., thickness 194 shown in Fig. ID) to fit within the middle of the compression springs 160, while allowing a portion of the spring sides to be seated within the spring chambers 142. At the same time, the output rotor 120 thickness 194 should be sufficient to withstand the torsional forces generated by the compression springs 160 without structural failure, yet remain smaller than the diameter 196 of the compression springs. In some embodiments, output rotor 120 has a thickness 194 ranging between 0.1 mm and 50 mm. In some embodiments, thickness 194 ranges from about 1 mm to 20 mm, or about 1 mm to 10 mm, and in a preferred embodiment the output rotor 120 has a thickness 194 of about 2.3 mm. In some embodiments, considering the output rotor thickness 194, the output rotor 120 should have a thickness 194 less than the diameter 196 of the compression spring 160. Accordingly, in some embodiments, the minimum diameter 196 of each compression spring 160 is about 3 mm, or preferably greater.

[0075] In some embodiments, each spring 160 has a diameter 196 ranging between 1 mm and 30 mm, 1 mm and 15 mm, 5 mm and 10 mm, or about 8 mm. In some embodiments, diameter 196 is about 7.62 mm. In some embodiments, actuator 100, and any components thereof (e.g., input member 140 and / or output rotor 120) may comprise a diameter ranging between 10 mm and 200 mm, 20 mm and 120 mm, 40 mm and 100 mm, or have a diameter of about 50 mm, 70 mm, 80 mm, 90 mm, or 100 mm. In some embodiments, actuator 100, and any components thereof (e.g., input member 140 and / or output rotor 120) may comprise a thickness or width ranging between 5 mm and 150 mm, Attorney Docket No.: 206572-0008-00WO

[0076] 10 mm and 100 mm, 20 mm and 60 mm, or has a thickness or width of about 10 mm, 20 mm, 30 mm, 40 mm, 50 mm, 50 mm, 60 mm, 70 mm, or 80 mm. Compression springs 160 may have any suitable spring constant (k), such a spring constant (k) ranging between 1 N / m to 5000 N / m, 100 N / m to 4000 N / m, 200 N / m to 3000 N / m, 300 N / m to 2000 N / m, 400 N / m to 1000 N / m, or has a spring constant (k) of about 100 N / m, 200 N / m, 300 N / m, 400 N / m, 500 N / m, 600 N / m, 700 N / m, 800 N / m, 900 N / m or 1000 N / m. A wide range of stiffness or spring constant may be used for compression spring 160. In some embodiments, practical values for single compression spring 160 stiffness typically range from about 10 N / m up to about 869,750 N / m.

[0077] Aspects of the present invention relate to a system comprising one or more actuators 100, in some examples referred to as an exoskeleton, “Strider”, and / or “Strider Ankle Unit”. Referring now to Figs. 2-5, shown is an exemplary system 200. Although this example system 200 shows the use of one actuator 100 used in an ankle-foot orthosis (AFO), it should be appreciated that system 200 may be configured to work with any orthosis and / or exoskeleton with any number of actuators 100. Referring in detail to Fig. 2, shown is an exemplary system 200 comprising one or more actuators 100 connected to an orthosis 210. In some embodiments, the one or more actuators 100 connect to an actuation unit 230 with one or more cables 240 (e.g., Bowden cables). In some embodiments, system 200 further comprises one or more power sources 250 (e.g., battery). Although this example shows system 200 controlling actuator 100 with a separate actuation unit 230 and / or one or more cables 240, it should be appreciated that system 200 may comprise a self-powered orthosis 210, wherein a motor directly connects to and actuates actuator 100. Further, the power source 250 may be contained within or attached to orthosis 210.

[0078] Referring now in detail to Fig. 3 A, shown is an exemplary orthosis 210 as fitted to a subject 400 comprising a bracket 212 (e.g., personalized shoe bracket), a shank 214 (e.g., 3D printed personalized shank) and one or more actuators 100. It should be understood that in this exemplary orthosis 210, input member 140 attaches to and is controlled by one or more cables 170, and the output shaft 110 and / or torque link 128 fixedly attaches to bracket 212 of orthosis 210. The bracket 112 and shank 214 may rotate, flex, move or translate relative to one another within at least one degree of Attorney Docket No.: 206572-0008-00WO freedom. In some embodiments, more than one actuator 100 enables more than one degree of freedom for orthosis 210, such as a two degree of freedom ankle orthosis. In some embodiments, bracket 212 connects to actuator 100 with a torque bracket 216 (also referred to as an additional “torque link”). Fig. 3B depicts an exemplary embodiment where output shaft 110 and torque link 128 connect to torque bracket 216. In some embodiments, bracket 212 and / or shank 214 comprise one or more sensors 218 measuring movement or rotation of the bracket 212 and / or shank 214 relative to one another, or movement of orthosis 210 relative to a position on subject 400. For example, in some embodiments, one or more sensors 218 comprise an ankle position sensor, or any sensor 665 disclosed for computer 600 discussed herein. In some embodiments, shank 214 comprises one or more cable anchoring points 220 for one or more cables 170. Further, shank 214 may comprise one or more cable sheaths 222 for one or more cables 170. Bracket 212 and / or shank 114 may comprise any number of securement or attachment means for securely affixing portions of system 200 to a subject. For example, shank 214 may comprise a strap 224 for affixing shank 214 to a portion of subject 400 (e.g., the subjects leg). Bracket 212 may be affixed to a subject’s shoes with clamps, bolts, screws, brackets, crossmembers, and the like.

[0079] Referring now to Figs. 4A & 4B, shown is an exemplary actuation unit 230. Fig. 4A shows two rear perspective views of the actuation unit. Fig. 4B shows a front perspective view of the actuation unit. In some embodiments, actuation unit 230 is used to move and control the one or more cables 170 that actuate the actuator 100. In some embodiments, actuation unit 230 comprises a housing 231 at least partially containing one or more motors 232 and one or more motor drives 234. In some embodiments, the one or more motors 232 connect to the one or more cables 170 with a spool 236 comprising a sleeve 238, that guides the wires from the spool with one or more cable aligner 240 to one or more cable tension module 242. In some embodiments, actuation unit 230 comprises one or more tensioner position adjusters 244. The one or more tensioner position adjuster 244 are used to control the tension of the one or more attached cable tension module 242. In some embodiments, each cable tension module 242 comprises one or more tensioner guard 246. In some embodiments, each cable tension module 242 comprises a track 248, wherein the tensioner adjuster 244 slides within track Attorney Docket No.: 206572-0008-00WO

[0080] 248 to adjust the cable tension module 242. In some embodiments, actuation unit 230 comprises a computer 250 (e.g., speedgoat unit) and a computer housing 252 (e.g., speedgoat unit housing). In some embodiments, actuation unit 230 comprises one or more air vent 254. In some embodiments, actuation unit comprises a cable housing 256 for the one or more cables 170 extending out from a portion of the housing 231.

[0081] In some embodiments, system 200 may comprise one or more weights 260 attached to a portion of system 200, such as attached to orthosis 210. In some embodiments, the one or more weights 260 are configured to generate a perturbation during ankle movement or gait of subject 400. In some embodiments, the one or more weights 260 are attached to bracket 212 of orthosis in a position forward of the ankle and above the foot of subject 400. Fig. 5 is an image showing two weights 260 (e.g., ankle weights, 1 kg each, orange box) attached to the distal end of bracket 212 to generate a perturbation. In some embodiments, one or more weights 260 can have any weight, such as between 0. 1 kg and 10 kg, or has a weight of about 0.5 kg, 1 kg. 1.5 kg, 2 kg, 2.5 kg, 3 kg, 3.5 kg, 4 kg, 4.5 kg or about 5 kg. Heavy loads (>5 kg) at the ankle can increase injury risk. Although sometimes used by athletes for strength training, they are typically not suitable for continuous walking. Therefore, a practical range for the weight of each weight of one or more weights 260 is between (virtually) 0 kg and 5 kg.

[0082] The development and characterization of a novel bi-directional elastic element to be used in SEAs for physical human robot interaction (pHRI) and small-scale robotic applications is detailed herein. In comparison with the state of the art, the disclosed design is more compact and lightweight. It offers high torque bandwidth and a wide deformation range while maintaining a linear response within this range. The performance / compact form blend is enabled by a novel configuration, wherein ten linear springs are arranged in an arc formation on two rotors mounted on an SEA output shaft, which rotate relative to an input rotor. The input rotor features chambers that enclose the springs undergoing deformation. Experimental results indicated high torque bandwidth and high fidelity in rendering a virtual impedance.

[0083] The high torque bandwidth, large deformation range with bidirectional linear response of the inventive spring element makes it suitable for various applications requiring rapid response and the ability to exert high force with precision. These features Attorney Docket No.: 206572-0008-00WO find applications in areas such as humanoid robots, which demand high torque bandwidth for agility in executing complex movements tasks, and exoskeletons and wearable robots, designed for rehabilitation or assistance / augmentation purposes. The wide deformation range acts as a buffer between the motor and the user's biological joints. Additionally, the present invention can be used in many other robotic applications requiring physical interaction, including powered orthoses / prostheses, haptic devices, co-robots for the industry, legged robots, etc. Such applications may be of particular interest for military organizations.

[0084] Another potential application is space exploration, in which robotic arms and rovers depend on high torque bandwidth and large deformation range for precise manipulation and mobility in the demanding environments of outer space. Similarly, in the medical field, surgical robots rely heavily on high torque bandwidth and high torque resolution for precise control and accurate force application, which are essential for ensuring patient safety and the success of medical procedures.

[0085] In some embodiments, the disclosed “Elastic Spinners” include an input rotor assembly (input element 140) and a pair of rigidly-connected output rotors 120. The input rotor assembly comprises a featured middle plate (e.g., middle portion 140a) and two cover plates (lateral portions 140b, 140c). This assembly holds cable tracks 150 that guide the driver cable loop (one or more cable 170), which transfers mechanical power to the elastic element. The output rotors 120 are mounted on an output shaft 110 supported by bearings 126 with extended inner rings (see Fig. 3B). The bearings 126 are fitted within the input rotor (input element 140), enabling the output rotors 120 to rotate relative to the input rotor (input element 140). Each output rotor 120 features five arc cutouts (slots 122) arranged circumferentially, which accommodate the helical springs (compression springs 160) and ensure their preload. The compression springs 160 are enclosed within spring chambers 142 in the input rotor. These spring chambers 142 are created by designing the cover plates and the middle plate with complementary chamber cutouts (e.g., cut out portions 142a, 142b, 142c). As the output rotors 120 rotate relative to the input rotor, all springs deflect by the same amount. Consequently, a reaction torque is generated on the output rotors 120. This torque is transmitted to an output link (e.g., torque link 128) using three barrel screws. Attorney Docket No.: 206572-0008-00WO

[0086] Compared to other linear spring arrangements, this configuration achieves high torque in a compact form factor and allows for larger deformation range while maintaining a linear response within the deformation range of the elastic element ( see Table 2 in Example 1 below). The specifications of Elastic Spinners as a whole are also shown (see Table 1 of Example 1 below). In an exemplary embodiment, the output rotors 120 are made of aerospace grade aluminum alloy (7075-T6) due to its high strength-to- weight ratio. In such an embodiment, the output shaft 110 is made of stainless steel (AISI 303), and the barrel screws are made of alloy steel. In some embodiments, the input element 140 (e.g., cover plates and the middle plate) are made of 6061 aluminum alloy.

[0087] The utility of Elastic Spinners lies in its innovative layout featuring linear compression springs arranged in an arc formation on two coaxial, rigidly-connected rotors mounted on the SEA output shaft, which rotate relative to an input rotor. The input rotor features chambers that enclose the springs undergoing deformation. Unlike previous designs that used linear springs, Elastic Spinners achieve a wide deformation range (±0.42 rad, or ±24 deg) while maintaining a highly linear (R2= 0.998) response, generating 43.8 Nm / rad stiffness without appreciable mechanical backlash or hysteresis in bidirectional loading. Moreover, despite a compact (82 mm outer diameter) and lightweight (0.217 kg) design, Elastic Spinners provide a torque capacity of 18 Nm.

[0088] While SEA elastic elements featuring off-the-shelf springs have been previously described in the literature, existing prototypes do not match Elastic Spinners’ deformation range. Compared with state-of-the-art SEA elastic elements, the innovative arc spring layout of Elastic Spinners produces the largest deformation range while also maintaining a linear response. Notably, a small deformation range implies a moderate torque capacity per unit of passive stiffness. This indicates that, in relation to its stiffness, the SEA elastic element cannot generate a significant amount of torque. Additionally, Elastic Spinners achieved an average percentage energy loss of just 2.87% over its deformation range. This value is substantially less than the 5% energy loss reported for other torsional springs in the literature, despite the deformation range of Elastic Spinner being far larger than most existing SEA elastic modules, and represents a clear advantage for portable and wearable applications, which are often battery-powered. Attorney Docket No.: 206572-0008-00WO

[0089] Several design features contribute to the minimal energy dissipation of Elastic Spinners. The springs are mounted with preload within arc slots in the output rotors, and equally protrude from each side of the rotor plate. This symmetric configuration keeps the spring coils centered with respect to the walls of spring chambers machined on the input rotor, allowing the springs to undergo ideal deformation. It also prevents sliding contacts between each spring and its chamber while the elastic element undergoes deformation. In addition, each output rotor is seated against the extended inner ring of a bearing, which provides axial clearance between the inner and the outer rotor surfaces and greatly reduces frictional forces as the rotors rotate relative to each other.

[0090] Elastic Spinners enable a large dynamic range (on the order of 1000: 1) and high torque bandwidth (exceeding 8.4 Hz at 75% of torque capacity). Both metrics are beneficial in dynamic applications that require both high torque sensitivity and large torque capacity, such as pHRI applications (e.g., rehabilitation and assistive powered orthoses and exoskeletons, active prostheses) and legged robots. The dynamic range of Elastic Spinners outperforms existing SEA torsional springs with comparable or even higher stiffness. In terms of closed-loop torque bandwidth, Elastic Spinners demonstrated superior performance to existing SEA elastic elements whose passive stiffness is within the same order of magnitude. The high torque bandwidth of Elastic Spinners results from a gearless transmission and a carefully designed spring chamber system. Although higher bandwidth values have been reported in the SEA literature, these designs are typically intended for low-torque applications and are therefore tested with smaller-amplitude chirp inputs.

