Robotic gripper

The present disclosure relates to a robotic gripper comprising a body and two robotic fingers mounted to the body. Each robotic finger includes a first link, a second link, a third link, a fourth link, a first joint, a second joint and a third joint. The first joint connects the first link and the second link, and the second joint connects the second link and the third link, and the third joint connects the third link and the fourth link. These links and these joints are comprised of elastic material and are formed in one piece.

BACKGROUND

1. Field of the Invention

The instant disclosure relates to a fully-flexural robotic gripper, which can be configured to perform in pinch and conforming grasp modes.

2. Description of Related Art

Robotic grippers have been developed for various applications. Many grippers are designed for only one application—in other words, they may reliably grasp only specific classes of objects.

For example, in one of various operation modes, the so-called ‘pinch grasp’ mode, one contact surface of a finger of a gripper may be configured to be substantially in parallel to another contact surface of another finger of the gripper. In this pinch mode, the parallel surfaces of each finger will contact the object to be manipulated or moved. Grippers operating in this pinch mode are especially capable at picking up relatively small or light objects, and rectangularly shaped objects.

Another example of an operation mode is the conforming mode. In this mode, at least one finger may deform to conform to the contour of the object. Grippers operating in this conforming mode are especially capable at picking up objects having cylindrical contours, spherical contours, irregular contours or other odd contours.

Under-actuated mechanical systems, which may include springs, triggers, or linkages, may be integrated into a gripper so that it performs both pinch and conforming grasp modes. For example, under-actuation may be introduced into the gripper's fingers, whereby the fingers have relatively less actuators than degrees of freedom, allowing their appendages to both rigidly grip a flat surface or conform naturally to the surface of the object they grasp, depending on the specific design of the under-actuation.

U.S. Pat. No. 8,973,958, granted in 2015 to Robotiq, describes the design of and a method for designing a linkage-driven robotic gripper finger that can perform both pinch and encompassing grasps. The inventions of U.S. Pat. No. 8,973,958 are based on the academic teachings of several papers written between 2004 and 2011, authored by researchers at various Canadian universities. To paraphrase the academic document ‘The kinematic preshaping of triggered self-adaptive linkage-driven robotic finger’ (Birglen, 2011), by carefully selecting the lengths of each link, one can define a ‘stable pinch region.’ This stable grasp region, combined with a pre-shaping spring, allows the finger to grasp in a pinch mode when the spring is not engaged, and to grasp in an conforming mode when it is. However, the mechanical system proposed by U.S. Pat. No. 8,973,958 has its own limitations. It serves as a prime example of the downsides of traditional under-actuated finger designs, including but not limited to: the difficulty of mass production, part count and assembly cost, and robustness. Most notably however, is the restriction of the gripper's compliance to 2 dimensions (2D). Because the mechanical systems uses ‘pin joints’, which are a 1 degree of freedom rotational joint, configured to lie all in the same plane, the resulting compliance can only lie within that plane. There is no out-of-plane bending or deformation.

To improve the overall compliance of grippers, hands like the ‘i-HY Hand’ have been developed. The hand is a 2012 collaborative project between the company iRobot, Yale University, and Harvard University. The i-HY hand improves upon the core concept, introduced some years earlier by Professor Aaron Dollar of Yale University, of using ‘flexural joints’ instead of traditional pin joints in robotic grippers. Flexural joints are different from traditional pin joints because they are a 6 degree of freedom joint; they can rotate along 3 axes and deform along 3 axes, albeit in a non-linear fashion. This 3D compliance allows the fingers to conform to a wider array of objects than a gripper with rudimentary 2D compliance can. Yet, just like U.S. Pat. No. 8,973,958, existing ‘flexural’ gripper fingers have their own drawbacks. They are generally cable-driven, increasing their assembly time. They are generally in-molded, increasing manufacturing costs. And most importantly, they only are able to achieve conforming grasp modes. Because they do not have a ‘stable pinch region’, they cannot perform a true pinch grasp mode.

SUMMARY OF THE INVENTION

The instant disclosure relates to a robotic finger that is capable of performing both pinch and conforming grasp modes but is able to conform to objects in 3 dimensions. Because it may be made from a single piece of rubber, plastic, or other highly flexible material, it has a number of advantages over both existing linkage-driven and flexure-based under-actuated gripper fingers.

