Mechanical finger with variable stiffness

Abstract

A mechanical finger may have a base. A phalanx linkage has phalanges, with a first phalanx rotationally connected the base, and at least a second phalanx rotationally connected to the first phalanx. A transmission linkage provides at least one rotational degree of freedom (DOF) between the base and a distal-most one of the phalanges. Passive rotational DOF joints are provided, whereby the mechanical finger has a passive state of actuation in which the phalanx linkage remains in a constant orientation through displacement of the base absent a contact of one of the phalanges with an object, and a grasping state of actuation in which a contact of one or more of the phalanges with an object causes a variation of the orientation. A stiffening link is configured to be releasably connected between a secured condition in which the stiffening link is secured between the transmission linkage and the phalanx linkage, and a released condition in which the stiffening link is released from the secured condition, the mechanical finger having a greater stiffness in the secured condition.

Description

MECHANICAL FINGER WITH VARIABLE STIFFNESS CROSS-REFERENCE TO RELATED APPLICATION

[0001] The present application claims the priority of United States Patent Application No.63 / 507,477, filed on June 12, 2024, and incorporated herein in its entirety. TECHNICAL FIELD

[0002] The present application relates to mechanical fingers of grasping apparatuses, for instance in robotic applications. BACKGROUND OF THE ART

[0003] In robotics, grasping objects of various geometries and material properties has been and still is a lasting and difficult challenge for robotic manipulators. Securing seized objects that are very different both in terms of shapes or textures calls for a versatile grasper / gripper capable of enveloping these objects and providing both form- and force-closure but also not exerting an excessive contact pressure that could lead to damages. In practical industrial robotics, the most commonly used grippers are simple two- or three- finger tools, often pneumatically driven, with high stiffnesses. Thus, simple industrial grippers are also often unsuitable for more delicate operations where the objects they must seize are fragile, and their use is a concern in human-robot interactions.

[0004] To address these issues, compliant or soft grippers have been proposed and define a novel category of robotic grippers. These soft grippers have a low intrinsic stiffness which can be taken advantage of both to provide an enveloping motion for the seized objects but also to mitigate or completely eliminate potential harmful interactions with a human during a collision. Another secondary advantage of soft grippers is that they are often significantly less expensive and lighter than their rigid counterparts. On the other hand, soft tools are generally weaker and far less precise. The expression “soft” in this context may mean that the grippers are deformable, even though they may be made of rigid materials.

[0005] To strike a balance between safety, versatility, and load capability is challenging and new designs of soft grippers are still currently revealed to this aim. An interesting avenue to solve these conflicting requirements is to dynamically change the stiffness of soft grippers. A soft gripper with variable stiffness can change from a stiff mode where it is capable of producing large forces and of providing a greater positional accuracy to a compliant mode where it can gently envelop objects and is safe in case of collision. Solutions on this front can be broadly sorted out in two categories: designs that achieve variable stiffness electronically, i.e., with a proper control algorithm, and designs that achieve variable stiffness by mechanical means, i.e. through a physical variation in the property of the device.

[0006] Among mechanical solutions, ”bulk locking” is commonly found and used with grippers composed of small-sized particles enclosed in a soft shell. This bulk locking is produced by changing the interactions of the embedded particles either by applying a magnetic field or by reducing the pressure insidethe shell which greatly stiffens the gripper. Another solution to achieve a variable stiffness mechanism is through the use of low melting alloy material allowing to change from a very stiff solid state to a soft liquid one, resulting in a dramatic drop in stiffness. A third approach yet to yield variable stiffness is to rely on inertial properties, with the cross-sections (and thus, second moment of inertia) of the flexure hinges in a finger are changed by a secondary actuator.

[0007] There however remains a need for mechanical fingers of simple construction that can have variable stiffness. SUMMARY

[0008] In accordance with a first aspect of the present disclosure, there is provided a mechanical finger comprising: a base adapted to be connected to an actuator for being displaced in at least one degree of actuation; a phalanx linkage having at least two phalanges, with a first phalanx rotationally connected at a proximal end to the base, and at least a second phalanx rotationally connected at a proximal end to a distal end of the first phalanx; a transmission linkage providing at least one rotational degree of freedom (DOF) between the base and a distal-most one of the phalanges; passive rotational DOF joints between the at least two phalanges, between the base and the first phalanx, and in the transmission linkage, whereby the mechanical finger has a passive state of actuation in which the base, the at least two phalanges and the transmission linkage remain in a constant orientation relative to one another through displacement of the base caused by the actuator absent a contact of one of the phalanges with an object, and a grasping state of actuation in which a contact of at least one of the phalanges with an object causes a variation of the orientation of at least one of the phalanges relative to the base through displacement of the base caused by the actuator; and a stiffening link between the transmission linkage and the phalanx linkage, the stiffening link configured to be releasably connected between a secured condition in which the stiffening link is secured between the transmission linkage and the phalanx linkage, and a released condition in which the stiffening link is released from the secured condition, the mechanical finger having a greater stiffness in the secured condition.

[0009] Further in accordance with the first aspect, for example, the passive rotational DOF joints are revolute joints, rotational axes of all said revolute joints being parallel.

[0010] Still further in accordance with the first aspect, for example, at least four of the revolute joints are provided. Still further in accordance with the first aspect, for example, there are three of said phalanges, wherein the distal-most one of the phalanges is a third phalanx rotationally connected at a proximal end to a distal end of the second phalanx, and further wherein the transmission linkage is connected to the third phalanx.

[0011] Still further in accordance with the first aspect, for example, the passive rotational DOF joints are living hinges.

[0012] Still further in accordance with the first aspect, for example, the phalanx linkage, the transmission linkage and the base concurrently part of a monolithic body including the living hinges.

[0013] Still further in accordance with the first aspect, for example, the stiffening link is part of the monolithic body.

[0014] Still further in accordance with the first aspect, for example, the stiffening link is connected to the transmission linkage by a rotational joint.

[0015] Still further in accordance with the first aspect, for example, the stiffening link is connected to a proximal link of the transmission linkage, the proximal link being connected to the base by a rotational joint.

[0016] Still further in accordance with the first aspect, for example, the stiffening link is releasably connected to an intermediate phalanx, with the phalanx linkage sequentially having a proximal phalanx, the intermediate phalanx, and a distal phalanx.

[0017] Still further in accordance with the first aspect, for example, a snap-fit complementary connector pair may be provided and may include a connector at an end of the stiffening link.

[0018] In accordance with another aspect of the present disclosure, there is provided a grasping apparatus comprising: at least two of the mechanical finger as described above, the mechanical fingers oriented for the phalanges of one said mechanical finger to face the corresponding phalanges of the other said mechanical finger; and at least one said actuator to displace the mechanical fingers toward and away from one another in the passive state of actuation and in the grasping state of actuation.

[0019] Further in accordance with the second aspect, for example, the at least one said actuator is a linear actuator imparting a translation movement between the at least two mechanical fingers.