[0091] One feature of the disclosed Elastic Spinners lies in the use of linear compression springs in a new arc formation, which enables a linear response within a wide passive deformation range, as well as low hysteresis, nearly null backlash, and relatively high torque capacity, in a compact and lightweight design. Indeed, the presented dual-rotor prototype can exert up to 18 Nm, offering a large passive deformation range of + / - 24 deg and a small (e.g., external diameter 82 mm; thickness 18.5 mm) and lightweight (e.g., 0.217 kg) form factor. The use of widely-available off- the-shelf linear compression springs help reduce the fabrication costs. While SEA elastic elements featuring off-the-shelf springs have been previously described in the literature, Attorney Docket No.: 206572-0008-00WO existing protypes do not match Elastic Spinners’ deformation range. For example, the deformation range of Elastic Spinners is significantly larger than + / - 10.3 deg and + / - 4.5 deg afforded by designs that utilize linear compression springs arrange tangentially, which traditionally introduces a non-linear stiffness response. The deformation range of Elastic Spinners also exceeds the values reported in prior literature for elastic elements based on linear tension springs. Such designs achieve good linearity over deformation ranges of approximately + / - 10 degrees. However, the use of tension springs typically limits the torque capacity of the elastic element in relation to its stiffness and form factor (e.g., torque capacity of 8 Nm with stiffness of 72.4 Nm / rad and 130 mm external diameter, and torque capacity of 11.3 Nm with stiffness of 64.2 Nm / rad and 96 mm external diameter. Compared with state-of-the-art SEA elastic elements, the inventive spring layout of the present invention produces the largest deformation range while also maintaining a linear response (see Fig. 16). Notably, a small deformation range implies a moderate torque capacity per unit of passive stiffness. This indicates that, in relation to its stiffness, the SEA elastic element cannot generate a significant amount of torque. Additionally, Elastic Spinners achieved an average percentage energy loss of just 2.87% over its deformation range. This value is substantially less than the 5% energy loss reported for the torsional spring observed in prior work, despite the deformation range of Elastic Spinner being over 1.5 times larger, and represents a clear advantage in portable and wearable applications that are often battery-powered. Several design features contribute to the minimal energy dissipation of Elastic Spinners. The springs are mounted with preload within arc slots in the output rotors, and equally protrude from each side of the rotor plate. This symmetric configuration keeps the spring coils centered with respect to the walls of spring chambers machined on the input rotor, allowing the springs to undergo ideal deformation. It also prevents sliding contacts between each spring and its chamber while the elastic element undergoes deformation (see Figs. 1 A-1E). In addition, each output rotor is seated against the extended inner ring of a bearing, which provides axial clearance between the inner and outer rotor surfaces and greatly reduces frictional forces as the rotors rotate relative to each other.

[0092] In evaluating the present invention, FEA followed by fatigue analysis informed material selection for a high-strength, lightweight, and durable design. The Attorney Docket No.: 206572-0008-00WO estimated service life (133,732 loading cycles) was detected appropriate for the intended application. For example, if the SEA is fitted to an ankle exoskeleton for gait rehabilitation and the device provides maximal assistance (18 Nm) once per gait cycle, the elastic element would need to be replaced after approximately 50 rehabilitation sessions, assuming a nominal pace of 120 steps per minute and a standard 45-minute PT exercise session.

[0093] Further details regarding the foregoing disclosures and what follows can be found in Example 1 below entitled “A Novel Compact Bidirectional Rotary Spring with Large Deformation Range for Series Elastic Actuators,” in Example 2 entitled “A Novel Personalized Ankle Exoskeleton with Co-Located SEA for Gait Training,” and in Example 3 entitled “Reinforcement Learning Assist-As-Needed Control Promotes Recovery of Walking Speed Following Ankle Weight Perturbations”.

[0094] Elastic Spinners enable a large dynamic range (on the order of 1000: 1) and high torque bandwidth (exceeding 8.4Hz at 75% of torque capacity). Both metrics are helpful in dynamic applications that require both high torque sensitivity and large torque capacity, such as pHRI applications (e.g., rehabilitation and assistive-powered orthoses and exoskeletons, active prostheses) and legged robots. The dynamic range of Elastic Spinners outperforms existing SEA torsional springs with comparable or even higher stiffness, including the monolithic spring (e.g., dynamic range of 101.3: 1, stiffness 98 Nm / rad) and the torsional elastic element based on linear tension springs in another prior application (i.e., dynamic range of 145.3; 1, stiffness 70.4 Nm / rad). In terms of closed- loop torque bandwidth, Elastic Spinners demonstrated superior performance to existing SEA elastic elements whose passive stiffness is within the same order of magnitude, such as monolithic designs at both high (e.g., 12 Nm) and moderate (e.g., 6 Nm) torque amplitudes, despite the monolithic designs having higher passive stiffness (e.g., 82 to 119 Nm / rad vs. 43.8 Nm / rad). The high torque bandwidth of Elastic Spinners results from a gearless transmission and a carefully designed spring chamber system. Although higher bandwidth values have been reported in the SEA literature (e.g., 39.6 Hz for an elastic element based on linear tension springs), these designs are typically intended for low- torque applications and are therefore tested with smaller-amplitude chirp inputs (e.g., 1 Nm amplitude). Furthermore, a design procedure was developed that enables the Attorney Docket No.: 206572-0008-00WO selection of suitable off-the-shelf springs based on the desired torque capacity and deformation range. This new workflow allows designers to generate an "Elastic Spinners" design with desired stiffness and deformation range. The detailed modeling and design procedure is explained Example 1 below. Although the design procedure was validated with a dual-rotor model featuring five springs mounted on each rotor, a wide range of passive stiffness values can be obtained by varying the number of output rotors, the number of springs per each rotor, or the type of linear compression spring. As such, Elastic Spinners align with recent trends in SEA design, which prioritize modular elastic elements that can be fine-tuned to a specific application, with minimal re-design efforts.

[0095] To validate the design procedure referenced above, and experimental characterization was carried out to measure the passive stiffness and hysteresis of Elastic Spinners. Results from the passive characterization can be found in Example 1 below.

[0096] Additionally, dynamic characterization was carried out. Dynamic tests included transient response analysis, sinusoidal torque tracking, frequency response analysis, and virtual impedance rendering. For the first three tests, the output rotors of Elastic Spinners were rigidly attached to the stationary frame using three barrel screws. For the virtual impedance rendering, the output rotors were unlocked, and a human operator interacted with the SEA through a torque handle. Results from the passive characterization can be found in Example 1 below.

[0097] Details regarding an ankle exoskeleton application of the present invention and associated EAS 101 analysis can be found in Example 2 below.

[0098] Aspects of device 100 and / or system 200 may comprise or communicatively and electronically connect to a computing device, such as computer 600 disclosed herein. Accordingly, in some aspects of the present invention, software executing the instructions provided herein may be stored on a non-transitory computer- readable medium, wherein the software performs some or all of the steps of the present invention when executed on a processor.

[0099] Aspects of the invention relate to algorithms executed in computer software. Though certain embodiments may be described as written in particular programming languages, or executed on particular operating systems or computing platforms, it is understood that the system and method of the present invention is not Attorney Docket No.: 206572-0008-00WO limited to any particular computing language, platform, or combination thereof Software executing the algorithms described herein may be written in any programming language known in the art, compiled, or interpreted, including but not limited to C, C++, C#, Objective-C, Java, JavaScript, MATLAB, Python, PHP, Perl, Ruby, or Visual Basic. It is further understood that elements of the present invention may be executed on any acceptable computing platform, including but not limited to a server, a cloud instance, a workstation, a thin client, a mobile device, an embedded microcontroller, a television, or any other suitable computing device known in the art.

[0100] Parts of this invention are described as software running on a computing device. Though software described herein may be disclosed as operating on one particular computing device (e.g. a dedicated server or a workstation), it is understood in the art that software is intrinsically portable and that most software running on a dedicated server may also be run, for the purposes of the present invention, on any of a wide range of devices including desktop or mobile devices, laptops, tablets, smartphones, watches, wearable electronics or other wireless digital / cellular phones, televisions, cloud instances, embedded microcontrollers, thin client devices, or any other suitable computing device known in the art.

[0101] Similarly, parts of this invention are described as communicating over a variety of wireless or wired computer networks. For the purposes of this invention, the words “network”, “networked”, and “networking” are understood to encompass wired Ethernet, fiber optic connections, wireless connections including any of the various 802.11 standards, cellular WAN infrastructures such as 3G, 4G / LTE, or 5G networks, Bluetooth®, Bluetooth® Low Energy (BLE) or Zigbee® communication links, or any other method by which one electronic device is capable of communicating with another. In some embodiments, elements of the networked portion of the invention may be implemented over a Virtual Private Network (VPN).

[0102] Fig. 6 and the following discussion are intended to provide a brief, general description of a suitable computing environment in which the invention may be implemented. While the invention is described above in the general context of program modules that execute in conjunction with an application program that runs on an Attorney Docket No.: 206572-0008-00WO operating system on a computer, those skilled in the art will recognize that the invention may also be implemented in combination with other program modules.

[0103] Generally, program modules include routines, programs, components, data structures, and other types of structures that perform particular tasks or implement particular abstract data types. Moreover, those skilled in the art will appreciate that the invention may be practiced with other computer system configurations, including handheld devices, multiprocessor systems, microprocessor-based or programmable consumer electronics, minicomputers, mainframe computers, and the like. The invention may also be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules may be located in both local and remote memory storage devices.

[0104] Fig. 6 depicts an illustrative computer architecture for a computer 600 for practicing the various embodiments of the invention. The computer architecture shown in Fig. 6 illustrates a conventional personal computer, including a central processing unit 650 (“CPU”), a system memory 605, including a random access memory 610 (“RAM”) and a read-only memory (“ROM”) 615, and a system bus 635 that couples the system memory 605 to the CPU 650. A basic input / output system containing the basic routines that help to transfer information between elements within the computer, such as during startup, is stored in the ROM 615. The computer 600 further includes a storage device 620 for storing an operating system 625, application / program 630, and data.

[0105] The storage device 620 is connected to the CPU 650 through a storage controller (not shown) connected to the bus 635. The storage device 620 and its associated computer-readable media provide non-volatile storage for the computer 600. Although the description of computer-readable media contained herein refers to a storage device, such as a hard disk or CD-ROM drive, it should be appreciated by those skilled in the art that computer-readable media can be any available media that can be accessed by the computer 600.

[0106] By way of example, and not to be limiting, computer-readable media may comprise computer storage media. Computer storage media includes volatile and nonvolatile, removable and non-removable media implemented in any method or technology Attorney Docket No.: 206572-0008-00WO for storage of information such as computer-readable instructions, data structures, program modules or other data. Computer storage media includes, but is not limited to, RAM, ROM, EPROM, EEPROM, flash memory or other solid state memory technology, CD-ROM, DVD, or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can be accessed by the computer.

[0107] According to various embodiments of the invention, the computer 600 may operate in a networked environment using logical connections to remote computers through a network 640, such as TCP / IP network such as the Internet or an intranet. The computer 600 may connect to the network 640 through a network interface unit 645 connected to the bus 635. It should be appreciated that the network interface unit 645 may also be utilized to connect to other types of networks and remote computer systems.

[0108] The computer 600 may also include an input / output controller 655 for receiving and processing input from a number of input / output devices 660, including a keyboard, a mouse, a touchscreen, a camera, a microphone, a controller, a joystick, or other type of input device. Similarly, the input / output controller 655 may provide output to a display screen, a printer, a speaker, or other type of output device. The computer 600 can connect to the input / output device 660 via a wired connection including, but not limited to, fiber optic, Ethernet, or copper wire or wireless means including, but not limited to, Wi-Fi, Bluetooth, Near-Field Communication (NFC), infrared, or other suitable wired or wireless connections.

[0109] As mentioned briefly above, a number of program modules and data files may be stored in the storage device 620 and / or RAM 610 of the computer 600, including an operating system 625 suitable for controlling the operation of a networked computer. The storage device 620 and RAM 610 may also store one or more applications / programs 630. In particular, the storage device 620 and RAM 610 may store an application / program 630 for providing a variety of functionalities to a user. For instance, the application / program 630 may comprise many types of programs such as a word processing application, a spreadsheet application, a desktop publishing application, a database application, a gaming application, internet browsing application, electronic mail application, messaging application, and the like. According to an embodiment of the Attorney Docket No.: 206572-0008-00WO present invention, the application / program 630 comprises a multiple functionality software application for providing word processing functionality, slide presentation functionality, spreadsheet functionality, database functionality and the like.

[0110] The computer 600 in some embodiments can include a variety of sensors 665 for monitoring the environment surrounding and the environment internal to the computer 600. These sensors 665 can include a position sensor, absolute position sensor, potentiometer sensor, hall effect sensor, rotary encoder sensor, optical encoder sensor, resolver sensor, ultrasonic position sensor, inductive sensor, capacitive position sensor, laser position sensor, rotary variable differential transducer, angular position sensor, torque sensor, Global Positioning System (GPS) sensor, a photosensitive sensor, a gyroscope, a magnetometer, thermometer, a proximity sensor, an accelerometer, a microphone, biometric sensor, barometer, humidity sensor, radiation sensor, or any other suitable sensor.

[0111] EXPERIMENTAL EXAMPLES

[0112] The invention is further described in detail by reference to the following experimental examples. These examples are provided for purposes of illustration only, and are not intended to be limiting unless otherwise specified. Thus, the invention should in no way be construed as being limited to the following examples, but rather, should be construed to encompass any and all variations which become evident as a result of the teaching provided herein.

[0113] Without further description, it is believed that one of ordinary skill in the art can, using the preceding description and the following illustrative examples, make and utilize the present invention and practice the claimed methods. The following working examples therefore are not to be construed as limiting in any way the remainder of the disclosure.

[0114] Example 1 : A Novel Compact Bidirectional Rotary Spring with Large Deformation Range for Series Elastic Actuators

[0115] This example presents the development and characterization of a novel bidirectional elastic element to be used in series elastic actuators (SEAs) for physical Attorney Docket No.: 206572-0008-00WO human robot interaction (pHRI) and small-scale robotic applications. In comparison with the state of the art, the disclosed design is more compact and lightweight. It offers high torque bandwidth and a wide deformation range while maintaining a linear response within this range. The performance / compact form blend is enabled by a novel configuration, wherein ten linear springs are arranged in an arc formation on two rotors mounted on the SEA output shaft, which rotate relative to an input rotor. The input rotor features chambers that enclose the springs undergoing deformation. Experimental results indicated high torque bandwidth and high fidelity in rendering a virtual impedance.