Because the robotic finger may be manufactured as a single part, both the manufacturing and assembly time costs are dramatically reduced. Manufacturing technologies like injection molding and hot-press molding can allow for the part to be mass-produced at relatively low cost.

Because the robotic finger may be comprised of a single piece of elastomeric material, it is inherently robust; it is physically resistant to bumps, vibrations, and shocks. Furthermore, the robotic finger is inherently waterproof—a growing requirement for marine robotic environments. In addition, the robotic gripper is easier to clean.

Most importantly, the robotic finger achieves both pinch and conforming grasp capability, while retaining all the advantages of flexural fingers. Because the geometry of the finger is designed with 6-axis forces and torques in mind, each of its joints can rotate in 3 dimensions and translate in 3 dimensions, albeit in a non-linear fashion. Similarly, each of its links can be considered as a rigid link in 3D space, depending on specific design parameters. This allows the finger to achieve both pinch and conforming grasp modes, much like existing linkage-driven under-actuated gripper designs. Additionally, it also allows the finger to achieve compliance in 3 dimensions, much like existing flexure-jointed under-actuated gripper designs.

The ‘joint’ and ‘link’ regions and the remaining details of the robotic gripper and finger are defined as follows.

According to one exemplary embodiment of the instant disclosure, a robotic finger includes a first link having a first end and a second end, a second link having a first end and at least one second end, at least one third link having a first end and a second end, a fourth link having at least one first end and a second end, a first joint between the second end of the first link and the first end of the second link, at least one second joint between the second end of the second link and the first end of the third link, and at least one third joint between the second end of the third link and the first end of the fourth link. The first, second, third and fourth links and the first, second and third joints include elastic material and are formed in one piece. As described above, manufacturing the finger as a single part as benefits for manufacturability, cost, and waterproofing.

According to another exemplary embodiment of the instant disclosure, a robotic finger includes a first link having a first end and a second end, a second link having a first end and at least one second end, at least one third link having a first end and a second end, a fourth link having at least one first end and a second end, a first joint between the second end of the first link and the first end of the second link, at least one second joint between the second end of the second link and the first end of the third link, and at least one third joint between the second end of the third link and the first end of the fourth link. The first, second, third and fourth links and the first, second and third joints are configured to be compliant in three dimensions. As described above, three-dimensional compliance allows the gripper to grasp a wider variety of oddly-shaped objects, and improves robustness.

According to another exemplary embodiment of the instant disclosure, a method for operating a robotic gripper includes providing a body which has a first driver, a first idle ground joint, a second driver and a second idle ground joint, providing a first robotic finger which includes a first link having a first end and a second end, a second link having a first end and at least one second end, at least one third link having a first end and a second end, a fourth link having at least one first end and a second end, a first joint between the second end of the first link and the first end of the second link, at least one second joint between the second end of the second link and the first end of the third link, and at least one third joint between the second end of the third link and the first end of the fourth link, wherein the first, second, third and fourth links and the first, second and third joints are configured to be compliant in three dimensions, and wherein the first end of the first link of the first robotic finger is mounted to one of the first driver and the first idle ground joint, the second end of the fourth link of the first robotic finger is mounted to the other one of the first driver and the first idle ground joint, providing a second robotic finger which includes a first link having a first end and a second end, a second link having a first end and at least one second end, at least one third link having a first end and a second end, a fourth link having at least one first end and a second end, a first joint between the second end of the first link and the first end of the second link, at least one second joint between the second end of the second link and the first end of the third link, and at least one third joint between the second end of the third link and the first end of the fourth link, wherein the first, second, third and fourth links and the first, second and third joints are configured to be compliant in three dimensions, and wherein the second end of the fourth link of the second robotic finger is mounted to one of the second driver and the second idle joint and the first end of the first link of the second robotic finger is mounted to the other one of the second driver and the second idle ground joint, and driving the first and second drivers so as to actuate the first and second robotic fingers to perform a pinch grasp or a conforming grasp of an object.

In order to further understand the instant disclosure, the following embodiments are provided along with illustrations to facilitate appreciation of the instant disclosure; however, the appended drawings are merely provided for reference and illustration, without any intention to limit the scope of the instant disclosure.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1is a perspective view of a robotic gripper100in accordance with some embodiments of the instant disclosure. The robotic gripper100may include a robotic finger1, a robotic finger2and a body3. The robotic finger1and the robotic finger2can be mounted to the body3.