[0020] In accordance with a third aspect of the present disclosure, there is provided a mechanical finger comprising: a base adapted to be connected to an actuator for being displaced in at least one degree of actuation; a phalanx member operationally connected to the base; a transmission member operationally connected to the base and to the phalanx member; the mechanical finger having a passive state of actuation in which the base, the phalanx member and the transmission member remain in a constant orientation relative to one another through displacement of the base caused by the actuator absent a contact of the phalanx member with an object, and a grasping state of actuation in which a contact of the phalanx member with an object causes an elastic deformation of the phalanx member relative to the base through displacement of the base caused by the actuator; and a stiffening link between the transmission member and the phalanx member, the stiffening link configured to be releasably connected between a secured condition in which the stiffening link is secured between the transmission member and the phalanx member, and a released condition in which the stiffening link is released from the secured condition, the mechanical finger having a greater stiffness of the phalanx member in the secured condition.

[0021] In accordance with a fourth aspect of the present disclosure, there is provided a method for manipulating at least one mechanical finger comprising: displacing the at least one mechanical finger to contact at least one object with a first stiffness level in a phalanx linkage of the mechanical finger; connecting a stiffening link between the phalanx linkage and a remainder of the mechanical finger to increase a stiffness of the phalanx linkage to a second stiffness level greater than the first stiffness level;and displacing the mechanical finger to contact at least one object with the second stiffness level in a phalanx linkage of the mechanical finger.

[0022] Further in accordance with the fourth aspect, for example, connecting the stiffening link includes snap-fitting the stiffening link at one end thereof to one of the phalanx linkage and the remainder.

[0023] Still further in accordance with the fourth aspect, for example, snap-fitting the stiffening link at one end thereof includes snap-fitting the stiffening link to the phalanx linkage.

[0024] Still further in accordance with the fourth aspect, for example, displacing the at least one mechanical finger includes imparting a movement between two of the mechanical fingers, to grasp at least one object therebetween.

[0025] Still further in accordance with the fourth aspect, for example, imparting the movement between the two of the mechanical fingers includes imparting a translational movement between the two of the mechanical fingers.

[0026] Still further in accordance with the fourth aspect, for example, the method may include disconnecting the stiffening link from between the phalanx linkage and the remainder of the mechanical finger to reduce a stiffness of the phalanx linkage to the first stiffness level. DESCRIPTION OF THE DRAWINGS

[0027] Embodiment of the present disclosure will now be described with reference to the accompanying drawings in which:

[0028] Fig.1A is an elevation view of a mechanical finger in accordance with a variant of the present disclosure, in a released condition exhibiting relatively low stiffness;

[0029] Fig.1B is an elevation view of a mechanical finger of Fig.1A, in a secured condition exhibiting relatively high stiffness;

[0030] Fig.2 is a schematic view of different configurations of the mechanical finger of the present disclosure, with a single (a-d) or no (e) crossbeam;

[0031] Fig.3 is a schematic view of a geometrical parameters of the mechanical finger of the present disclosure;

[0032] Fig.4 is a perspective view of FEA simulations of the fingers from Table I;

[0033] Fig.5 is a graph representation of norms of the resulting grasp force on x-axis for all versions vs angles;

[0034] Fig.6 is a schematic view of a illustrative grasp of a cylindrical object;

[0035] Fig.7 is a perspective view of a snap-fit joint on a mass produced plastic box;

[0036] Fig.8 is a graph representation of Force-displacement stiffness ellipsoid for a simulated displacement of 1mm in the plotted directions;

[0037] Fig.9 is a schematic view of a selected geometry of annular snap-fit joint;

[0038] Fig.10 is a perspective view of a CAD of the finger;

[0039] Fig.11 is a perspective view of a Low- and high-stiffness grasp examples of the optimal fingers;

[0040] Fig.12A-12C show schematic views of different arrangements of the mechanical finger of Fig.1A, arranged in a pair as part of a gripper;

[0041] Fig.13 is a graph representation of resulting horizontal contact forces in the two stiffness modes (solid lines: finger 1R, dotted lines: finger W) for different positions of a cylindrical object (Ø40mm), see arrows in upper left corner;

[0042] Fig.14 is a graph representation of computed x-axis stiffness in the two stiffness modes (solid lines: version 1R, dotted lines: version W) for different positions of a cylindrical object (Ø40mm), see arrows;

[0043] Fig.15 is a graph representation of comparison between the forces from the theoretical model, the FEA analysis and experimental measurements with the prototype for a cylindrical object contact (Ø40mm) at the blue arrow location;

[0044] Fig.16 is a perspective view of a CAD model of the hand assembly on the electric gripper of a Baxter robot;

[0045] Fig.17 is a perspective view of engagement of the snap-fit joint: pinching motion of the fingertip and the same pinch can be obtained by the fingers themselves as a tool; and

[0046] Fig.18 is a perspective view of disengagement of the snap-fit joint: (a) introduction of the switching tool between the phalanges and the crossbeam; (b) Twisting of the tool to disconnect the joint. Again, the same effect can be obtained by the fingers themselves as a tool. DETAILED DESCRIPTION

[0047] Referring to Figs.1A and 1B, there is illustrated a mechanical finger 10 in accordance with a variant of the present disclosure. “Mechanical finger” is one of the numerous expressions that may be used to designate the item 10 of Figs.1A and 1B, other expressions including gripper, finger, arm, jaw, etc. In a given condition, referred to herein as a released condition, the mechanical finger 10 may have a relatively low stiffness, or lower stiffness, such that in such condition it may be referred to or qualify as being soft robotics, though this is optional. In another condition, referred to as a secured condition, the mechanical finger 10 can have an increase in its stiffness, a higher stiffness. Stiffness values are not provided as they may not be considered relevant in absolute values. An important aspect is that the stiffness varies for a same device, i.e., the finger 10, by changing condition, with the stiffness between conditions being relatively lower or higher. Although the environment of the mechanical finger 10 is not shown, the mechanical finger 10 may be used as part of a hand, a grasping apparatus, a gripping apparatus, a robotized arm, etc. The mechanical fingers 10 may or may not be provided with motorization.

[0048] The mechanical finger 10 has a base 10A that is configured to be mounted to an actuator, such as a gripper jaw and / or a radial gripper, for translational movement and / or rotational movement, in a single or dual degrees of actuation. The base 10A may be the interface of the mechanical finger 10 with a remainder of a gripping apparatus or like component. In Figs.1A and 1B, the base 10A is shown as being a link, that has a length or like dimension, and an optional flat surface. As other examples, the base 10Amay be in the form of a circular female connector of a revolute joint (a male connector could be used as well). Other configurations are considered, but a revolute joint shape of base 10A is well suited to interconnect two mechanical fingers 10 about a common pivot, such that a pair of mechanical fingers 10 may rotate about a common axis of rotation, although the pair of mechanical fingers 10 could rotate about separate axes of rotation as well. The base 10A may alternatively be connected to a linear actuator, for translation movement, as another possibility among others.