[0116] Series Elastic Actuators (SEAs) are commonly used in robots designed for physical Human-Robot Interaction (pHRI), including humanoid robots [Paine et al., 2015], service robots [Yoon et al., 2003], and those developed for assistive [Lee et al., 2023] and rehabilitation [Zhong et al., 2021] purposes. Key advantages of integrating an elastic element in series with the actuation system include precise control of interaction forces, backdrivability, and improved operational safety by decoupling the end effector from the motor inertia [De Santis et al., 2008], Indeed, the elastic element enables direct measurement of the applied load by measuring the spring deflection, while the intrinsic compliance of the SEA’s elastic element ensures low system impedance across the frequency spectrum, as the closed-loop impedance of the system reduces to the passive impedance of the spring when the frequencies of the external disturbances exceed the controller bandwidth [Carpino et al., 2012], Another advantage of SEAs is their ability to store and release energy. Paluska and Herr [Paluska and Herr, 2006] have demonstrated through numerical simulations and experiments that the SEA elastic element can store energy and deliver peak powers greater than the power limit of the SEA motor by factor of 1.4. In addition, by selecting an appropriate spring rate, the energy that an actuator can deliver can be quadrupled. These properties are commonly utilized in the design of running and hopping robots [Raibert, 1986; Koditschek and Buehler, 1991; Brown and Zeglin, 1998], allowing them to function with minimal energy input from the control system [Raibert, 1986], [Hurst et al., 2004], On the other hand, major drawbacks of series elasticity include a reduction in force bandwidth compared to rigid actuation [Hurst et al., 2004], and an upper boundary to the maximum stiffness that can be achieved, which is Attorney Docket No.: 206572-0008-00WO limited by the physical stiffness of the elastic element [Vallery et al., 2008], unless advanced control methods are applied [Lee et al., 2021],

[0117] The elastic element is a critical component of a SEA, as it determines its range of actuation and torque resolution, and affects its closed-loop bandwidth [Lee et al., 2023], A compliant element allows for accurate torque feedback from displacement measurements. However, higher compliance necessitates larger spring deformations to achieve large torques, such as those required in rehabilitation and assistive robots [Carpino et al., 2012], Therefore, designing an elastic element requires a trade-off between compliance and deformation range, and designing compact and lightweight SEA with high torque capabilities remains a challenge [Kuru et al., 2022],

[0118] The elastic elements in rotary SEA designs can be classified into two broad categories: those with linear springs and those having torsional springs. The first category employs arrangements of compression springs [Veneman et al., 2006; Wyeth, 2006; Tsagarakis et al., 2009; Toubar et al., 2022] or tension springs [Tiseni et al., 2021], [Zhao et al., 2024], Linear compression springs are often arranged tangentially around a circular frame. This configuration allows for a reduced form factor but limits the deformation range of the spring element and results in a non-linear stiffness response [Tsagarakis et al., 2009], In contrast, designs that implement linear tension springs achieve a good linearity response [Zhao et al., 2024] at the expense of a reduced torque capacity (e g., 8 Nm for the design in [Tiseni et al., 2021], and 11.3 Nm for the design in [Zhao et al., 2024], despite their high stiffness values of 72.4 Nm / rad and 64.2 Nm / rad, respectively). Importantly, a small deformation range implies a low torque capacity per unit of passive stiffness, i.e., for the amount of maximum stiffness it can offer, the SEA elastic element cannot generate much torque. Linear stiffness responses can also be achieved using an agonistic-antagonistic configuration of linear compression springs connected to an actuator disk by a cable loop [Veneman et al., 2006], In this design, the deformation range and passive stiffness of the elastic element can be controlled with a proper selection of actuator disk diameter, maximum spring compression, and spring stiffness. However, this arrangement often leads to bulky designs that are hardly suitable for space-constrained applications, such as wearable robots. Attorney Docket No.: 206572-0008-00WO

[0119] The second category of SEA elastic elements includes commercial torsional springs and custom torsional springs. Commercial torsional springs [Lee et al., 2023], [Kong et al., 2009; Kong et al., 2010; Kong et al., 2011] usually feature low stiffness, low torque capacity, and large deformation range. In these designs, the torsional elastic element is typically fitted between the output shaft of a geared motor and the SEA interaction port [Kong et al., 2009] or, less often, in-between a non-backdrivable and a backdrivable geared transmission [Kong et al., 2011], The latter solution results in a more compact and more compliant spring for a given maximum interaction torque and allows for more precise control of the generated torques [Kong et al., 2011], Custom torsional springs can be monolithic or two-element planar springs. Monolithic designs [Carpino et al., 2012], [Kuru et al., 2022], [Knox and Schmiedeler, 2009; Lagoda et al., 2010; Diftler et al., 2011; Accoto et al., 2013; Cummings et al., 2016; Dos Santos et al., 2017; Georgiev and Burdick, 2017; Kim et al., 2021; Al-Dahiree et al., 2023; Stienen et al., 2009; Wang et al., 2013; Yoo et al., 2017] are machined from solid stock and feature one or more spiral arms with both ends fully constrained (i.e., fixed-fixed geometry) which favors high stiffness and low deflection. However, monolithic design prevent the spiral arms from undergoing ideal bending under load. This restricts their useful deflection range, limiting the energy capacity of the spring. Several monolithic designs have been proposed over the last fifteen years. In [Wang et al., 2013], a custom made double winding elastic element was introduced, based on two previous designs [Lagoda et al., 2010], [Stienen et al., 2009], This design exhibits a highly linear load-deflection curve, nearly zero backlash, and good fatigue life (0.14 million cycles). The main advantage of the double winding pattern is to cancel out radial forces acting on the center of the spring during loading and unloading, thereby reducing the radial load on the SEA’s output shaft. Double winding designs often result in a nearly linear response during loading, until the windings come into contact. However, significant hysteresis is generated during the unloading phase. Additionally, modeling the load-deflection response in these designs remains a challenge, as highlighted by the significant difference between expected and measured stiffness values [Lagoda et al., 2010], Another double spiral spring with linear response was presented in [Georgiev and Burdick, 2017], In this design, the spiral arms feature cutouts to reduce the spring’s weight. However, the deformation range is still Attorney Docket No.: 206572-0008-00WO limited (10 deg). A triple spiral pattern was introduced in [Yoo et al., 2017], featuring cross-parallel connected springs with opposing spiral directions. This configuration enables higher maximum torques and a symmetric load-deflection profile. However, the stiffness varies depending upon the load. The custom spiral spring presented in [Knox and Schmiedeler, 2009] was designed to drive the actuator in a single direction. Although this unidirectional design is not suited for applications that require compliance in both directions, it is beneficial for legged robots as it offers compliance in the direction of ground impact loading and precision in the returning direction. Other designs of monolithic springs emphasize linearity and torque resolution, but often exhibit significant mechanical backlash and a deformation range limited to 10 deg or less [Paine et al., 2015; Carpino et al., 2012; Dos Santos et al., 2017; Kim et al., 2021],

[0120] Two-element planar springs are targeted towards more energy efficient applications. The planar spring features one or more arms connecting a central bore to an outer rim with a fixed-free / hinged geometry. The fixed-free boundary conditions allow for greater deflection, usually trading some of the stiffness that can be achieved with a fixed-fixed boundary condition. For example, a cantilever-based design was introduced in [Bons et al., 2023], building upon a previous prototype [Mooney et al., 2017], This design uses equally spaced cantilever beams, with one end allowed to rotate at the interface with a camshaft, and the other end fixed to a rim. Although this design allows for a larger deformation range (approximately 12 deg), it results in different stiffness values depending on the load direction. The designers also reported appreciable hysteresis, possibly due to the sliding contact between the cantilever arms and the camshaft resulting in energy loss [Bons et al., 2023],

[0121] Fig. 7 is an image depicting a front view of an exemplary actuator, referred to in some examples as “Elastic Spinners”, featuring a small (82 mm external diameter, 18.5 mm thickness) and lightweight (0.217 kg) form factor.

[0122] Disclosed herein is an exemplary actuator (e.g., an SEA), referred to in some examples as “Elastic Spinners” (see Fig. 7), a compact, bidirectional elastic element for rotary SEAs. In some embodiments, the uniqueness of Elastic Spinners lies in its innovative layout featuring linear compression springs arranged in an arc formation on two coaxial, rigidly-connected rotors mounted on the SEA output shaft, which rotate Attorney Docket No.: 206572-0008-00WO relative to an input rotor. In some embodiments, the input rotor features chambers that enclose the springs undergoing deformation. Unlike previous designs that use linear springs [Tsagarakis et al., 2009; Toubar et al., 2022; Tiseni et al., 2021], the disclosed Elastic Spinners achieves a wide deformation range (±0.42 rad, or ±24 deg) while maintaining a highly linear (R2= 0.998) response, generating 43.8 Nm / rad stiffness without appreciable mechanical backlash or hysteresis in bidirectional loading. Moreover, despite a compact (82 mm outer diameter) and lightweight (0.217 kg) design, Elastic Spinners provides a torque capacity of 18 Nm.

[0123] ELASTIC SPINNERS DESIGN: Design Procedure: In this section, the design workflow to obtain an Elastic Spinners design with desired stiffness and deformation range is presented. Motivated by the application to an assistive ankle exoskeleton, the design peak torque was set to Tmax = 18 Nm, and its deformation range set to AOmax = ±24°. The selected Tmax corresponds to approximately 15% of the peak ankle plantarflexion torque for a 75 kg adult male walking at normal pace, while A0maxexceeds the expected range of motion for ankle plantarflexion and dorsiflexion during walking [Winter, 1991], To simplify the low-level control of the SEA, a linear torque deflection response in the elastic element is desirable [Carpino et al., 2012], The most compliant linear elastic element that achieves both requirements has a passive torsional stiffness KES = 43.8 Nm / rad. To achieve the target KES and AOmax with a compact design, a set of N identical helical compression springs arranged circumferentially on the output rotor of the elastic element is relied upon. The passive torsional stiffness of each spring was approximated using the model introduced by Chen et al. for arc helical springs with circular cross-section subjected to circumferential force [Chen et al., 2006]

[0124] _ Gd4R2Kac8D3n Equation 1 where D and d are the average diameter of the spring and the diameter of the spring wire, respectively, R is the radius of the circumference along which the coil axis of the helical spring lies, n is the number of active coils, and G is the shear modulus. Attorney Docket No.: 206572-0008-00WO

[0125] Because all springs in the output rotors act in parallel, the desired torsional stiffness for each spring is:

[0126] Equation 2

[0127] Since arc springs are specialized components that are not widely available, conventional linear compression springs were used instead. Comparing Equation 1 to Wahl’s model of axially-loaded cylindrical helical spring [Wahl, 1963], the equivalent stiffness for conventional linear compression springs was obtained: Equation 3

[0128] Substituting Equation 2 into Equation 3, the following was obtained:

[0129] Equation 4

[0130] Additionally, to enable a maximum deflection angle AOmax, the free length Sf and the solid length Si of each compression spring must satisfy the following inequality:

[0131] Equation 5 where indicates the spring preload. Equation 4 and Equation 5, can be used to inform the selection of an appropriate off-the-shelf compression spring. The mechanical properties of the selected spring are summarized in Table 1. Considering the shear modulus of AISI 316 Stainless Steel (G =74.23 GPa), and a radius R = 31 mm to achieve a compact design suitable for wearable applications, the calculated spring torsional stiffness is 4.6 Nm / rad. Thus, a dual-rotor design with 5 springs mounted on each secondary rotor results in an overall calculated stiffness of 46 Nm / rad, which is a Attorney Docket No.: 206572-0008-00WO good approximation of the design value. Furthermore, Equation 5 indicates that the selected spring can achieve AOmax with a preload ~ 3 - 4 mm. This preload is critical to keep the spring in place on each output rotor and avoid backlash. To implement this preload, each spring chamber was machined as a 52 degree arc slot.

[0132] Table 1: Elastic Spinners’ Compression Spring

[0133] Table 2: Specifications of Elastic Spinners Figs. 1A & IB are images depicting rendered views of an exemplary actuator (i.e., Elastic Spinners) Fig. 1A depicts an assembled view, illustrating the driver cable loop terminating at the cable grip pad. Fig. IB depicts an exploded view, showing the main components of an exemplary Elastic Spinners.

[0134] Mechanical Design: As shown in Figs. 1A & IB, the exemplary Elastic Spinners comprise an input rotor assembly and a pair of rigidly-connected output rotors. Attorney Docket No.: 206572-0008-00WO

[0135] In some embodiments, the input rotor assembly comprises a featured middle plate and two cover plates. In some embodiments, this assembly holds cable tracks that guide the driver cable loop (see Fig. 1A), which transfers mechanical power to the elastic element. In some embodiments, the output rotors are mounted on an output shaft supported by bearings with extended inner rings. In some embodiments, the bearings are fitted within the input rotor, enabling the output rotors to rotate relative to the input rotor. In some embodiments, each output rotor features five arc cutouts arranged circumferentially, which accommodate the helical springs and ensure their preload. In some embodiments, the springs are enclosed within spring chambers in the input rotor. In some embodiments, these chambers are created by designing the cover plates and the middle plate with complementary chamber cutouts. As the output rotors rotate relative to the input rotor, all springs deflect by the same amount. Consequently, a reaction torque is generated on the output rotors. This torque is transmitted to an output link using three barrel screws. Compared to other linear spring arrangements [Tsagarakis et al., 2009], [Toubar et al., 2022], this configuration achieves high torque in a compact form factor and allows for larger deformation range while maintaining a linear response within the deformation range of the elastic element (see Table 2). In some embodiments, the output rotors are made of aerospace grade aluminum alloy (7075-T6) due to its high strength-to-weight ratio. In some embodiments, the output shaft is made of stainless steel (AISI 303), and the barrel screws are made of alloy steel. In some embodiments, the cover plates and the middle plate are made of 6061 aluminum alloy.

[0136] Figs. 8A & 8B are images depicting a Finite Element Analysis model. Fig. 8A depicts loads applied at the output rotors. Magenta arrows indicate circumferential forces at the contact locations between each spring and the output rotors. The yellow arrow indicates the bearing load between the output shaft and the output rotor (second bearing load not shown). Fig. 8B depicts computed von Mises stress distribution on the output rotors and shaft. Locations of the computed maximum von Mises stress and maximum alternating stress amplitude (Sa) are indicated.