[0049] The mechanical finger 10 has a phalanx linkage 11. The phalanx linkage 11 may have two or more phalanges. Sequentially, in the illustrated embodiment showing a three-phalanx configuration, the phalanx linkage 11 may have a proximal phalanx 12, an intermediate phalanx 13 and a distal phalanx 14. The proximal phalanx 12 is connected at opposed ends to the base 10A and to the intermediate phalanx 13 by way of rotational joints R (a.k.a., hinge, rotational degree of freedom (DOF) joint, pivot joint, etc), providing a rotational degree of freedom (DOF). Likewise, the intermediate phalanx 13 is connected at opposed ends to the proximal phalanx 12 and to the distal phalanx 14, by way of rotational joints R, again providing a rotational DOF. A transmission linkage 15 interconnects the distalmost phalanx, i.e., distal phalanx 14 in the illustrated embodiment, to the base 10A. The transmission linkage 15 may have one or more links. In the illustrated embodiment, the transmission linkage 15 is shown having a proximal link 16, an intermediate link 17 and a distal link 18. The proximal link 16 is connected at opposed ends to the base 10A and to the intermediate link 17, by rotational joints R. The intermediate link 17 is connected at opposed ends to the proximal link 16 and to the distal link 18, by rotational joints R. The distal link 18 is also connected at opposed ends to the intermediate link 17 and to the distalmost phalanx, i.e., distal phalanx 14 by rotational joints R. In a variant, the distal phalanx 14 and the distal link 18 are pivotally connected by a rotational joint R at their tips, though this is optional. Moreover, while discrete phalanges are shown in Figs.1A and 1B, the phalanx linkage 11 may instead be a phalanx member 11 that may be a continuous member without visible articulations. The same may apply to the transmission linkage 15, i.e., it may instead be a transmission member 15 that may be a continuous member without visible articulations.

[0050] Still referring to Figs.1A and 1B, the mechanical finger 10 has a stiffening link 20, also known as a crossbeam. The stiffening link 20 extends between the phalanx linkage 11 and the transmission linkage 15. The stiffening link 20 in the illustrated embodiment is connected to the proximal link 16 by a rotational joint R. The stiffening link 20 is shown as being on the proximal link 16, but could be at any other location on the transmission linkage 15, such as on any of the links 16, 17 or 18, or on the rotational joints between the links. In a variant, the transmission linkage is unconnected to any of the phalanges other than the distalmost one of phalanges. In another variant, the stiffening link 20 may have one end connected to the base 20A, and the other end to connected to the phalanx linkage 11. In a variant, the stiffening link 20 may be said to be connected (i.e., directly connected) at one end to the phalanx linkage 11 (or phalanx member in a variant), and to a remainder of the finger 10 at the other end (e.g., the transmission linkage 15 or base 10A). This may apply to all variants described herein.

[0051] The stiffening link 20 may have at its free end a connector 20A that is configured to be connected to a complementary connector 11A in the phalanx linkage 11. The connector 11A is shown as being on the intermediate phalanx 13, but could be at any other location on the phalanx linkage 11, such as on any of the phalanges 12, 13 or 14, or on the rotational joints between the phalanges.

[0052] Thus, as shown in Fig.1B, the stiffening link 20 is configured to be releasably connected between a secured condition in which the stiffening link 20 is secured between the transmission linkage 15 and the phalanx 11, and a released condition in which the stiffening link 20 is released from the secured condition. In the released condition, the connector 20A is separated from the connector 11A, such that the end of the stiffening link 20 is free. In the secured condition, the connector 20A is connected to the connector 11A, such as in a snap-fit engagement as shown, in which the connector 20A relies on the elastic deformation of the connector 11A to be matingly received therein. Other connection arrangements could be provided for the complementary engagement of the stiffening link 20 to the phalanx link 11, such as an actuatable magnetic pair, threaded fasteners, latch, pin, etc, to name a few of the multiple options available. Moreover, while the stiffening link 20 is shown pivotally connected to the transmission linkage 15, it could alternatively be pivotally connected to the phalanx linkage 11. Also, even if the stiffening link 20 is shown being permanently to the transmission linkage 15 (or phalanx linkage 11), it could have both of its ends separable from the linkages 11 and 15, to be added and connected at its opposed ends when necessary, for example without rotational joints R. The illustrated embodiment, in which the stiffening link 20 is pivotally connected at an end, allows the stiffening link 20 to move out of the way when not used.

[0053] The mechanical finger 10 has a greater stiffness in the secured condition of Fig.1B. Indeed, the stiffening link 20 blocks some of the movements between the linkages 11 and 15, such that the finger 10 exhibits greater stiffness when the phalanx linkage 11 is applied against an object. The greater stiffness may also be exhibited by a reduced or blocked movement of the phalanges 12, 13, and or 14 relative to one another.

[0054] In the mechanical finger 10, the rotational axes of all of these rotational joints R may be parallel to one another, as shown. According to an embodiment, the mechanical finger 10 described herein is entirely formed of passive joints in that, during use, none of the rotational joints of the mechanical finger 10 are directly actuated. Instead, the mechanical finger 10 as a whole is moved, and movement of some parts of the mechanical finger 10 relative to others is caused by grasping contact of an object, as described hereinafter. Thus, in a variant, it may be said that the phalanges 12, 13 and 14 (if present) and the transmission linkage 15 remain in a constant orientation relative to one another through displacement of the base 10A caused by the actuator absent a contact of one of the phalanges with an object, and a grasping state of actuation in which a contact of one or more of the phalanges with an object causes a variation of the orientation of one or more of the phalanges relative to the base 10A through displacement of the base caused by the actuator. Stated differently, the mechanical finger 10 may be said to be in a passive state of actuation absent some contact with the object or with some specific contacts with the object, and in the grasping state of actuation when the finger 10 deforms to the contact of the object.

[0055] In Figs.1A and 1B, the mechanical finger 10 is monolithically formed from a single material, although it is considered to use a different or additional material in the phalanges 12, 13, 14, and / or in the transmission linkage 15. For instance, materials of all sorts may be used, such as resilient pads or even rigid pads for particular uses, such as a tungsten carbide insert as contact pad. In the embodiment of Figs.1A and 1B, in which the finger 10 is a monolithic piece, the phalanx linkage 11 and the transmission link 15 have thinner portions that are typically designed to act as flexure bearings (a.k.a., living hinges, used interchangeably herein with flexure bearing) and deform within or beyond the elastic deformation range to allow movement of the phalanges 12, 13 and / or 14, and the links 16, 17 and / or 18 into some of the grasps. However, this is merely optional. The stiffening link 20 may also be part of the monolithic piece and may also be connected via a living hinge. Alternatively, the living hinges may consist of a material or materials have a lower modulus of elasticity than that of the material or materials of phalanges and / or links. As a result, each of the living hinges may allow one or more rotational degree of freedom to allow enveloping grasp or pinch grasp of objects. As an alternative, or for one or more of the rotational joints R, revolute joints may be used, as a possibility.

[0056] It is considered to have more than the two mechanical fingers 10 in a gripper. For example, three of the mechanical fingers 10 could be used to perform an enveloping grasp of spherical objects such as balls. In such instances, it may be considered to have the bases 10A share a rotational axis, or the bases 10A of the fingers 10 may each have its own rotational axis. It is also considered to underactuate the mechanical fingers 10, by using an appropriate transmission. The bases 10A may also translate relative to one another, such as in parallel or coincident directions, though this is merely optional.

[0057] Additional stiffening links or like crossbeams 20 could be present in the mechanical finger 10, though just one is shown in Figs.1A and 1B. Adding as few as a single stiffening link, which acts as a stiffener for the finger 10, greatly increases stiffness. The actual geometry of this crossbeam 20 and especially the position where it is connected to the finger 10 may have an impact on the resulting forces. By discretizing the front and back surfaces of the finger 10 into three rigid links connected by flexures (i.e., the phalanx linkage 11, the transmission linkage 15, and the rotational joints R therebetween), four connecting combinations are found, as shown in (a) to (d) of Fig.2.

[0058] By convention, with the exclusion of Figs.1A and 1B, in all figures showing the schematic of a finger 10 herein, the front side of the finger 10 (intended for contacting objects, the phalanx link 11) is on the left (points O, A, B) and the back of the finger 10 is on the right (points F, E, D, the transmission linkage 15), unless otherwise specified. The links closest to the base are referred to as proximal, while these that are the farthest from the base are the distal links. Between the proximal and distal links on each side one finds the intermediate front and back links, as in Fig.3. Front links are also referred to as phalanges since their are meant for contacting objects. To distinguish between the four design variants illustrated in Fig.2, they are all designated with a unique shorthand notation as shown in the figure captions. These four configurations for the finger 10 have different kinematic structures. The optional prismatic joint at the base of the fingers 10 stands for the actuating gripper they are attached to. The fingers 10 can be connected toother types of joints or structures, whether it be in Fig.2 or any other embodiments. For example, with reference to Figs.12A to 12C, pairs of the finger 10 are shown with respect to one another, as part of a gripper, anamorphic hand, etc. The fingers 10 in Figs.12A-12C are as in Figs.1A and 1B, but may be in accordance with any other embodiment described herein. For instance, the stiffening link 20 could be between other parts of the finger 10, etc. Thus, Figs.12A-12C, in addition to Fig.16, show various actuation configurations for two or more of the fingers 10, regardless of the embodiment of the fingers 10 that are used with such actuators. In Fig.12A, each finger 10 is connected to a common base 30 by respective rotational joints 31. Thus, the rotational joints 31 may each be actuated in rotation, such as by an electric motor, a rotary actuator, with or without a transmission, etc. The fingers 10 may thus be moved in rotation relative to the base 30 by the actuator of the rotational joints 31. In Fig.12B, the fingers 10 are connected by their bases 10A by at a common point of rotation 32. This common point of rotation 32 means that the relative rotation between the fingers 10 is about a common rotational axis. The common point of rotation 32 may include two coincident rotational joints, or a single rotational joint. There may consequently be two rotational actuators at the common point of rotation 32, or a single one. A transmission could be present for a single rotational actuator at the common point of rotation 32 to impart a rotation to both fingers 10, or to a single finger 10, the other being fixed. In Fig.12C, each finger 10 is connected to the common base 30 by respective four-bar mechanisms 33, that may optionally be parallelograms. There may consequently be two rotational actuators, i.e., one for each of the four-bar mechanisms 33.

[0059] The main objective of the kinematic analysis of the finger 10 in its various configurations is to establish the force-displacement relationships they produce in order to determine their stiffness. These relationships can be obtained by calculating the forces required to maintain static equilibrium for a known configuration (angles between the links) and the most convenient method to compute these forces is by means of establishing the virtual work of each finger. In order to obtain this virtual work, the first step is to establish the kinematic coefficients relating the angular rate in all joints where a torque is acting as functions of the selected degrees of freedom (DOF). In the present application, as the finger 10 may be said to be soft in a given condition, all rotational DOF joints of the pseudo-rigid body models depicted in Fig.2 have an acting elastic torque. It is worth noting that the accurate computation of the contact forces produced by soft fingers is a challenging issue and most of the available literature focuses on deformation modeling. Contact forces are generally obtained through finite-element analysis (FEA) and although this method indeed leads to very accurate results it is very computationally intensive and thus, not ideal for design optimization. The present description sets out a virtual work approach to compute grasp forces of soft fingers, that may lead to accurate results for the finger 10 considered here. The accurate and fast computation of the grasp forces produced is essential for the optimization of the soft fingers with a robust algorithm simulating thousands of designs and grasps as discussed below.

[0060] Fig.3 depicts the general geometry and nomenclature of the finger 10 introduced in Figs.1A, 1B and Fig.2. A reference frame is attached to each finger at point O and the x-axis of this frame is aligned with the direction of the prismatic joint driving the finger 10. The relative angles between the front (F) andback (B) links 11,15 of the finger 10 are ^^ி^^ ൌ 1, 2, 3,4^ and ^^^^^ ൌ 1, 2, 3^ respectively. The contact forces between the finger 10 and theare assumed normal to the link where they occur and of magnitudes^^^^ ൌ 1, 2, 3, 4^. Note that the^contact force introduced in Fig.3 exists to statically constrain the finger but is not used during normal operations as will be discussed. The force^^at the base of the finger 10 corresponds to the linear actuation moving the finger 10 in translation toward the objects, i.e. the gripper to which the fingers 10 are attached. The position of a contact force of magnitude^^along its phalanx is measured by ^^. Herein, rXYwill be used to refer to the vector going from point X to point Y and lXYis the norm of that vector. For instance, rOAis the vector from O to A, i.e. along the contact surface of the proximal phalanx, and lOA= צrOAצ is the length of this phalanx. A few lengths are designated by a shorthand notation, namely: l0= lOF, l1= lOA= lFE, l2= lAB= lED, l3= lBC= lDC, see Fig.3. All lengths are constant for a specific design of the finger 10. As the proximal and intermediate links are ternary by nature, potentially connecting a crossbeam 20, the vectors ^^ிand ^^^are used to parameterize the location of these potential attachment points and they are defined as going from the middle of the ^௧^link to the nearest crossbeam joint on the same link. Keeping the symmetry of the fingers, is is assumed that:

[0061] The angle between ^^and the associated front or back link issee Fig. 3, and is a constant as well as angle ^^. Other angles ^^and ^^are also defined in Fig.3 and correspond to the angles between the internal crossbeam of finger X and its attachment link on the front and back side respectively. Conversely to and , angles ^^, and are variable and depend on the configuration of the finger. Once the geometry of the fingers is completely parameterized, the first step to compute the virtual work of the fingers is to determine the number of DOF for each finger. The four finger configurations in Fig.2 have three DOF.

[0062] Once the number of DOF for the different finger configurations is known, the second step is to determine the overall velocity equations relating the angles selected as the DOF to all the other angles in the linkage in order to be able to compute the overall virtual work of the linkage. The choice of which variables are DOF is arbitrary and in this description, the front phalanx angles were selected. With the version W finger, a fourth angle ^ସிis added as shown in Fig.3. For three-DOF fingers, the velocity equation of the linkage has thewith ^ א ^1^, 2^, 1^, 2^^. Matrices AX and VX are of dimensions 6×6 and 6×3 respectively and can be obtained by vector closure equations. These equations are obtained by equaling to zero the sums of position vectors in each kinematic loop of the linkage (e.g. the vector from O to G plus the vector from G to H and the vector from H to F and finally, the vector from F to O). For finger W, the velocity equation becomes:and matrices AW and VW are × × W has no crossbeam, the internal angles associated with the connection points of this crossbeam vanish from the left-hand side of the equation. Then, assuming matrix AX is not singular (e.g. by numerically computing the condition number of the matrix), one can relate the rate of the driven (non-DOF) angles of the fingers as a function of the DOF with a single matrix:with ^^^1^, 2^, 1^, 2^,^^.