[0137] Finite Element Analysis: Static Analysis: A static finite element analysis (FEA) with large displacement was performed in SOLIDWORKS Simulation to validate the design of Elastic Spinners. Distributed circumferential forces of 32 N (equivalent to Attorney Docket No.: 206572-0008-00WO

[0138] 20 Nm pure torque) were applied at each contact surface between the springs and the output rotor (Fig. 8A, magenta arrows). The tensile force applied by the driver cable loop was rendered as a 290 N bearing load with a sinusoidal distribution at the contact surface between each bearing and the output shaft (Fig. 8A, yellow arrow). Fixed boundary conditions were applied at the shaft and at the barrel screw holes. The geometry was meshed using a tetrahedral mesh with three elements across the thickness of each output rotor. Element sizes were refined near areas where high stresses are expected. All global interactions were modeled as bonded for simplicity. Computed results, shown in Fig. 8B, indicate a maximum von Mises stress of 187 MPa at the contact location between the barrel screws and the output rotors, corresponding to a minimum safety factor of 2.68.

[0139] Fatigue Analysis: A load cycle was applied to the finite element model. To this end, a static FEA simulation was performed first, where circumferential forces of 32 N each were applied in one direction (Fig. 8A). Then, a second simulation was performed where the direction of the applied forces was reversed. Subsequently, the computed von Mises stresses in each simulation were used to determine location and value of the peak alternating stress amplitude Sa (Fig. 8B), and the Goodman model was applied to estimate the mean corrected stress Se as a function of the mean stress Sm = (Smax + Smin) / 2, the alternating stress amplitude Sa, and the ultimate strength Su:

[0140] SaSe ~ c (l - ) u

[0141] Equation 6

[0142] From the computed von Mises stress contours (Fig. 8B) it was found that Sa = 116.9 MPa, and Sm= 128.55 MPa, resulting in Se = 150.9 MPa. The fatigue life, estimated using the S-N curve for notched 7075-T6 alloy [Smith, 1966], was 133,732 cycles.

[0143] PASSIVE STIFFNESS CHARACTERIZATION: Experimental Setup: To validate the design procedure described in this example, a first prototype of Elastic Spinners was fabricated, and experimental characterization was carried out to measure its passive stiffness and hysteresis. In the test setup (see Fig. 9), the input rotor assembly was rigidly attached to a stationary frame, while the output shaft was connected to a torque Attorney Docket No.: 206572-0008-00WO sensor via a flange. The deformation of Elastic Spinners was measured using the onboard position sensor (micro-optical encoder E16, US Digital, USA) with 16384 pulses per revolution (PPR), whose housing was attached to one of the cover plates (see Figs. 1A & IB). A custom-made data acquisition and conditioning (DAQ) board that includes a 32-bit microcontroller (Teensy 3.5, PJRC, USA), an EtherCAT shield (EasyCAT Pro, AB&T Sri, Italy), and a 12-bit ADC (AD7890ANZ-10, Analog Devices, USA) was connected to a Unit Real Time Target Machine (Speedgoat GmbH, Switzerland), allowing data collection from position and torque sensors over EtherCAT bus at 1 kHz.

[0144] Fig. 9 is an image depicting a testing rig used for passive response characterization of the disclosed actuator (i.e., Elastic Spinners). The input rotor assembly was fixed to a stationary frame, and a torque sensor was connected between the output shaft of Elastic Spinners and a torque handle, which was used to manually apply a quasi-periodic load.

[0145] Using a torque handle connected to the output port of the torque sensor, an experimenter applied an approximate sinusoidal trajectory spanning the useful deformation range of Elastic Spinners. Passive stiffness and hysteresis were quantified using data collected from 29 loading / unloading cycles.

[0146] Figs. 10A & 10B are plots showing results for the passive stiffness response of the disclosed actuator. Fig. 10A shows the applied deflection on the spring element - periodic deflection (gray) and corresponding measured torque (blue). Fig. 10B shows the linear response (stiffness: 0.765 Nm / deg, or 43.8 Nm / rad) over a useful deformation range of ±24 deg.

[0147] Results: The measured torque and deformation angle, shown in Fig. 10A, indicate that the disclosed Elastic Spinners has a useful deformation range of 24 deg. The system exhibits a linear response with an estimated passive stiffness of 43.8 Nm / rad (0.765 Nm / deg) within the deformation range (Fig. 10B). The estimated stiffness closely matches the design value KES, being only 6.5% lower than the value predicted by the design calculations in this example. The average percentage energy loss, estimated over a total of 29 cycles of loading and unloading, was 2.87%, indicating the actuator’s small hysteresis. Indeed, this outperforms the value reported in [Bons et al., 2023], despite the Attorney Docket No.: 206572-0008-00WO passive deformation range of Elastic Spinners exceeding the deformation range of the design presented in [Bons et al., 2023] by more than 1.5 times.

[0148] The dynamic range of a SEA, defined as the maximum output torque divided by the minimum resolvable output torque increment of the actuator, provides a measure for how sensitive the actuator is to small torques with respect to its torque capacity [Robinson, 2000], Considering the disclosed Elastic Spinners’ useful deformation range, the resolution of the onboard position sensor, and its passive stiffness, the estimated torque resolution is 16.8 mNm, which represents 0.093% of its torque capacity. Thus, the actuator demonstrates a large dynamic range (exceeding 1070: 1), indicating high versatility for use in both very sensitive tasks and in large force situations, which is desirable in pHRI applications [Robinson, 2000],

[0149] DYNAMIC RESPONSE CHARACTERIZATION: Experimental Setup: To evaluate the dynamic performance of the disclosed Elastic Spinners, the elastic element was integrated in a cable-driven SEA (Fig. 11). The SEA comprises a brushless DC (BLDC) motor (EC90-flat, 600W, Maxon Group, Switzerland) with integrated encoder (Maxon Mile Encoder) featuring 4096 counts per turn (CPT), a motor driver (Maxon EPOS4 Compact 50 / 15 EtherCat), as well as the Unit Real Time Target Machine and the DAQ board described in this example. The Real Time Target Machine, the motor driver, and the DAQ communicate over EtherCAT bus at 1kHz. The system is powered by a custom built Li-ion battery with peak voltage of 29.4 V and maximum continuous discharge current of 30 A.

[0150] Fig. 11 is an image depicting a testing rig used for dynamic response characterization of the disclosed Elastic Spinners. The elastic element was driven by a BLDC motor through a cable loop connecting a threaded motor spool to the input rotor.

[0151] In the testing apparatus, a cable loop connects a threaded spool fixed on the shaft of the BLDC motor to the output rotor of Elastic Spinners. The threaded spool, which is supported by a sleeve to reduce radial loads on the motor shaft, allows for cable winding / unwinding without overlapping. The effective diameters of the input rotor and the threaded spool are 76.6 mm and 12.4 mm, respectively, thereby the resulting transmission ratio is approximately 6:1. The cable loop is pretensioned to effectively eliminate backlash and reduce the system response time during bidirectional dynamic Attorney Docket No.: 206572-0008-00WO loading. This is achieved by adjusting the height at which the motor is located on the tower frame supporting the testing rig, with respect to the elastic unit. The frame on which the elastic unit is installed was fabricated as a square bracket to improve frame rigidity and reduce the vibrations induced at high excitation frequencies.

[0152] Fig. 12 is a diagram depicting an exemplary cascaded torque-velocity controller.

[0153] A cascaded-torque velocity controller (See Fig. 12) was implemented for the SEA, whereby a Proportional-Integral (PI) compensator in the outer loop (PiTorque) generates the reference velocity wa for an inner-loop PI compensator (PIveiocity) based on the difference between the desired interaction torque Td and the measured torque rm[Vallery et al., 2008], [Wyeth, 2006], The deformation of Elastic Spinners 9m was used to estimate rmfrom the linear model derived in this example, while the measured velocity com was retrieved from the motor driver. The gains for the inner loop velocity controller were auto-tuned using EPOS Studio v3.7, whereas the outer loop gains were tuned manually to achieve a desired transient response. The sample rate of the low-level controller was 1 kHz. Dynamic characterization tests included transient response analysis, sinusoidal torque tracking, frequency response analysis, and virtual impedance rendering. For the first three tests, the output rotors of Elastic Spinners were rigidly attached to the stationary frame using three barrel screws. For the virtual impedance rendering, the output rotors were unlocked, and a human operator interacted with the SEA through the torque handle described in this example.

[0154] Figs. 13A-13C are plots showing results of the closed-loop response of the disclosed actuator (e.g., SEA). Fig. 13A shows transient response to 6 Nm, 9 Nm and 12 Nm step inputs. Fig. 13B shows torque tracking of a 6 Nm sinusoidal commanded torque with frequency of 0.5 Hz and 2 Hz. Fig. 13C shows torque tracking of a 12 Nm sinusoidal commanded torque at the same two frequencies.

[0155] Results: Transient Response: The system responses to step commanded torques with amplitudes 6 Nm, 9 Nm, and 12 Nm are shown in Fig. 13 A. The percent overshoot was moderate: 12.79% for 6 Nm, 5.12% for 9 Nm, and 3.58% for 12 Nm. The motor saturation velocity and the cable pretension were dominant factors in determining Attorney Docket No.: 206572-0008-00WO the system’s rise time. Nonetheless, even in the most demanding test (12 Nm step), the rise time was 50 ms, indicating good responsiveness.

[0156] Sinusoidal Torque Tracking: The torque tracking performance of the SEA was evaluated by feeding a sinusoidal reference signal with two amplitudes: 6 Nm (Fig. 13B), and 12 Nm (Fig. 13C). Each signal was tested at 0.5 Hz and 2 Hz. The SEA could accurately track the commanded torque at 0.5 Hz, yielding a root-mean-square error (RMSE) of 0.20 Nm and 0.41 Nm for the 6 Nm and 12 Nm amplitudes, respectively. At 2 Hz, the corresponding RMSE was 0.50 Nm for the 6 Nm amplitude, and 0.95 Nm for the 12 Nm amplitude. Thus, in relative terms, the RMSE errors were below 3.4% and 8.3% for the 0.5 Hz tests and the 2 Hz tests, respectively, indicating good torque tracking accuracy despite a decline in performance at higher dynamic loading conditions - likely due to the increasing effects of motor saturation and mechanical impedances (e g., inertia and friction).

[0157] Figs. 14A & 14B are plots showing results for the closed-loop dynamic response of the disclosed Elastic Spinners within SEA configuration with locked output shaft. Fig. 14A shows the commanded torque rd (chirp signal, 12 Nm amplitude, 0-20 Hz frequency) and measured response Tm. Fig. 14B shows corresponding Bode plots derived by fitting experimental data to LTI transfer functions (4 poles, 2 zeros). The 3dB closed- loop bandwidth fnw is 15.05 Hz for 6 Nm, 9.67 Hz for 9 Nm, and 8.49 Hz for 12 Nm torque amplitudes. At fsw, the maximum phase lags are -117.0 deg, -90.1 deg, and -76.3 deg, respectively.

[0158] Frequency Response: The 3 dB torque bandwidth few indicates the frequency at which the magnitude of the closed-loop transfer function HSEA(joj) = — , determined with infinite output impedance (i.e., locked output shaft), falls to approximately 70% of its DC value. As such, it is a common performance metric indicating the frequency range within which a SEA can maintain effective torque tracking with acceptable attenuation [Robinson, 2000], Since HSEA (j co) is a LTI approximation of the actual frequency response of a SEA, it generally varies with the magnitude of ra, and so does fnw. To empirically estimate fsw, the SEA was excited with three chirp signals with torque amplitudes of 6 Nm, 9 Nm, and 12 Nm. Each torque amplitude was swept across frequencies ranging from 0 to 20 Hz. In Fig. 14A, a representative chirp stimulus Attorney Docket No.: 206572-0008-00WO id with 12 Nm amplitude is shown, along with the measured response rm. The transfer function HSEA (j CO) for each applied torque magnitude was estimated using MATLAB System Identification Toolbox. The Bode plots, shown in Fig. 14B, indicated a bandwidth of 15.05 Hz for 6 Nm, 9.67 Hz for 9 Nm, and 8.49 Hz for 12 Nm of applied torque. The corresponding phase lags at few were -117.0 deg, -90.1 deg, and -76.3 deg, respectively. These results highlight stable closed-loop behavior and excellent dynamic performances.

[0159] Figs. 15A-15C are plots showing the results for virtual stiffness rendering. Fig. 15A shows the virtual spring with null stiffness (zero impedance test). Fig. 15B shows the virtual spring with one-third of Elastic Spinners’ passive stiffness (14.33 Nm / rad). Fig. 15C shows the virtual spring with two-thirds of Elastic Spinners’ passive stiffness (28.67 Nm / rad, left of dashed vertical line) and full stiffness (43.8 Nm / rad, right of vertical dashed line).

[0160] Virtual Impedance Rendering: Tests were performed to evaluate the ability of the SEA to render virtual torsional springs with different stiffness values. To this end, a torque handle was installed on the output shaft of Elastic Spinners, using the same setup shown in Fig. 11. The angular position of the torque handle (0) was measured using an absolute position sensor (NP24HS-lkQ, P3 America, Inc., USA). During testing, the handle was manually rotated by an experimenter to generate a quasi-periodic perturbation by following a reference signal displayed on a screen, whose frequency and amplitude (0.5 Hz, 30 deg) were selected to ensure a comfortable tracking at different stiffness values. The commanded torque was set to ra = kvs(9 - 0o), where kvs is the desired virtual stiffness and 0o = 0 rad indicates the unperturbed position of the virtual spring. In the first test (Fig. 15 A), kvs was set to a null value to assess the transparency of the SEA [Colgate and Brown, 1994], The measured interaction torque rmexhibited small fluctuations that peaked at each inversion of motion, but never exceeded ±0.25 Nm.

[0161] The RMSE was 0.135 Nm, which is approximately 0.75% of the torque capacity of Elastic Spinners. In the following tests, the SEA was commanded to render a virtual spring with progressively larger stiffness: kvs = KES / 3 (Fig. 15B), kvs = 2KES / 3 (Fig. 15C, left of dashed line), and kvs = KES (Fig. 15C, right of dashed line), with KES = 43.8 Nm / rad being the passive stiffness of Elastic Spinners. The RMSE between rd and Attorney Docket No.: 206572-0008-00WO tm was 0.704 Nm, 0.985 Nm, and 2.138 Nm for the three stiffness values, respectively. Overall, these figures suggest that the system is able to render a wide range of stiffness values, with good fidelity, across its allowable range.