[0063] In order to compute the W matrices defined in Eq. (4), the values of many position vectors must be established. That means one must express the positions of all the joints as functions of DOF. To this aim, expressing the geometric loop-closure of all fingers yields:whereandwith U א {B, F } allowing to distinguish between angles on the front-side (F) or back-side (B) of the finger. Using the shorthand variables a1, a2, and a3, one has:

[0064] Using the previous equations, all the angles of the 7-bar linkage OABCDEF are defined as functions of ^^ி, ^ଶி, ^ଷி, ^ସி. These equations are valid for all finger configurations but for those with three DOF (1R, 1L, 2R, 2L) one of the previous four angles can be related to the three others. For example, with version 1R the angle ^^^can be expressed from ^^ி, ^ଶிusing geometrical equations pertaining to the 5-bar OAIHF, namely:where a4, a5, and a6 are also shorthand notations. Angle is defined in Fig.3 and calculated as:

[0065] Finally, the angles ^^ோand ^^ோcan be obtained as:

[0066] With all the angles of the linkage known, all position vectors can be easily defined and thus, the velocity equations computed.

[0067] In order to apply the virtual work principle, the mechanically working forces in the linkage must be established, namely the input actuator force, the output contact forces, and the elastic torque modeling the soft structure of the finger. Indeed, all joints of the fingers are compliant and a pseudo-rigid body model (PBRM) can be used to compute their associated virtual work. The PRBM consists in associating to each joint of the linkages shown in Fig.2 a virtual rotational spring. The rotational stiffness of these virtual springs is assumed identical for all joints and designated by k while the torque resulting of a rotation of magnitude ^ െ ^^at a joint is noted ^ఏ, where ^ and ^^are the current and at rest angle of the joint respectively. These elastic torques are then

[0068] For all 3-DOF fingers (1L, 2L, 1R, 2R), the total virtual work of the PRBM is:withand X א {1L, 2L, to greater W yields a slightly different expression:with In the n × n identity matrix and

[0069] For all fingers,n^ is a grasp Jacobian matrix of dimension n and^^௧^^ೕis the element at the^ line and ^௧^column of that matrix, i.e.:

[0070] As a reminder, parameters ^^, ^^and ^^are defined in Fig.3 and ^^ிis defined in Eq. (6).

[0071] All forces and torques applied to the finger are conservative and therefore, the virtual work of each PRBM is zero at equilibrium, i.e. įW = 0. Based on this application of the virtual work principle, a relationship between the configuration of the finger defined by the DOF and the produced contact forces can be established. For example, with the three-DOF finger 1R, one has:and therefore, a mathe p ques of the fingers. In turn, these forces can be used to establish the stiffness of the fingers as the variation of these forces for a known displacement.

[0072] To validate these results, a multi-body simulation software (MSc Adams) was first used and each PRBM of the fingers was built in that software. Torsional springs of identical stiffness were added to all joints in the simulation. Several sets of measurements were obtained for all models in which the angles ^^ிfixed and the forces corresponding to^and needed to maintain static equilibrium wereby the software. This scenario to a typical power grasp where the object makes contact with the proximal and intermediate phalanges but not on the distal one (hence^= 0 and^=^= 0 for finger W). A comparison could then be made between the forces obtained from these simulations to the ones produced by using the methodology presented in Section III. The results of one example amongst many of these comparisons between methods is shown in Tab. I for the 1R and W fingers and these results are typical from all simulations. The fingers and grasp scenarios from the latter table include simulations using a Finite Element Analysis (FEA) software, namely Ansys, see Fig.4. The computed forces from the FEA analyses were recorded and compared to the theoretical forces. As one can plainly see in Tab. I, the differences between both the multibody and FEA softwares with the model from Section III remain small in all cases thereby validating the proposed approach which is more general in terms of design parameters and less computationally intensive.

[0073] At this point, the choice of retaining only versions 1R and W of the finger as the most promising designs for prototyping was made based on the results obtained in terms of contact force magnitudes. Both fingers 1R and W exhibited the largest spread for contact forces and are therefore ideal candidates for a finger switching between different stiffness levels. To illustrate this point, the horizontal grasp forces of all fingers are shown in Fig.5 for the geometrical parameters listed in Tab. II. As can be seen in the figure, the force created by the finger 1R is noticeably greater than all the others and this force is predictably at its lowest with finger W. These plots were created using the same grasp scenario as before, namely that there were no contacts on the distal phalanges and therefore, forces^and^are both equal to zero. Fig 5 also clearly shows that if one switch from the three-DOF 1R finger to the four-DOF W finger, a significant drop in the applied forces could be achieved. This switch can be conveniently achieved by disconnecting one of the two attachment point of the crossbeam. To this aim, the present invention introduces a new snap-fit annular joint design. Annular snap-fit joints are a convenient design solution for a rotational joint that can be easily assembled and disassembled during manufacturing and / or operations if needed. See Fig.7 for an example demonstrating the snap-fit joint used with the lid of a plastic box. Snap-fit are a staple of mass produced consumer goods due to their low cost but they are very rarely been used in robotics research and are proposed here for the first time for kinematic reconfiguration to the best of the authors’ knowledge.

[0074] With the intention of achieving the largest difference in stiffness between the 1R and W fingers, an optimization is now conducted. Since the only change in the design of both fingers is the presence and location of the crossbeam, maximizing this difference in stiffness means one must search for a suitable crossbeam geometry producing the largest stiffness in finger 1R. To define the corresponding optimization problem, a realistic grasp scenario for the finger is first defined, namely the power grasp of a cylindrical object with a diameter r equal to half the length of the proximal phalanx (^^ / 2) and where the center of this object is located at the same vertical distance as point A (at the intersection of the first two phalanges), see Fig.6. This cylindrical object is fixed and the finger moves in translation along the x-axis of the reference frame to perform the grasp. The size and position of this target object approximates the intended use case of the gripper.

[0075] With the grasp geometry accordingly defined, the contact locations at the proximal and intermediate phalanges, ^^and ^ଶ, characterizing the position of the contact forces^^and^^between the cylinder and the front phalanges can be readily calculated:where ^ is the radius of the as ^^^, ^^^ of the center of this object can also be calculated as:with ^^and ^^defined in Fig.3.

[0076] To conduct the optimization, an evaluation of the grasp stiffness must first be obtained. However, this stiffness is different depending on which direction in the plane is considered (the object being assumed cylindrical, there is no rotational stiffness), and a stiffness matrix characterizes the relationship between forces and displacements. To compute this matrix, a numerical approach was used where small discrete displacements are applied to the object and variations of the grasp forces obtained from Eqs. (22) are recorded. These grasp forces are then projected along the directions of the reference frame, namely the x and y axes, and summed up. An example of the resulting force variations from an equilibrium position for a set of displacements is shown in Fig.8. Values of the parameters used for this figure are the ones from Tab. II and the configuration of the static equilibrium (at rest) for the grasp corresponds to ^^ி= 70.4° and ^ଶி= 26.1°.

[0077] As one can clearly see from the figure, resulting force variations from a grasp produce an elliptic pattern which is typical for a planar stiffness matrix. The expression of the stiffness matrix corresponding to the geometrical characteristics of the ellipse (major-axis, minor-axis, and the angle ^ between the major axis and the x-axis) can be found using the approach proposed in

[0035] . Based on the numerical parameters of the ellipse, eigenvalues (^^and ^ଶ) and eigenvectors (^^and ^ଶ) of the stiffness matrix can be computed. The eigenvectors to the and minor axes areand the stiffnesswith

[0078] For example, with the data used in Fig.8, one obtains:

[0079] Different geometries of fingers 1R can now be compared based on their resulting stiffness matrices. Indeed, as previously mentioned, the purpose of the optimization is to maximize the stiffness of finger 1R, which is equivalent to maximizing the smaller of the two eigenvalues of the stiffness matrix. An appropriate optimization index (to be minimized) can therefore be defined as:

[0080] which will maximize the minimal stiffness of a grasp produced by finger 1R. Note that for the optimization, the stiffness matrix of finger 1R will be calculated with the grasp of a cylindrical object such as the one defined before and shown in Fig.6.

[0081] The parameters of the optimization are the ones defining the position of the crossbeam of the finger. Thus, the variables one needs to find are the attachment locations of this crossbeam to the intermediate phalanx and the back proximal link for finger 1R. Using the geometrical parameters defined in Fig.3, the corresponding variables and their selected ranges are: •• ^^and ^ଶin [30, 150]°.

[0082] All the other geometrical parameters stay the same between fingers 1R and W and based on early practical fabrication of finger W, the values listed in Tab. II were selected. The optimization problem therefore has four variables and to solve it, the genetic algorithm tool from Matlab was used to minimizethe performance index defined in Eq. (29). To ensure the robust convergence of the algorithm to a solution, the tool was run several times with an initial population of 50 individuals and using a maximal of 2,800 generations resulting in the simulation of hundreds of thousands of grasps. This large number of simulations requires fast force computations, i.e. analytical expressions as established above, to be practical. The obtained results are listed in Tab. III. Once these parameters are obtained, the sensitivity of the performance index to each of the optimal parameters was also studied. Tab. IV shows the absolute values of the average change in value of the optimization index for a ±1% deviation of the optimal parameters. The most influential design parameter is ^1 as this 1% variation of its value yields a 2.50% variation of the global performance criterion. Conversely, ^ଶis the parameter with the weakest impact on the optimization criteria (0.87%).

[0083] The soft finger 10 with the optimal parameters may be 3D printed in thermoplastic polyurethane (TPU, shore 95A, red) in order to proceed with experimental validation of the change in stiffness and its usefulness in practical applications, in an example among others of parameters. To toggle between the two stiffness modes a geometry of snap-fit joint may be similar to the one illustrated in Fig.7. The geometry of this snap-fit is shown in Fig.9. This particular geometry was designed through experimentation with various values of clearances to ensure a proper fit and includes a shoulder, or any other abutment, to prevent the rotation of its circular part inside the associated cavity during the grasp in order for the flexure of the crossbeam to deform and produce the same elastic torque as the other joints. The shoulder or like abutment may be located at a neck of the connector 20A, and may come into contact with a periphery of the complementary connector 11A. Again, in any embodiment or variant described herein, the male connector and female connector in the pair of 11A and 20A may be reversed. Practical considerations on the geometry of the snap-fit joints limits the maximal forces that the finger can applied before buckling occurs. A 3D CAD view of the optimal finger using this snap-fit is presented in Fig.10. An exemplary finger 10 was 3D printed twice and the two fingers are shown in Fig.11 grasping a metal canister both in low- and high- stiffness mode. The specific design of the snap-fit shown in Fig.9 allows for minimal interferences between the disconnected crossbeam and the front and back links of the finger as the crossbeam simply slides on these links.

[0084] To characterize the finger in terms of stiffness, a test bench was designed using a force sensor attached to a motorized translational stage (eTrack series from Newmark) in order to compare the forces produced by the finger as a function of displacements in both the stiff and soft modes, see Fig. 12. The force sensor used is a traction-compression load cell (3138 S-type 100kg) with a Wheatstone bridge including a USB compatible output (PhidgetBridge 4-Input 10460). A Labview software handles both the movement of the translational stage and load cell measurements synchronously. The artifact object used for characterization is a 40 mm cylinder attached to the force sensor and linear stage thereby allowing to apply a precise displacement while measuring the resulting force. Forces were measured in discrete steps of 0.4 mm displace-ments. To compare between the two stiffness mode, three sets of force measurements are obtained for contact points at different locations on the front face of the finger with or without the internalcrossbeam engaged. The resulting force profiles are shown in Fig. 13, each color stands for a specific contact location on the finger while solid lines correspond to the high-stiffness mode and dotted lines to the low-stiffness mode. Fig.14 shows the x-axis stiffness computed from the forces of Fig.13. Note that the values of the (instantaneous) stiffnesses changes for the different displacements of the finger as one could expect, the finger being a complex mechanism, but these stiffnesses follow a similar trend both in low- and high-stiffness modes so their ratios tend to stay around the same values.

[0085] The experimental ratios of the stiffness between the high-and low-stiffness modes are listed in Tab. V. On average, the stiffness is amplified by a factor of more than 4 when the snap-fit joint is engaged and the crossbeam contributes to the grasps. From these results one can also see that the stiffness of the finger tends to be greater when a contact occurs closer to the base of the finger. This also points out that fragile objects should be grasped with the most distal part of the finger that is physically achievable. Fig.15 shows a comparison between the forces computed with the theoretical model and the forces measured with the prototype. Results are consistent as the plots stay generally close over the whole grasp range. However, there is a notable difference between these forces when large displacements are considered. This discrepancy is conjectured to come from two combined causes. First, when excessively large deformations occur the internal crossbeam makes contact with the back of the finger. This is why with large displacements the measured forces are noticeably greater than predicted by the theoretical model. A second source of error comes from the difficulty of achieving an accurate torque model for the compliant joints. Indeed, a simple linear equation was used while for large displacements, the actual force-deformation relationship might be more complex. Additionally, for large displacements, links that were assumed rigid also slightly bend and contribute to the deformation of the finger. Yet and despite these inaccuracies, the proposed model clearly demonstrated its efficiency to capture the most important parts of the finger force- displacement relationship and shows a similar degree of precision as the FEA simulation that is far more computationally intensive. To validate the previous results, additional FEA simulations were conducted using Ansys with the produced optimal finger, similarly to the ones from Section IV. These simulations allowed to validate both the theoretical model and the optimization results. Comparisons are shown in Fig. 15 and again demonstrate an excellent degree of correspondence between the different models and the experiments.