[0162] This example discloses the design and characterization of Elastic Spinners, a novel bidirectional torsional elastic element for rotary SEAs. Elastic Spinners features a set of identical off-the-shelf linear compression springs arranged in an arc formation on rigidly connected, coaxial output rotor plates. This configuration results in a reaction torque that is linearly proportional to the deformation angle between the input and output rotors. Presented in this example was a design procedure that enables the selection of suitable off-the-shelf springs based on the desired torque capacity and deformation range. Although the design procedure was validated with a dual-rotor model featuring five springs mounted on each rotor, a wide range of passive stiffness values can be obtained by varying the number of output rotors, the number of springs per each rotor, or the type of linear compression spring. As such, Elastic Spinners aligns with recent trends in SEA design, which prioritize modular elastic elements that can be fine-tuned to a specific application, with minimal re-design efforts [Bons et al., 2023],

[0163] Fig. 16 is a plot showing a comparison of deformation ranges (i.e., torque capacity per unit of passive stiffness) between Elastic Spinners and state-of-the-art devices. Blue circles represent monolithic designs, blue-green circles represent two- element planar springs, blue-red circles represent elastic elements that use linear springs, and the red circle indicates Elastic Spinners.

[0164] A key novelty of the disclosed Elastic Spinners lies in the use of linear compression springs in a new arc formation, which enables a linear response within a wide passive deformation range, as well as low hysteresis, nearly null backlash, and relatively high torque capacity, in a compact and lightweight design. Indeed, the presented dual-rotor prototype can exert up to 18 Nm, offering a large passive deformation range of ±24 deg, and a small (external diameter 82 mm, thickness 18.5 mm) and lightweight (0.217 kg) form factor. The use of widely-available off-the-shelf linear compression springs help reduce the fabrication costs. While SEA elastic elements featuring off-the-shelf springs have been previously described in the literature, existing prototypes do not match Elastic Spinners’ deformation range. For example, the Attorney Docket No.: 206572-0008-00WO deformation range of Elastic Spinners is significantly larger than the ±10.3 deg and ±4.5 deg afforded by designs that utilize linear compression springs arranged tangentially [Tsagarakis et al., 2009], [Toubar et al., 2022] - a design solution that introduces the additional drawback of a non-linear stiffness response. The deformation range of Elastic Spinners also exceeds the values reported in [Tiseni et al., 2021], [Zhao et al., 2024] for elastic elements based on linear tension springs. Such designs achieve good linearity over deformation ranges of approximately ±10 degrees. However, the use of tension springs typically limits the torque capacity of the elastic element in relation to its stiffness and form factor (e.g., torque capacity of 8 Nm with stiffness of 72.4 Nm / rad and 130 mm external diameter [Tiseni et al., 2021], torque capacity of 11.3 Nm with stiffness of 64.2 Nm / rad and 96 mm external diameter [Zhao et al., 2024]). Compared with state-of-the-art SEA elastic elements, the innovative arc spring layout of Elastic Spinners produces the largest deformation range while also maintaining a linear response (see Fig. 16). Notably, a small deformation range implies a moderate torque capacity per unit of passive stiffness. This indicates that, in relation to its stiffness, the SEA elastic element cannot generate a significant amount of torque. Additionally, Elastic Spinners achieved an average percentage energy loss of just 2.87% over its deformation range. This value is substantially less than the 5% energy loss reported for the torsional spring in [Bons et al., 2023], despite the deformation range of Elastic Spinner being over 1.5 times larger, and represents a clear advantage in portable and wearable applications that are often battery- powered. Several design features contribute to the minimal energy dissipation of Elastic Spinners. The springs are mounted with preload within arc slots in the output rotors, and equally protrude from each side of the rotor plate. This symmetric configuration keeps the spring coils centered with respect to the walls of spring chambers machined on the input rotor, allowing the springs to undergo ideal deformation. It also prevents sliding contacts between each spring and its chamber while the elastic element undergoes deformation (see Figs. 1 A & IB). In addition, each output rotor is seated against the extended inner ring of a bearing, which provides axial clearance between the inner and the outer rotor surfaces and greatly reduces frictional forces as the rotors rotate relative to each other. Attorney Docket No.: 206572-0008-00WO

[0165] FEA was utilized followed by fatigue analysis to inform material selection for a high-strength, lightweight, and durable design. The estimated service life (133,732 loading cycles) was deemed appropriate for the intended application. For example, if the SEA is fitted to an ankle exoskeleton for gait rehabilitation and the device provides maximal assistance (18 Nm) once per gait cycle, the elastic element would need to be replaced after approximately 50 rehabilitation sessions, assuming a nominal pace of 120 steps per minute and a standard 45-minute PT exercise session.

[0166] The disclosed Elastic Spinners enables a large dynamic range (on the order of 1000: 1) and high torque bandwidth (exceeding 8.4 Hz at 75% of torque capacity). Both metrics are critical in dynamic applications that require both high torque sensitivity and large torque capacity, such as pHRI applications (e.g., rehabilitation and assistive powered orthoses and exoskeletons, active prostheses) and legged robots. The dynamic range of Elastic Spinners outperforms existing SEA torsional springs with comparable or even higher stiffness, including the monolithic spring in [Carpino et al., 2012] (dynamic range of 101.3: 1, stiffness 98 Nm / rad) and the torsional elastic element based on linear tension springs in [Tiseni et al., 2021] (dynamic range of 145.3: 1, stiffness 70.4 Nm / rad). In terms of closed-loop torque bandwidth, Elastic Spinners demonstrated superior performance to existing SEA elastic elements whose passive stiffness is within the same order of magnitude, such as the monolithic designs in [Sergi et al., 2012] and [Dos Santos et al., 2017], at both high (12 Nm) and moderate (6 Nm) torque amplitudes, despite the monolithic designs having higher passive stiffness (82 to 119 Nm / rad, vs. 43.8 Nm / rad). The high torque bandwidth of Elastic Spinners results from a gearless transmission and a carefully designed spring chamber system. Although higher bandwidth values have been reported in the SEA literature (e.g., 39.6 Hz for an elastic element based on linear tension springs in [Tiseni et al., 2021]), these designs are typically intended for low-torque applications and are therefore tested with smaller- amplitude chirp inputs (e.g., 1 Nm amplitude for the design in [Tiseni et al., 2021]).

[0167] While the results of this example are promising and may pave the way for the use of Elastic Spinners in several pHRI applications, it was noted that the SEA performance presented in this example are based on a testing rig fabricated ad-hoc, where the elastic element was driven by a cable loop. Thus, the closed-loop torque bandwidth of Attorney Docket No.: 206572-0008-00WO the SEA may slightly degrade in practical applications requiring the use of Bowden cables for remote actuation, because of the additional mechanical impedance. Conversely, the dynamic performances can be further improved by directly connecting Elastic Spinners to the output shaft of a BLDC motor, a common SEA configuration.

[0168] In this example, the disclosed Elastic Spinners were configured with a gearless actuator and a cable loop realizing a moderate (6: 1) transmission ratio to enhance the SEA’s torque bandwidth [Veneman et al., 2006], [Robinson et al., 1999], However, this came at the cost of a less compact SEA actuator for the desired torque capacity. Although gearboxes may produce more compact and potentially lighter SEA designs [Zhao et al., 2024] — key advantages in portable applications — they also increase energy losses and mechanical impedance, in addition to introducing non-linearities such as stiction, backlash, and cogging [Howard, 1990], making torque control more challenging [Kong et al., 2011], In some embodiments, Elastic Spinners may comprise any additional configurations featuring multirotor designs. This approach extends the torsional stiffness and dynamic range of the dual-rotor configuration presented in this example, while maintaining its deformation range. In some embodiments, the disclosed Elastic Spinners may be used with an exoskeleton (e.g., ankle exoskeleton), where the backdrivability, wide passive deformation range, and high bandwidth of Elastic Spinners are leveraged to ensure safe physical assistance to the wearer.

[0169] Introduced herein was the design of Elastic Spinners, a novel bidirectional torsional elastic element for rotary SEAs. The innovative layout of Elastic Spinners features rigidly connected coaxial output rotors housing linear compression springs in a new arc formation, enabling a linear response within a wide passive deformation range, as well as low hysteresis, nearly null backlash, and relatively high torque capacity, in a compact and lightweight assembly.

[0170] Dynamic characterization tests performed on Elastic Spinners configured within a SEA demonstrated high fidelity in torque tracking. Overall, the combination of a small and lightweight form factor, high torque capacity and dynamic range, and linear response over a large deformation range makes Elastic Spinners suitable for a wide range of robotic applications. Attorney Docket No.: 206572-0008-00WO

[0171] Example 2: A Novel Personalized Ankle Exoskeleton with Co-Located SEA for Gait Training

[0172] Gait rehabilitation programs help individuals who sustained a brain injury or severe lower-leg trauma realize their full recovery potential. While robotic exoskeletons have emerged as promising tools for gait rehabilitation, high costs and “one- size-fits-all” designs that sacrifice user comfort and fit hinder their wider adoption in clinical settings.

[0173] In this example, disclosed is a new modular ankle exoskeleton featuring a personalized Ankle Unit and a portable Actuation Unit. The Ankle Unit is fabricated using affordable additive manufacturing processes to conform to the user’s leg morphology. The Actuation Unit, which can be shared across different Ankle Units, utilizes a cable loop to transfer mechanical power to a first-of-its-kind, lightweight, high- stiffness rotary elastic module co-located with the ankle joint to ensure accurate bidirectional torque tracking. Promising results from bench testing and treadmill walking indicate feasibility of the proposed design.

[0174] Neurological conditions and lower-limb trauma are frequently associated with persistent gait impairments [Potter et al., 2018], Task-specific gait training has been shown to promote motor recovery and improve gait function. Given that the ankle plays a crucial role in stabilizing and propelling the body [Winter, 1991], ankle exoskeletons are among the most common lower-limb robotic technologies proposed to enhance or restore ambulatory function through exercise training [Bae et al., 2018; Kobsar et al., 2020; Lee et al., 2023], Despite these advances, how to design ankle exoskeletons to best promote recovery of walking function is still an open research problem. In this regard, a key aspect of traditional exercise-based therapy, i.e., the importance of personalizing the interventions to the patient, has been largely overlooked. The mechanical structure of most ankle exoskeletons is handmade by professional orthotists using plaster molding and thermoplastic vacuum forming, in a similar fashion to traditional passive orthoses [Zhang et al., 2019] - a process that offers limited design options and involves significant labor. Readjustments are often required to improve comfort and fit, but these cannot completely prevent skin abrasions, bruises, pressure sores, and blisters from developing with orthotic use [Menger et al ., 2016], Since discomfort is the leading cause of low Attorney Docket No.: 206572-0008-00WO patient compliance with orthotic interventions [Swinnen et al., 2018], there is a compelling need for a new design methodology to enable the fabrication of personalized orthoses. This need is even more critical for powered orthoses and exoskeletons, which provide active assistance to the wearer, resulting in larger human-orthosis interaction forces [Langlois et al., 2018],

[0175] Optimizing the weight distribution can also contribute to improving comfort in wearable robots [Lee et al., 2023], To this end, ankle exoskeletons often rely on cable actuation to remotely transfer mechanical power to the lower leg [Bae et al., 2018; Kobsar et al., 2020; Lee et al., 2023; Zhong et al., 2023], This design solution allows the heaviest components to be worn close to the body center of mass to reduce the exoskeleton’s burden on the user [Bae et al., 2018; Gasparri et al., 2019], On the other hand, cable actuation introduces additional frictional forces that are challenging to compensate using feed-forward models alone, making it difficult to accurately estimate the applied ankle torques unless co-located force transducers are used. Bae et al. [Bae et al., 2018] utilized two load cells mounted in-line with the distal ends of the two actuation cables of a soft ankle exosuit. This approach results in added costs and design complexity and requires knowledge of the wearer’s anatomical parameters to estimate the ankle interaction torque, which may affect its accuracy and ease of applicability. Additionally, while exosuits do naturally conform to the wearer’s body, thereby ensuring good fit, they do not provide the level of mediolateral ankle support that semi-rigid exoskeletons can afford. For this reason, semi-rigid designs are more suited for patients with moderate to severe impairments.

[0176] Series elastic actuators (SEA) are often used in physical Human-Robot Interaction (pHRI) for their ability to implement “safety by design, performance by control,” a key pHRI paradigm [Albu-Schaeffer et al., 2005], Indeed, a system’s closed- loop impedance reduces to the SEA passive impedance when external disturbances are beyond the controller bandwidth [Carpino et al., 2012], In addition, the SEA compliance may improve torque tracking performance by reducing non-linearities such as those due to friction and backlash in cable-driven wearable robots [Carpino et al., 2012], The elastic element is a critical component of a SEA, as it determines its range of actuation and torque resolution, and contributes to its closed-loop bandwidth [Lee et al., 2023], When Attorney Docket No.: 206572-0008-00WO the elastic element of a SEA is co-located with the human joint it is designed to assist, interaction torques can be directly estimated from the deformations of its elastic element, thereby providing an accurate and nearly zero-lag reference for the low level-controller. Yet, designing compact and lightweight co-located SEAs for ankle exoskeletons remains a significant challenge given the ankle’s high torque demands. Most solutions proposed to date are rather bulky, which may pose obstacles to their routine use by individuals with gait impairments [DeBoer et al., 2022; Langlois et al., 2018; De Gaitani et al., 2022], An alternative solution is to use non-collocated SEAs. Zhong et al. [Zhong et al., 2023] introduced a pair of backpack-mounted SEAs for a unilateral cable-driven knee-ankle exoskeleton. While their design improves the exoskeleton’s mass distribution on the user body, it does not allow for accurate estimations of the interaction torques due to unmodeled friction forces in the transmission cables. Lee et al. [Lee et al., 2023] proposed a pair of compact hip-pack mounted SEAs for a cable-driven ankle exoskeleton and developed a feed-forward friction compensator informed by the current gait phase. Although their compensator can effectively improve the exoskeleton’s force tracking performances, it assumes a predefined level of assistance, it requires subject-specific calibration, and it does not account for the effects of varying walking speed or changing cable bending angles on the frictional forces. Moreover, their design requires two motors to actuate a single degree of freedom, a solution shared by other designs [Bae et al., 2018; Zhang et al., 2019], which nonetheless is suboptimal for a wearable device where weight is a key design constraint.

[0177] Fig. 2 is an image depicting front and back views of a prototype of an exemplary portable exoskeleton, referred to in some examples as “Strider”, developed to assist walking exercises in individuals with lower-limb impairments.

[0178] In this example, disclosed is a new modular ankle exoskeleton, referred to as “Strider” (see Fig. 2), featuring a personalized Ankle Unit and a backpack Actuation Unit. The Ankle Unit is fabricated using a design workflow that builds upon previous work [ASME Int. Meeh. Eng. Congr. and Expo, 2021], which generates a subject-tailored model from 3D scans that capture essential user-specific anatomical parameters. Strider is equipped with a lightweight, high-stiffness, wide range-of-motion, rotary elastic module co-located with the wearer’s ankle and powered by the backpack Actuation Unit via a Attorney Docket No.: 206572-0008-00WO single cable loop. This solution ensures accurate interaction torque tracking while keeping a favorable mass distribution, without relying on friction compensators or dedicated load cells. While a similar concept has been recently proposed by Du et al. [Du et al., 2023], their ankle exoskeleton is designed to provide dorsiflexion assistance only, and therefore their device does not meet the high torque requirements needed to assist the ankle during push-off.

[0179] Fig. 17 is a flowchart illustrating the proposed design workflow to generate personalized Ankle Units.

[0180] PERSONALIZED DESIGN WORKFLOW: Previous work on individualized ankle exoskeletons relied on a two-step workflow [ASME Int. Meeh. Eng. Congr. and Expo, 2021], First, a one-time generic model was created. This parameterized model allowed customization during the second step, based on the features extracted from a 3D scan of the wearer’s leg. Building upon previous work, a refined workflow was introduced which aims to automate the design of a subject-tailored ankle-foot orthosis that serves as Strider’s Ankle Unit.

[0181] Shank Bracket Design: The proposed algorithm calls five tools to process the data collected at the scanning step and constructs the shank bracket design (see Fig. 17). Each tool is modular, allowing independent use. The algorithm can be executed from a Graphical User Interface (GUI), offering an accessible way for loading the data, identifying references on new points, and creating new designs. The input of the pipeline is a point cloud representing the scanned surface of the wearer’s leg. The algorithm is written in Python and uses Open3D.

[0182] The first tool (Markers Detector) identifies key references. It receives a point cloud ( ply) file as an input and returns the center and radii for each of the four reflective markers located at bony landmarks (medial / lateral femoral condyles and malleoli) to identify knee and ankle anatomical axes. To this end, the point cloud is first divided into 4 subpoint clouds after finding midpoints between the vertices of the original bounding box. Subsequently, the new bounding boxes, each containing one marker, are processed using the Random Sample Consensus (RANSAC) [Fischler and Bolles, 1981] algorithm to find clusters in the data selected by the user through a point picker application. Then, the algorithm fits a sphere to the data in the cluster. Attorney Docket No.: 206572-0008-00WO

[0183] The second tool (Mapper) receives an array of coordinates representing the center of the detected markers and the point cloud as inputs. The output is a point cloud containing the points that represent the surface on the calf. The references are the center of the markers detected using the first tool, and can be selected from a drop down menu in the GUI. These references define new axes and key points for the shank bracket design. The points from the point cloud whose height lies between the height of the top and bottom markers (i.e., points A, B, C, and D in Fig. 17) are kept. The point cloud is then split into posterior and anterior volumes by defining a plane that passes through the midpoint between the top markers (point E) and the ankle markers (points C, D).

[0184] The third tool (Mesher) uses the Ball Pivoting algorithm [Bernardini et al., 1999] to interpolate the surface of the split point-cloud, returning a triangle mesh (. stl) file as output. This algorithm uses a ball of user-specified radius which pivots around an edge, starting from a seed triangle, generating the mesh triangles every time it touches three points without “falling” through the points. To define the radius of the sphere, the distance between points in the point-cloud is required to be less than half the size of the features of interest. This requirement is easily achieved since most current scanners produce dense samplings. For the disclosed implementation, spheres with radii 0.1, 1.0, and 5.0 mm were used. Subsequently, triangles that reference the same three vertices and have the same orientation as well as unreferenced vertices are removed from the mesh, and triangle and vertex normals are computed before retrieving the final mesh.

[0185] Since the output of the previous step is a surface, its topological representation is a 2D manifold. To build a 3D solid, the fourth tool (Slicer) receives the mesh from step 3 and slices it using a set of planes orthogonal to the shank longitudinal axis, obtaining a set of curves that discretize the surface. Each curve contains the points that represent the contour of the user’s shank at certain height. New points are created by finding the centroid of the curve and extrapolating the new points in the direction of the centroid-data vector by a predefined thickness value. This thickness value is constrained by two factors: stiffness / strength, and kinematic constraints. The desired stiffness and strength define the minimal amount of material for the shank bracket to be strong but comfortable to wear. The kinematic constraint refer to the coupling between the shank and shoe brackets. The new points surround and close the original curve, allowing the Attorney Docket No.: 206572-0008-00WO creation of one face per slice. Subsequently, the points defining each face are exported to .csv files, one per slice.

[0186] The fifth and last tool (Solid Generator) builds a solid by connecting the points on the contours and constructing triangles in-between. After reading the points in the faces, artificial triangles are created to bind adjacent faces, hence obtaining a 3D object that is exported as a mesh (. stl) file for printing.

[0187] Shoe Bracket Design: The shoe bracket is designed following a similar process as described in this example. First, the leg scan is trimmed to the section of interest containing the shoe. An offset surface is created from the shoe, with 1 mm offset. The surface is then thickened to create a solid, and trimmed to an aesthetic profile design. To control the exterior shape of the shoe bracket, the solid is sliced into multiple profiles, a spline tool is used to create splines, and these splines are lofted together to obtain the final design (see Fig. 17).

[0188] Fig. 3 is an image depicting a perspective view of the exemplary exoskeleton (i.e., Strider Ankle Unit). Red parts indicate personalized components.

[0189] SYSTEM DESCRIPTION: In some embodiments, Strider comprises a personalized Ankle Unit, an Actuation Unit fitted on a protective back shield, and a custom-built Li-ion battery anchored on a waist belt. In some embodiments, mechanical power is transmitted from the Actuation Unit to the wearer’s ankle through a novel bidirectional torsional rotary SEA, whose elastic module is co-located with the user’s ankle joint (see Fig. 3), via a Bowden cable loop. In some embodiments, assistive torques from the SEA are transmitted to the user’s ankle via a custom bracket attached to the wearer’s shoe using screws. Unlike ankle exoskeleton designs based on shoe inserts, the disclosed solution leverages the shoe’s padding to improve user comfort. The weight of the Ankle Unit is 0.8 kg. The heaviest components (5.2 kg Actuation Unit, 1.3 kg Li-ion battery) are located near the body center of mass, to reduce undesired effects of the device’s inertia on the wearer’s natural gait. Herein the mechatronic design of the Strider exoskeleton is described in detail.

[0190] Ankle Unit: An exemplary Ankle Unit is illustrated in Fig. 3, and comprises a personalized shank fabricated from Carbon fiber-PLA (CF-PLA) utilizing FDM 3D printing technology. This shank is constructed ad-hoc, following the workflow Attorney Docket No.: 206572-0008-00WO described in this example. In some embodiments, a 3 mm soft foam layer, contoured to match the inner curvature of the shank using laser cut technology, is positioned as a cushioning interface between the shank module and the wearer’s skin. This layer can be easily removed and washed to maintain cleanness and hygiene. In some embodiments, the shank is secured to the wearer’s shinbone using a wide Velcro strap to ensure comfort. In some embodiments, the shank also provides anchoring points for the Bowden cables operating the SEA elastic element. In some embodiments, the SEA output shaft is connected to a torque-link, which attaches to the lateral side of the personalized shoe bracket. In some embodiments, the SEA elastic element comprises co-axial inner and outer rings, which can rotate ±24° relative to each other. In some embodiments, the outer ring comprises a groove for the Bowden cable loop (steel cable, 1.1 mm diameter) and is connected to a pair of inner rings, rigidly connected to the SEA output shaft via two sets of 5 compression springs arranged circumstantially, to generate an equivalent torsional spring (see Figs. 18A & 18B). In some embodiments, the SEA elastic element is equipped with a miniature optical encoder (El 6 — US Digital with 16384 PPR) to measure the deformation of the SEA, thereby providing torque feedback for the closed- loop torque controller. In some embodiments, a second position sensor (NP24HS-lk Q, P3 America, Inc.) is connected to the medial side of the ankle bracket and is used to measure the ankle plantar and dorsiflexion angle. In some embodiments, the shoe is instrumented with or comprises a Force Sensing Resistor (FSR) underneath the heel to detect initial contacts during walking.

[0191] Fig. 18A is an image depicting a side view of an exemplary SEA elastic module. Fig. 18B is a plot showing the results for the characterization of SEA passive stiffness.

[0192] Figs. 4A & 4B are images depicting views of an exemplary actuation unit for the disclosed exoskeleton (i.e., Strider). Fig. 4A shows a front perspective view of the actuation unit. Fig. 4B shows two rear perspective views of the actuation unit.

[0193] Fig. 19 is a diagram depicting an exemplary torque-velocity cascaded PI controller.

[0194] Actuation Unit: In some embodiments, the Actuation Unit (see Figs. 4A & 4B) comprises a backpack-like enclosure (260 mm high, 134 mm thick, 230 mm max Attorney Docket No.: 206572-0008-00WO width), which is fitted on an articulated protective shield (Motorcycle Back Protector, Ridbiker) and can be used to power either left- or right-side Ankle Units. In some embodiments, the actuator comprises a brushless motor (EC-90-flat, 600 W, Maxon Group, Switzerland), with integrated encoder (Maxon Mile Encoder 4096 CPT), a motor driver (Maxon EPOS4 Compact 50 / 15), a Unit Real Time Target Machine (Speedgoat GmbH, Switzerland), and a custom-made data acquisition and conditioning (DAQ) board that features a 32-bit microcontroller (Teensy 3.5, PJRC, USA), an EasyCAT PRO shield (AB&T Sri, Italy) and a 12-bit ADC (Analog Devices, Wilmington, MA, USA). The Real Time Target Machine, the motor driver, and the DAQ communicate over EtherCAT bus. In some embodiments, the motor output shaft is connected to a threaded spool (effective diameter: 12.4 mm) to allow for cable winding / unwinding without overlapping. In some embodiments, cable aligners featuring a pair of needle roller bearings are used to keep the cables within pulley grooves. In some embodiments, a cable tensioner, which can be relocated using a friction-based positioning lock to fit different users, prevents the cables from slacking during operation. In some embodiments, the outer ring of the SEA has an effective diameter of 76.6 mm, thereby generating a transmission ratio of approximately 6: 1. In some embodiments, the maximum assistive torque provided by the exoskeleton is 18 Nm, which corresponds to approximately 15% of the peak ankle PDF torque for a 75 kg adult male walking at normal pace [Winter, 1991], Notably, this is achieved without the use of a gearbox, thus making the ankle exoskeleton backdrivable.

[0195] Li-ion Battery: A custom Li-ion battery is designed with a peak current of 30 A, a nominal voltage of 29.4 V (close to the motor’s nominal voltage 30 V), and capacity of 7000 mAh. The battery is made of a custom assembly of SANYO NCR18650GA Li-ion Batteries (Sanyo Electric Co., Ltd., Japan) with on-board battery management system and voltage indicator.

[0196] Figs. 20A & 20B are plots showing the results from a torque-tracking performance test of the disclosed exoskeleton. The exoskeleton’s ankle joint was manually moved to track a sinusoidal trajectory (Fig. 20 A), and the commanded torque id (Fig. 20B, blue line) was generated by a virtual torsional spring. The measured torque (Fig. 20B, red line) largely matched the commanded torque, indicating good tracking performances (RMSE = 0.40 Nm). Attorney Docket No.: 206572-0008-00WO

[0197] Fig. 21 is an image of a subject walking on a treadmill, with the Strider exoskeleton fitted to his left leg.

[0198] Fig. 22 is a plot showing interaction torque measured at the ankle joint during zero impedance treadmill walking at 1.3 m / s.

[0199] LOW LEVEL CONTROLLER: As shown in Fig. 19, the disclosed exoskeleton (i.e., Strider) utilizes a cascaded velocity torque controller whereby a PI compensator in the outer loop (PlTorquc) generates the reference velocity for an inner loop PI compensator (Plvelocity) [Vallery et al., 2008], The SEA deformation is used to estimate the current interaction torque. By adopting a high-resolution miniature encoder, the SEA can appreciate angular deformations as small as 79.1 arcsec, corresponding to approximately 16.8 mNm (see Fig. 18). The gains for the outer loop velocity controller are auto-tuned using EPOS Studio v3.7, whereas the outer loop gains are tuned manually.

[0200] PERFORMANCE EVALUATION: Torque-tracking performance test: A torque-tracking performance test was conducted by simulating the ankle range of motion expected during locomotion. The commanded torque rd was obtained by rendering a zero-length torsional spring with a spring rate k = 0.3 Nm / deg. To perform the test, the shank bracket was secured to a workbench using ratcheting bar clamps, and the shoe was manually rotated relative to the shank bracket to track a sinusoidal reference trajectory (frequency: 0.5 Hz, amplitude: 20°) displayed on a computer screen, which resulted in id oscillating between ±6 Nm. As shown in Fig. 20, the controller tracked the reference torque well, with a root mean square error (RMSE) of approximately 0.40 Nm.