[0086] After the characterization of the prototyped fingers, these fingers were used in a more practical scenario, i.e. with the actual gripper of a robot and more specifically a Baxter collaborative robot. It is a humanoid robot without legs but with two seven-DOF arms. These arms are equipped in this work with theirstandard electric grippers (40 mm translation total stroke) which set the achievable grasp force range as the latter is not a property of the fingers but of the gripper onto which they are affixed. To attach the fingers on these electric grippers, plastic adapters were designed and 3D printed. These adapters have two roles, the first and most obvious is to provide a way of attaching the flexible fingers to the translating parts of the gripper but a second important role is to allows for the connection and disconnection of the snap-fit joint in order for the robot to be able to change the stiffness mode of the finger on its own. The CAD model of these adapters connecting the fingers to the electric gripper shown in Fig.16.

[0087] The procedure for engagement and disengagement of the crossbeam using the stiffness switching tool of the adapter is illustrated by Figs.17 and 18. The engagement is shown in Fig.17 and is the easiest of the two procedures. The tip of the finger attached to one hand of the robot is inserted into the stiffness switching tool of the other hand. This tool is simply constituted by two rigid beams separated by a small distance sufficient to insert the soft finger and its geometry can be adjusted to various sizes of snap- fit joints and crossbeams. As shown in Fig.17b, the compression of each side of the finger during insertion engages the crossbeam. The second procedure, i.e. the disconnection of the snap-fit joint, is shown in Fig. 18. One prong of the stiffness switching tool is inserted between the front links of the finger and the crossbeam (Fig.18a). Then, a rotating motion of the tool pulls on the snap-fit joint and disengages it from the phalanx it was attached to (Fig.18b). Of course, this two-pronged stiffness switching tool can also be attached to a support structure inside the robot workspace, i.e. it does not need to be part of the adapters to the gripper but it is convenient to use when located there.

[0088] The engagement force of the snap fit was measured with a load cell (Shimpo FGV-100XY) and average to 0.73 kg (with a 0.08 standard deviation) which correlates well with the predicted mating force W = 0.76 kg for annular snap fit, considering the part are 3D printed. The predicted mating force of this geometry of joint is:andusing μ = 0.36 as the friction coefficient, ^ = 69.3ƕ as the joint lead angle, ^ = 0.15 mm as the undercut, ^ = 4 mm and ^^= 4.5 mm as the inside and external diameter of the joint, ^ = 30.7 MPa as secant modulus, and where ^ = 0.3 is Poisson’s ratio. All parameters are constant for a geometry of snap fit joint.

[0089] Because the switch from high to low stiffness modes requires the insertion of a fixture prong between the back of the finger and the crossbeam, sufficient space needs to be available. This insertion could be addressed explicitly in the optimization of the design by introducing a geometric constraint tohandle the case when one would converge to a solution where this space is insufficient. For instance a penalty function could be added to Eq.29 to ensure a minimal circle can be inserted in the finger.

[0090] Additionally, a series of experiments were conducted to estimate the payload of the electric gripper when equipped with the proposed finger and compare it to other tools. To this effect, the pullout force of a standardized Schedule 40 PVC pipe out of the gripper was measured and compared to the same gripper when equipped with: Festo DHAS fingers, a rigid finger with soft round contact pad (printed with 5% infill ratio), the same rigid finger with stiff contact pads, see Fig.22. All contact surfaces are made from the same TPU material used to manufacture both our and Festo’s fingers to quantify the intrinsic performance of the kinematic structure proposed in this paper, independently from contact material effects. Similarly, the same electric gripper was commanded with the same input (maximal closing force and stroke) to remove dependence to the gripper characteristics. The results are listed in Tab. VII and indicate that the newly proposed finger has a significantly better payload than Festo’s original design while providing a greater adaptability than rigid finger with pads in addition to a unique selectable stiffness. The grasp range of all grippers are 0-80 mm and the usable finger length is 95 mm.

[0091] The present disclosure may encompass in some embodiments a design of a novel soft finger, inspired by the Fin-Ray Effect, that can switch from a low- to high-stiffness. First, the kinematic analysis of these FRE finger with one or no crossbeam was conducted in order to be able to predict the forces they generate and thus, their resulting grasp stiffness. Then, an optimization aiming at producing fingers with the largest difference between the soft and stiff modes was shown. In future work, this optimization could include all potential designs shown in Fig.2. A novel technique allowing to switch from one design to the other and based on the introduction of an annular snap-fit joint was then presented. This snap-fit reconfiguration allows for the changing of the kinematic structure of the finger which yields a very different behavior of the finger. A greater range of stiffness variation could also be achieved using multiple internal crossbeams equipped with similar detachable snap-fit joints. Finally, a prototype was 3D printed and experiments were conducted to measure the actual stiffness of the two modes and show how one can switch between modes without adding new actuators, as well as to illustrate that stiffness levels can beadapted to practical grasp scenarios. Engaging or disengaging crossbeams in a soft finger is a simple and efficient technique to provide robots or cobots with a finer degree of force control that can be typically achieved using commonly driven pneumatic or electric grippers due to practical issues such as backlash and friction. With the proposed finger 10, the same displacement of the gripper actuator can result in a greatly different grasp stiffness for the seized objects and thus, largely varying grasp forces. The stiffness switch took approximately 4s with the Baxter robot which is only consistently slower than bulk locking but outperforms most other methods and is orders of magnitude faster than material change techniques (e.g. low melting point alloys, shape memory polymers, biomaterials, etc.). The required duration for a stiffness switch of our fingers is only limited by the dynamics of the handling robot and faster robots could achieve dramatically faster switches. Furthermore, while stiffness change of bulk locking is indeed generally very fast, the stiffness variation the latter produces is actually small compared to our technique. For instance, a maximal stiffness variation of 36 % is reported in conventional systems while the average stiffness variation measured for the configurations of the finger 10 is 452 %. This change of stiffness achieved with out proposed design is greater than what can be obtained with fluidic and braided sleeve structures or electroactive polymers and similar to the range of magnetorheological elastomers. See the latter reference for more details on other stiffness changing techniques in soft robotics.

[0092]

[0093] In a variant, the phalanx linkage and the transmission linkage are not linkages, but are instead a phalanx member and a transmission member having a relative elasticity (i.e., they may deform in the elastic range, such as rubbery materials). Alternatively, the phalanx member may be described as including all phalanges and joints therebetween, and may also be referred to as phalanx linkage. For example, in Figs.1A and 1B, the phalanx member may include the phalanges 12, 13 and 14 (or more or fewer depending on the configuration of the finger 10), and the R joints between the phalanges and between a phalanx and the base 10A. Hence, the mechanical finger 10 could be described as having a base adapted to be connected to an actuator for being displaced in one or more degrees of actuation. The mechanical finger 10 would have a phalanx member operationally connected to the base (e.g., by a rotational joint R, in the form of a revolute joint, a living hinge, etc). A transmission member would be operationally connected to the base and to the phalanx member (e.g., by a rotational joint R, in the form of a revolute joint, a living hinge, etc, at both ends). The mechanical finger may have a passive state of actuation in which the base,the phalanx member and the transmission member remain in a constant orientation relative to one another through displacement of the base caused by the actuator absent a contact of the phalanx member with an object, and a grasping state of actuation in which a contact of the phalanx member with an object causes an elastic deformation of the phalanx member relative to the base through displacement of the base caused by the actuator. A stiffening link such as that shown at 20 in Figs.1A and 1B may be between the transmission member and the phalanx member, the stiffening link configured to be releasably connected between a secured condition in which the stiffening link is secured between the transmission member and the phalanx member, and a released condition in which the stiffening link is released from the secured condition, the mechanical finger having a greater stiffness of the phalanx member in the secured condition.