[0201] Treadmill Walking Test with Zero Impedance: To test Strider’ s closed- loop transparency, an able-bodied individual (31 year old male, 178 cm height, 77 kg weight) walked on a treadmill at his comfortable walking speed (1.3 m / s) for 3 minutes (see Fig. 21), while the exoskeleton was controlled in zero-torque mode (i.e., rd = 0 Nm). Fig. 22 shows the results from a one-minute section of the full test. The RMSE was 0.27 Nm and the peak torque error was approximately 0.6 Nm. These torques correspond to 0.21% and 0.48% of the expected maximum biological ankle moment for normal-pace walking, respectively [Winter, 1991],

[0202] In this example disclosed was a personalized cable-driven exoskeleton (i.e., Strider) designed to provide bidirectional ankle assistance to individuals with Attorney Docket No.: 206572-0008-00WO walking impairments during exercise therapy. The exoskeleton leverages a new design workflow that automates the creation of personalized Ankle Units from a 3D scan of the user’s lower leg. To reduce the exoskeleton’s burden on the user while ensuring accurate torque tracking, the proposed design features a single, non-collocated backdrivable actuator and a co-located SEA elastic module. In some embodiments, the Ankle Unit weights 0.8 kg, including the series elastic module (0.2 kg), and can exert up to 18 Nm at the user’s ankle. This is in line with the 0.7 kg weight of the design recently presented in [Du et al., 2023], which nonetheless can only apply up to 12.5 Nm at the ankle, and outperforms the weight (2.85 kg) of the ankle exoskeleton introduced in [DeBoer et al., 2022], which however features a highly geared, co-located actuator. Notably, Strider’s maximal torque assistance also exceeds the 14 Nm limit reported in [Zhong et al., 2021], despite not relying on gearboxes. Compared with the ankle exoskeleton presented in [Orekhov et al., 2021], which showcases an impressive 30 Nm peak torque at the ankle and a low distal mass of 0.415 kg per leg, the Strider’s Ankle Unit is heavier but may result in better torque tracking (i.e., RMSE of 0.4 Nm vs. 1.75-5.20 Nm) by eliminating the gearbox and integrating a co-located SEA. Strider’s SEA design guarantees very good closed-loop transparency. While the peak interaction torque during walking at 1.3 m / s was 0.6 Nm, which seemingly exceeds the 0.28 Nm peak reported by Zhong et al. [Zhong et al., 2021], their zero-torque response was measured at the proximal end of the Bowden cables, thereby neglecting the mechanical impedance of the cable transmission, and at slow pace (0.88 m / s). Strider’s SEA leverages affordable off-the-shelf springs in a compact parallel arrangement that ensures excellent linearity. This is in contrast to other SEA designs utilizing off-the-shelf parts [Du et al., 2023; Qian et al., 2022], which obtained highly non-linear responses that may limit the SEA stability region [Sun et al., 2020] and require the implementation of iterative numerical methods in the low-level control loop. Efforts are directed toward evaluating the benefits of the personalized design workflow in terms of comfort and fit, thorough tests with able-bodied individuals and those with motor impairments, using both subjective and objective metrics. In some embodiments, the system comprises an adaptive controller to enable robot-assisted overground walking exercises. Attorney Docket No.: 206572-0008-00WO

[0203] Example 3: Reinforcement Learning Assist- As-Needed Control Promotes Recovery of Walking Speed Following Ankle Weight Perturbations

[0204] Self-selected walking speed is a key outcome for exercise-based rehabilitation programs following lower extremity trauma. This example discloses a novel reinforcement learning-based assist-as-needed (RL-AAN) controller for ankle exoskeletons, aimed at gait speed training. Built on an actor-critic architecture, the RL- AAN controller integrates a control objective that balances the trade-off between expected stride velocity (SV) errors and exoskeleton assistance. This approach allows the exoskeleton to progressively reduce ankle plantar- and dorsiflexion (PDF) assistance as the user’s performance improves, promoting active participation. The desired assistive torque is computed as the product of the actor output and the wearer’s biomechanical ankle PDF moment, estimated by a subject-agnostic model, thereby ensuring personalized and biomechanically relevant assistance. In a proof-of-concept study with healthy individuals walking on a self-paced treadmill, the RL-AAN controller facilitated the recovery and retention of natural walking speed following ankle weight-induced perturbations, outperforming a conventional fixed-gain controller in both immediate and short-term training effects. This finding highlights the potential of RL-AAN control for subject-tailored gait training, with promising clinical implications for exercise based rehabilitation in individuals with neurological or musculoskeletal gait impairments.

[0205] High-Energy Lower Extremity Trauma (HELET) represents a significant health concern, particularly within military populations, where combat-related blast and blunt injuries frequently result in severe damage to the lower limbs [Gordon et al., 2015], Among civilians, vehicle accidents and falls account for over 40% of the 862,000 trauma- related hospitalizations recorded in North America each year [Chang, 2016], Advances in reconstructive surgery have enabled an increasing number of limb salvages in HELET cases [Black et al., 2021], However, individuals with reconstructed lower limb often exhibit motor deficits that can resemble, or even exceed, those seen in patients who undergo amputation [Major Extremity Trauma Research Consortium, 2021], Selfselected walking speed is among the key outcomes for HELET rehabilitation programs [Potter et al., 2018], Although growing evidence suggests that dynamic (i.e energystoring) ankle-foot orthoses (AFOs), when combined with a high-intensity rehabilitative Attorney Docket No.: 206572-0008-00WO regimen, effectively improve gait speed in HELET patients [Highsmith et al., 2016], these passive AFOs resist normal plantarflexion movements, which may lead to undesirable compensatory strategies and poor gait mechanics [Mangan et al., 2016], Powered orthoses and exoskeletons may address these limitations by injecting controlled torques that reduce limb loading without restricting plantar- or dorsiflexion motions, promoting a more natural and biomechanically efficient gait. However, the use of powered AFOs in HELET rehabilitation to facilitate the recovery of walking function, and gait speed in particular, remains largely underexplored [Esposito et al., 2018], Lower-limb exoskeletons can offer personalized adaptive support tailored to a patient’s specific needs, to assist or rehabilitate their walking function [Shi et al., 2019; Arunkumar and Jayakumar, 2024], While whole leg exoskeletons offer the most significant improvements in walking performance [Franks et al., 2021], single-joint devices are often more efficient in terms of weight, size, and cost. Among single-joint exoskeletons for the hips, knees or ankles, the latter class provides the greatest enhancement in energy efficiency [Franks et al., 2021], The controller plays a crucial role in the design of powered orthoses and exoskeletons. Learning based control strategies have gained popularity in both assistive and rehabilitative applications [Belal et al., 2024], with reinforcement learning (RL) based methods gaining traction in recent years [Zhang et al., 2024], Zhang et al. proposed both stride-dependent [Zhang et al., 2019; Zhang et al., 2020] and phase-dependent [Zhang et al., 2022] RL controllers to elicit desired ankle joint adaptations during robot-assisted training with a powered AFO. Tu et al. [Tu et al., 2021] developed a data-driven RL framework to dynamically personalize the assistive torque profde of a unilateral hip exoskeleton for reducing user effort. Luo et al. [Luo et al., 2023] introduced a robust RL -based control approach for a multi-joint lower limb rehabilitation exoskeleton, integrating a musculoskeletal model and domain randomization to handle uncertain patient conditions and ensure stable, autonomous walking assistance.

[0206] Several powered ankle devices have demonstrated immediate improvements in users’ self-selected walking speed. Orekhov et al. [Orekhov et al., 2020] reported a 6.3% increase in overground walking speed when individuals with cerebral palsy walked with an untethered powered AFO that provided a fraction of the Attorney Docket No.: 206572-0008-00WO instantaneous biological plantar- and dorsiflexion (PDF) moment. Sloot and colleagues [Sloot et al., 2023] reported a 6.7% increase in the overground walking speed of hemiparetic patients who walked with a unilateral cable-driven ankle exosuit that provided timed support to assist push-off and ground clearance. Song et al. [Song and Collins, 2021] applied a human-in-the-loop on-line optimization method to fine-tune a parameterized reference torque profile for the wearer of a tethered ankle exoskeleton, reporting a 42% increase in self-selected treadmill walking speed compared to unassisted walking in healthy adults. However, all these controllers were designed to provide immediate assistance to the user; therefore, their value for exercise training cannot be assessed, as retention tests were not conducted.

[0207] Active effort is a critical enabler of motor recovery during exercise-based rehabilitation [Huang and Krakauer, 2009], Thus, it has been postulated that robotic trainers should act transparently when the user performs well and intervene only when the user experiences difficulty in completing the task, correcting excessive movement errors. Control strategies that align with this principle are commonly referred to as “assist-as-needed” (AAN) controllers [Emken et al., 2007], In this example, disclosed is the first RL-based AAN controller (RL-AAN in short) targeting walking speed rehabilitation. Building upon the actor / critic structures presented in [Zhang et al., 2019; Zhang et al., 2020], and the subject-agnostic ankle PDF moment estimator introduced in [Zhao et al., 2024], the RLAAN controller modulates the level of AFO assistance - defined in terms of percentage of the wearer’s biomechanical ankle PDF moment - based on the wearer’s recent training performance, to elicit a target stride velocity. The RLAAN controller was implemented in the Strider exoskeleton [Eraky et al., 2024] and tested against a conventional fixed-gain controller with a group of able-bodied individuals on a self-paced treadmill using a perturbed-gait protocol.

[0208] Fig. 23 is an image showing an exemplary Strider exoskeleton [Eraky et al., 2024] fitted on a study participant. Fig. 5 is an image showing two ankle weights (1 kg each, orange box) attached to the distal end of the exoskeleton’s shank bracket to generate a perturbation.

[0209] METHODS: Ankle Exoskeleton: A unilateral, cable-driven, untethered ankle exoskeleton with a subject-tailored design was developed. As shown in Fig. 23, the Attorney Docket No.: 206572-0008-00WO exoskeleton features a personalized ankle unit, obtained from a 3D scan of the subject’s leg using an automated design workflow and fabricated with fused deposition modeling (FDM) 3D printing technology in carbon fiber- PLA (CF-PLA) to ensure a customized fit [Eraky et al., 2024],

[0210] The actuation unit, mounted on an articulated protective shield, can be used to power either the left or right ankle unit. In some embodiments, the actuation unit houses a brushless motor (EC-90-flat, 600 W, Maxon Group, Switzerland), a motor driver (FE060-25-EM, ADVANCED Motion Controls, USA), a Real-Time Target Machine (Speedgoat GmbH, Switzerland), and a custom-made data acquisition and conditioning (DAQ) board. In some embodiments, the motor output shaft drives a threaded spool (effective diameter: 12.4 mm) to enable cable winding / unwinding without overlapping. In some embodiments, a Bowden cable loop transmits mechanical power to a lightweight (200 g), high-stiffness (43 Nm / rad) bidirectional rotary elastic module at the ankle joint. In some embodiments, the elastic module has an effective diameter of 76.6 mm, providing a transmission ratio of approximately 6:1, resulting in a maximum assistive torque of 18 Nm. In some embodiments, a magnetic encoder (AS5048A, AMS- Osram, Austria) measure the elastic element’s deformation to estimate interaction torques, which are used as feedback for the low-level cascaded torque-velocity controller. In some embodiments, A potentiometer (NP24HS, P3 America, USA) measures the ankle PDF angle. Additionally, In some embodiments, an 8-cell force sensitive resistor (FSR) array (IEE S.A., Luxembourg) and a 9-degree-of-freedom inertial measurement unit (3- Space IMU, Yost Labs Inc. OH, USA) embedded in the exoskeleton’s shoe module inform the online ankle PDF moment estimator. In some embodiments, the Real-Time Target Machine, motor driver, and DAQ board communicate over an EtherCAT bus at 1 kHz. Further details about the Strider exoskeleton design and its low-level controller can be found in [Eraky et al., 2024],

[0211] Subject- Agnostic Ankle Moment Estimator: To generate personalized and biomechanically relevant plantarflexion assistance, the subject-agnostic online ankle moment estimator introduced in [Zhao et al., 2024] was utilized. The estimator, which is based on ensemble Gaussian Process Regression (GPR) models, integrates data from the in-shoe 8-cell FSR array, the IMU, and the ankle PDF angle, alongside the current gait Attorney Docket No.: 206572-0008-00WO phase estimated by a pool of adaptive oscillators. The output of the estimator, representing the instantaneous PDF moment j ointly exerted by the human muscles and the device, is subsequently subjected to half- wave rectification and scaled by a factor K, providing the reference torque signal for the ankle exoskeleton.

[0212] RL-AAN Controller for Walking Speed Training: The Reinforcement Learning Assist-as-Needed (RL-AAN) controller is designed to elicit desired stride velocity (SV) adaptations towards a target walking speed, while simultaneously reducing the level of assistance provided by the device. It leverages the Action-Dependent Heuristic Dynamic Programming (ADHDP) [Si and Wang, 2001] framework, a modified Heuristic Dynamic Programming algorithm that is well suited for complex systems and features convenient uniformly ultimate boundedness (UUB) properties [Sokolov et al., 2015], A single-feedback state and an actor-critic learning architecture update the controller policy after each initial contact (heel-strike), extending a previous RL-based AAN approach [Zhang et al., 2019] to focus specifically on SV regulation. Both the actor and the critic neural networks (NNs) are nonlinear feedforward NNs with one hidden layer and sigmoid activation functions [Si and Wang, 2001], with training occurring online at each stride. At the i-th gait cycle, the state is defined by the SV error

[0213] Equation 7 where SVtarget is the target SV for the gait training session and SV (i) is the current SV. Since ESV (i) > 0 indicates that the subject is walking slower than the target SV, ESV (i) is also used to define the immediate negative reward r(i) incurred at the i-th gait cycle via the following expression:

[0214] 1 r(i) = 2£sv(02

[0215] Equation 8

[0216] The critic network estimates the approximated long-term cost V (i) of the current policy, based on the current state ESV (i) and the current action K(i), by Attorney Docket No.: 206572-0008-00WO minimizing the squared temporal difference (TD) error td(i) derived from the Bellman equation [Bellman,

[0217] Equation 9 where y = 0.5 is a discount factor. The actor NN learns an optimal policy for updating K(i), the percentage of the ankle PDF moment contributed by the exoskeleton at the i-th stride, which minimizes the cost function:

[0218] Equation 10 where Uc(i) is a specified control objective. Since the actor output is bounded to the interval [0, 1] by the sigmoid activation function, a scaling factor is introduced to restrict K(i) within the feasible range [0, 10]%, where the lower and upper bound indicate no assistance (transparent control) and maximum assistance, respectively. The control objective Uc(k) in Equation 10 is updated after each gait cycle based on the user’s performance over the last m cycles, through the following law:

[0219] Equation 11 where £sv (i) is the arithmetic mean of the SV error measured over the last m = 10 cycles and P = 0.1 is the rate of change of Uc(i). Because Uc(i) G [0, 1] by definition, Equation 10 is the squared convex combination of V(k), representing combined SV errors, and K(i), indicating the current level of exoskeleton assistance, with their relative importance modulated by Uc(i). In essence, Uc embeds the AAN paradigm by dynamically balancing the tradeoff between minimizing long-term SV errors and reducing assistance. If ssv (i) remains low for m consecutive strides, Uc(i) is increased, thereby shifting the trade-off toward minimizing K(i). Conversely, if performance deteriorates, Uc(i) is decreased to prioritize expected SV errors. This adaptive mechanism automatically tunes the level of assistance such that, as the subject recovers their walking Attorney Docket No.: 206572-0008-00WO speed, the controller progressively reduces its intervention to encourage active effort. The overall control architecture is illustrated in Fig. 24. Importantly, the adaptive assistance provided by the RL-AAN controller remains biomechanically relevant, since it is grounded on real-time estimations of the wearer’s biological ankle moment.