[0094] With reference to the figures shown and described herein, the fingers 10 described herein may be operated according to a method for manipulating a mechanical finger that may include: displacing the at least one mechanical finger to contact at least one object with a first stiffness level in a phalanx linkage of the mechanical finger; connecting a stiffening link between the phalanx linkage and a remainder of the mechanical finger to increase a stiffness of the phalanx linkage to a second stiffness level greater than the first stiffness level; and displacing the mechanical finger to contact at least one object with the second stiffness level in a phalanx linkage of the mechanical finger. The method may also include one or more of: connecting the stiffening link by snap-fitting the stiffening link at one end thereof to one of the phalanx linkage and the remainder; snap-fitting the stiffening link at one end thereof by snap-fitting the stiffening link to the phalanx linkage; displacing the at least one mechanical finger by imparting a movement between two of the mechanical fingers, to grasp at least one object therebetween; imparting the movement between the two of the mechanical fingers by imparting a translational movement between the two of the mechanical fingers; and / or by disconnecting the stiffening link from between the phalanx linkage and the remainder of the mechanical finger to reduce a stiffness of the phalanx linkage to the first stiffness level.

Claims

CLAIMS:

1. A mechanical finger comprising: a base adapted to be connected to an actuator for being displaced in at least one degree of actuation; a phalanx linkage having at least two phalanges, with a first phalanx rotationally connected at a proximal end to the base, and at least a second phalanx rotationally connected at a proximal end to a distal end of the first phalanx; a transmission linkage providing at least one rotational degree of freedom (DOF) between the base and a distal-most one of the phalanges; passive rotational DOF joints between the at least two phalanges, between the base and the first phalanx, and in the transmission linkage, whereby the mechanical finger has a passive state of actuation in which the base, the at least two phalanges and the transmission linkage remain in a constant orientation relative to one another through displacement of the base caused by the actuator absent a contact of one of the phalanges with an object, and a grasping state of actuation in which a contact of at least one of the phalanges with an object causes a variation of the orientation of at least one of the phalanges relative to the base through displacement of the base caused by the actuator; and a stiffening link between the transmission linkage and the phalanx linkage, the stiffening link configured to be releasably connected between a secured condition in which the stiffening link is secured between the transmission linkage and the phalanx linkage, and a released condition in which the stiffening link is released from the secured condition, the mechanical finger having a greater stiffness in the secured condition.

2. The mechanical finger according to claim 1, wherein the passive rotational DOF joints are revolute joints, rotational axes of all said revolute joints being parallel.

3. The mechanical finger according to claim 2, comprising at least four of the revolute joints.

4. The mechanical finger according to any one of claims 1 to 3, comprising three of said phalanges, wherein the distal-most one of the phalanges is a third phalanx rotationally connected at a proximal end to a distal end of the second phalanx, and further wherein the transmission linkage is connected to the third phalanx.

5. The mechanical finger according to claim 1, wherein the passive rotational DOF joints are living hinges.

6. The mechanical finger according to claim 5, wherein the phalanx linkage, the transmission linkage and the base concurrently part of a monolithic body including the living hinges.

7. The mechanical finger according to claim 6, wherein the stiffening link is part of the monolithic body.

8. The mechanical finger according any one of claims 1 to 7, wherein the stiffening link is connected to the transmission linkage by a rotational joint.

9. The mechanical finger according to claim 8, wherein the stiffening link is connected to a proximal link of the transmission linkage, the proximal link being connected to the base by a rotational joint.

10. The mechanical finger according to claim 8 or claim 9, wherein the stiffening link is releasably connected to an intermediate phalanx, with the phalanx linkage sequentially having a proximal phalanx, the intermediate phalanx, and a distal phalanx.

11. The mechanical finger according to any one of claims 1 to 10, further including a snap-fit complementary connector pair including a connector at an end of the stiffening link.

12. A grasping apparatus comprising: at least two of the mechanical finger according to any one of claims 1 to 11, the mechanical fingers oriented for the phalanges of one said mechanical finger to face the corresponding phalanges of the other said mechanical finger; and at least one said actuator to displace the mechanical fingers toward and away from one another in the passive state of actuation and in the grasping state of actuation.

13. The grasping apparatus according to claim 12, wherein the at least one said actuator is a linear actuator imparting a translation movement between the at least two mechanical fingers.

14. A mechanical finger comprising: a base adapted to be connected to an actuator for being displaced in at least one degree of actuation; a phalanx member operationally connected to the base; a transmission member operationally connected to the base and to the phalanx member; the mechanical finger having a passive state of actuation in which the base, the phalanx member and the transmission member remain in a constant orientation relative to one another through displacement of the base caused by the actuator absent a contact of the phalanx member with an object, and a grasping state of actuation in which a contact of the phalanx member with an object causes an elasticdeformation of the phalanx member relative to the base through displacement of the base caused by the actuator; and a stiffening link between the transmission member and the phalanx member, the stiffening link configured to be releasably connected between a secured condition in which the stiffening link is secured between the transmission member and the phalanx member, and a released condition in which the stiffening link is released from the secured condition, the mechanical finger having a greater stiffness of the phalanx member in the secured condition.

15. A method for manipulating at least one mechanical finger comprising: displacing the at least one mechanical finger to contact at least one object with a first stiffness level in a phalanx linkage of the mechanical finger; connecting a stiffening link between the phalanx linkage and a remainder of the mechanical finger to increase a stiffness of the phalanx linkage to a second stiffness level greater than the first stiffness level; and displacing the mechanical finger to contact at least one object with the second stiffness level in a phalanx linkage of the mechanical finger.

16. The method according to claim 15, wherein connecting the stiffening link includes snap- fitting the stiffening link at one end thereof to one of the phalanx linkage and the remainder.

17. The method according to claim 16, wherein snap-fitting the stiffening link at one end thereof includes snap-fitting the stiffening link to the phalanx linkage.

18. The method according to any one of claims 15 to 17, wherein displacing the at least one mechanical finger includes imparting a movement between two of the mechanical fingers, to grasp at least one object therebetween.

19. The method according to claim 18, wherein imparting the movement between the two of the mechanical fingers includes imparting a translational movement between the two of the mechanical fingers.

20. The method according to any one of claims 15 to 19, further including disconnecting the stiffening link from between the phalanx linkage and the remainder of the mechanical finger to reduce a stiffness of the phalanx linkage to the first stiffness level.

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