[0220] Fig. 24 is a diagram depicting an exemplary Strider control architecture. EXPERIMENTAL SETUP: Protocol: Eight healthy male subjects (weight: 80±12 kg, age: 25±4 yrs, height: 178 ± 8 cm) participated in this study, which was approved by the U.S. Army Office of Human Research Oversight (OHRO) under protocol E03214.1a-l . All study participants provided written informed consent before testing. A self-paced treadmill was implemented by configuring a conventional split-belt instrumented treadmill (BERTEC) with a SV feedback loop leveraging inputs from treadmill-embedded force plates and a 9-camera motion capture system (VICON), as described in [Song and Collins, 2021], This method, which relied on a single marker located on the posterior side of the exoskeleton’s shoe bracket, enabled accurate quantification of SV while allowing subjects to freely adjust their SV in response to perturbations induced by ankle weights (2 kg total, Fig. 5) and assistive torques. Stride- by-stride estimations SV (i) were transmitted via Wi-Fi using UDP to the on-board Real- Time Target Machine to inform the RL-AAN controller according to Equation 7.

[0221] Fig. 25 is a diagram depicting an experimental protocol.

[0222] The experimental protocol consisted of three laboratory visits. The first visit included a leg scan, which was used to fabricate a subject-tailored exoskeleton [Eraky et al., 2024], During each of the subsequent two visits, after donning the exoskeleton on their left leg, participants were exposed to either the RLAAN controller or a conventional fixed-K controller with an intermediate level of assistance (K = 6%), which was introduced for comparison. The order of the controllers was balanced across participants and the visits were conducted at least 24 hours apart. Each training visit comprised ten walking bouts (Fig. 25). In the Familiarization bout (FAM), subjects walked both with and without ankle weights, under a transparent (zero-torque) controller, to become acquainted with the exoskeleton and the self-paced treadmill. During the Baseline bout (BSL), subjects walked in the zero torque controlled exoskeleton without ankle weights. The average SV measured during this session determined each Attorney Docket No.: 206572-0008-00WO participant’s SVtarget. Next, ankle weights were re-applied to the exoskeleton and never removed until the end of the visit. The Perturbation bout (PRT) was similar to BSL, except for the presence of the ankle weights. This bout was used assess how the additional inertia induced by the weights would affect subjects’ natural SV. Subsequently, subjects performed four 10-minute Training bouts (T#), with 5-minute resting periods included in-between bouts, under one of the two controllers. Lastly, three 5-minute Post- Training bouts (PT#), starting 1, 10, and 20 minutes after the end of the last Training session were administered to evaluate the extent to which study participants were able to retain SV improvements achieved during training. The testing conditions during these three bouts replicated PRT.

[0223] Fig. 26 is a plot showing results for stride-by-stride velocity SV(i) and RL-AAN assistance level K(i) for a representative subject. Blue horizontal lines indicate average values within each walking bout.

[0224] Statistical Analysis: The average SV error (ESV) measured during each walking bout was selected as the dependent variable. First, one sample t-tests were carried out on PRT data to confirm that ankle-weight-induced perturbations caused significant changes in participants’ baseline SV. Next, linear regression analyses were applied to T# data to inspect trends in ESV induced by walking with each controller. For the RL-AAN controller, a similar analysis was performed for the average assistance level (A) measured during each training bout. Lastly, for each PT session, one-sample t-tests and paired t-test were used to evaluate and compare retention results between the two controllers. All statistical analyses were carried out using IBM SPSS Statistics 29.0.

[0225] Figs. 27A & 27B are plots showing results for a training session. Fig. 27A shows group averages of velocity errors Esv across the walking bouts for fixed-K (light shades) and RL-AAN (dark shades) controllers. Fig. 27B shows group averages of assistance level K, as modulated by the RL-AAN controller, during the training sessions.

[0226] RESULTS: Figs. 27A & 27B shows stride-by-stride trajectories of SV (i) and K(i) for a representative subject during tests with the RLAAN controller. The application of ankle weights caused a 20% drop in SV (approximately 20 cm / s) between BSL and PRT, which was progressively recovered during the training sessions. Notably, this was achieved while the RLAAN gradually reduced K(i), indicating that the subject Attorney Docket No.: 206572-0008-00WO progressively became less reliant on the external assistance. Post-test data indicate good retention of SVtarget following training, with a slight overshoot in early PT1.

[0227] Table 3: T-Tests

[0228] One-sample t-test on ssv for PRT revealed significant alterations in subjects’ baseline SV (p < .001 for both Fixed- K and RL-AAN controllers), with a mean difference of 13 cm / s. Thus, the applied ankle weights effectively slowed the study participants. Interestingly, linear regression analysis revealed a significant (p < .01) reduction in Esv during training for the RL-AAN controller, which was not observed for the fixed-K controller (Fig. 27A). Correspondingly, there was a significant trend toward decreasing level of RL-AAN assistance K (p < .01) (Fig. 27B). Overall, this indicates that participants not only improved their performance during training, gradually approaching their baseline SV despite the perturbation, but also did so while increasingly reducing their reliance on external assistance, stepping up their active effort. In contrast, the fixed- K controller helped partially reducing the effect of the perturbation, though SV performances did not improve over time, suggesting that a conventional assistive controller may be suboptimal in promoting participant’s engagement in gait speed training. It is worth noting that the 95-percentile for K(i) across all participants and all RL-AAN training sessions was 5.86%, indicating that the RL-AAN assistance remained lower than the constant assistance level provided by the fixed-K controller (6%) during most of the training. Thus, while the Fixed-K controller, on average, provided more assistance to the study participants to help them compensate for the perturbation, it did not motivate them to walk faster. This was also reflected in post-test results. Indeed, paired t-tests on PT# data showed significantly (p < .05) lower £sv for the RL-AAN controller compared to the Fixed-K controller in all post tests, indicating better retention Attorney Docket No.: 206572-0008-00WO of SVtarget. One-Sample t-tests further suggested that ESV significantly deviated from zero (p < .05) during all Fixed-K post tests, indicating that significant deviations from SVtarget following training, which was not observed for the RL-AAN controller. Collectively, these findings suggest that the RL-AAN controller not only facilitates adaptive reduction in exoskeleton assistance but also elicits both immediate SV improvements and short term training effects that last at least 25 minutes post training and outperform those observed under a conventional controller contributing a fixed fraction of the wearer’s biomechanical PDF torque.

[0229] This example disclosed a novel reinforcement learning assist-as-needed (RL-AAN) controller for gait speed training. The disclosed controller constitutes the first RL-based AAN strategy capable of modulating a powered orthosis’s assistive torque in real time based on the user’s performance, to elicit a target stride velocity. Because it is grounded on real-time estimations of the wearer’s biological ankle moment, the disclosed controller generates biomechanically relevant assistance while dynamically adjusting the level of assistance “on the fly” to reduce assistive torques as the wearer’s performance improves. While training with the RL-AAN controller, the study participants received progressively less assistance over successive training bouts and concurrently increased their SV toward their baseline (pre-perturb ati on) value, stepping up their active effort. As a result, subjects adapted to the target SV and retained faster SV even when walking without assistance, indicating effective short-term motor adaptations.

[0230] Compared with recent works that proposed controllers for powered ankle devices aimed at improving self-selected walking speed [Orekhov et al., 2020; Sloot et al., 2023; Song and Collins, 202], the disclosed example offers two key contributions. First, none of these studies employed an adaptive controller capable of modulating its level of assistance to encourage the user’s own effort. Second, previous studies primarily focused on eliciting immediate gains in SV, with none demonstrating retention after external assistance was removed. In the disclosed gait training sessions with the RL-AAN and Fixed-K controllers, the average increase in SV relative to the perturbed SV was 14.2% and 10.02%, respectively. While these figures do not match the 42% gain reported by Song et al. in healthy individuals during unperturbed gait [Song and Collins, 2021], their assistive controller was specifically tuned to elicit immediate changes in self- Attorney Docket No.: 206572-0008-00WO selected SV. The assistive controller presented by Orekhov et al. [Orekhov et al., 2020], similar to the disclosed Fixed-K controller, provided a fixed percentage of the user’s estimated ankle PDF moment, resulting in a 6.3% increase in walking speed in individuals with cerebral palsy. Though beneficial in terms of immediate effects, the disclosed example suggests that such a fixed-gain approach may be suboptimal for encouraging long-term training effects in SV. In this regard, controllers that adaptively modulate the level of assistance provided to the wearer, such as the disclosed RL-AAN controller, may be preferable.

[0231] The disclosed RL-AAN controller extends previous work [Zhang et al., 2019; Zhang et al., 2020] by explicitly incorporating user effort into the actor’s cost function and dynamically balancing movement error minimization with external assistance reduction. This enables individualized assistance modulation, better accommodating an individual’s varying abilities and learning dynamics, and yielding a more tailored solution for gait training. Moreover, the use of NNs allows the controller to capture complex relationships between the robot’s actions and the user’s behaviors. In contrast, conventional adaptive AAN strategies, such as iterative learning control (ILC) [Emken et al., 2007; Maggioni et al., 2018], rely on simplistic assumptions about humanrobot co-adaptation dynamics, offering limited adaptability across individuals and making fine-tuning intrinsically challenging.

[0232] The adaptive nature of the disclosed RL-AAN controller shows potential for individuals recovering from lower-extremity trauma, who often require intensive gait retraining to restore mobility. The ability of RL-AAN to personalize the assistance level in real time ensures that patients are consistently challenged at an appropriate level, providing enough support to ensure safety and functional performance while preventing over-reliance on device assistance. This tailored therapy could benefit HELET patients as well as individuals with neurological gait impairments, helping them regain normal walking patterns more effectively.

[0233] Although the disclosed technology may work with well defined spatial gait perturbation in healthy subjects, it also addresses numerous challenges present in clinical populations. For example, the technology accommodates for more diverse and ecologically valid walking tasks with the controller’s adaptability to real -world Attorney Docket No.: 206572-0008-00WO rehabilitation scenarios. The disclosed technology may address subjects with any gait impairments (e.g., HELET patients and stroke survivors). The disclosed example establishes the RL-AAN controller’s potential as a versatile tool to deliver individualized gait training.

[0234] References:

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[0331] The disclosures of each and every patent, patent application, and publication cited herein are hereby each incorporated herein by reference in their entirety. While this invention has been disclosed with reference to specific embodiments, it is apparent that other embodiments and variations of this invention may be devised by others skilled in the art without departing from the true spirit and scope of the invention. The appended claims are intended to be construed to include all such embodiments and equivalent variations.

Claims

Attorney Docket No.: 206572-0008-00WOCLAIMSWhat is claimed is:

1. An elastic actuator, comprising: an output shaft; at least one output rotor comprising at least one slot arranged in an arc formation on the output rotor, wherein the at least one output rotor is coaxially and rigidly mounted on the output shaft; an input member interfaced with the at least one output rotor comprising at least one spring chamber, wherein the input member is configured to rotate relative to the at least one output shaft; at least one compression spring positioned at least partially within the at least one slot of the at least one output rotor and the at least one spring chamber of the input member.

2. The actuator of claim 1, wherein the input member is an input rotor, or an input shaft.

3. The actuator of claim 1, wherein the at least one output rotor comprises a number of output rotors ranging between 1 and 5.

4. The actuator of claim 1, wherein the at least one compression spring comprises a number of compression springs ranging between 1 and 10.

5. The actuator of claim 1, wherein the at least one spring chamber comprises a number of spring chambers ranging between 1 and 10.

6. The actuator of claim 1, wherein each slot of the at least one slot in the at least one output rotor is spaced equally in the arc formation.

7. The actuator of claim 1, wherein the arc formation of the at least one slot is arranged symmetrically, or asymmetrically, on the at least one output rotor.Attorney Docket No.: 206572-0008-00WO8. The actuator of claim 1, wherein the at least one compression spring protrudes laterally from at least one side of the at least one output rotor.

9. The actuator of claim 1, wherein the at least one compression spring protrudes laterally from both sides of the at least one output rotor.

10. The actuator of claim 1, wherein the at least one spring chamber comprises at least one cut out region configured as a relief for the at least one compression spring.

11. The actuator of claim 1 , wherein the at least one compression spring is positioned within at least one of the slot and the at least one spring chamber with preload on the spring.

12. The actuator of claim 1, wherein the at least one slot and the at least one spring chamber retain the at least one compression spring when the at least one compression spring is undergoing deformation.

13. The actuator of claim 1, wherein the at least one compression spring compresses to a first end or a second end of the at least one spring chamber when the input member is rotated.

14. The actuator of claim 1, wherein the at least one output rotor comprises two output rotors, wherein the input member comprises a middle portion and two lateral portions, and the at least one spring chamber is formed by aligned cut out regions in the middle and lateral portions.

15. The actuator of claim 1, wherein each output rotor comprises 5 equally spaced slots and 5 compression springs.Attorney Docket No.: 206572-0008-00WO16. The actuator of claim 1 , wherein the at least one compression spring comprises least one type of spring selected from the group consisting of: straight coil springs, convex springs, concave springs, linear springs, non-linear springs, variable rates springs, and progressive springs.

17. The actuator of claim 1, further comprising at least one bearing with an extending inner ring positioned between at least one output shaft and at least one input member.

18. A wearable system comprising: at least one actuator of claim 1 attached to an exoskeleton or orthosis; an actuation unit connected to the at least one actuator, wherein the actuation unit rotates the input member.

19. The system of claim 18, wherein the actuation unit rotates the input member with one or more cables.

20. The system of claim 18, wherein the actuation unit rotates the input member with one or more motors.

21. The system of claim 18, wherein each output rotor comprises 5 equally spaced slots and 5 compression springs.

22. The system of claim 18, wherein the exoskeleton or orthosis comprises one or more weights configured to generate a perturbation in the movement or gait of the subject.

23. The orthosis of claim 18, wherein the orthosis is an ankle-foot orthosis.

24. An exoskeleton comprising at least one actuator of claim 125. An orthosis comprising at least one actuator of claim 1.

Images