FIG. 2Ais a perspective view of a robotic finger1in accordance with some embodiments of the instant disclosure. The robotic finger1may include four links11,12,13and14and three joints15,17and19. The link11may have two ends111and112which are opposite to each other. The link12may have two ends121and122which are opposite to each other. The link13may have three ends,131,132and133. The link14may have two ends141and142, which are opposite to each other. The joint15may connect the end112of the link11and the end121of the link12, and the joint17may connect the end122of the link12and the end131of the link13, and the joint19may connect the end132of the link13and the end141of the link14. These links11,12,13and14and these joints15,17and19may include elastic material and are formed in one piece, and they are configured to be compliant in three dimensions.

Please note that the X, Y and Z axes described below use a three-dimensional Cartesian coordinate system. The positive Z-axis may extend in the general direction from the end111of the link11to the end133of the link13and can be interpreted to be substantially vertical in the primary linkage plane. The positive X-axis extends in the general direction from the end142of the link14to the end112of the link11and can be interpreted to be substantially horizontal in the primary linkage plane. The remaining Y axis is defined using the right-hand rule.

[Exemplary Bending Modes and Design Parameters]

At least three exemplary deformation modes for the gripper finger as discussed above are described below.

The first mode can be the bending of the finger in the primary linkage plane, the X-Z plane. Bending in the primary linkage plane allows for pinching and conforming grasps of objects. In order for the finger to be able to both pinch and conform, the spring strength of the first joint must be significantly greater than the spring strength of the second and third joints. However, the second and third joints should not be too thin practically, or else the gripper will not be robust or able to transmit high amounts of gripping force through the fingertip. These are but a few of the design considerations in the primary linkage plane.

The second mode can be what we call ‘fingertip roll’, or torsion of the finger about the Z-axis. Fingertip roll allows the surface of the fingertips to conform to objects that are not simple 2-D contours, but rather 3-D surfaces. To increase fingertip roll, the length of the second and third joints may be much greater than the thickness of the second and third joints. However, doing so comes at a price: out of plane deflection will be increased. As one can quickly see, changing one parameter to improve one deflection mode has ramifications for other deflection modes.

The third mode can be ‘out-of-plane bending,’ which is deflection along the Y-axis, or almost equivalently, bending about the X-axis. There is a balance required in this design space. Too much out of plane bending, and the gripper will not be able to lift anything heavy; it will flop over and be too limp. Too little out of plane bending, and the gripper will not be robust to out of plane shocks or bumps and it will be prone to breakage, much like existing linkage-driven underactuated grippers.

Achieving the appropriate amount of deformation for each critical mode requires careful consideration of the design parameters of the finger. The modes are all interrelated and changing one physical parameter will have different effects on all modes. The specifics below are the parameters we have theoretically and empirically found that work best for our use cases.

FIG. 2Bis a top view of a robotic finger1in accordance with some embodiments of the instant disclosure. With reference toFIG. 2B, the thickness of the end112of the link11and the thickness of the end121of the link12may be greater than the smallest thickness of the joint15. The thickness of the end122of the link12and the thickness of the end131of the link13may be greater than the smallest thickness of the joint17. The thickness of the end132of the link13and the thickness of the end141of the link14may be greater than the smallest thickness of the joint19. That is, the thickness of the link11,12,13or14may be greater than the thickness of the joint15,17or19to which it connects. In one embodiment, the smallest thickness of the joint17or joint19may be around 2.5 mm. Especially, the largest thickness of the link12may be about 9 times greater than or equal to the smallest thickness of the joint17, and the largest thickness of the link14may be about 9 times greater than or equal to the smallest thickness of the joint19. In one embodiment, the largest thickness of the link12and the largest thickness of the link14may be greater than or equal to 22.5 mm. Further, since the thickness of the joint15,17,19may be substantially smaller than the thickness of the link11,12,13,14, the joint15,17,19will be more flexible and deformable than the link11,12,13,14. The joint15,17,19will act as a joint connecting to two links. Referring toFIG. 2B, the joint15will act as a joint connecting the links11and12, the joint17will act as a joint connecting the links12and13, and the joint19will act as a joint connecting the links13and14.

The joints15,17and19can be considered as joints with rotation around out-of-plane axes as having a low spring rate, and rotation about in-plane axes as having a high spring rate. Further, the links11,12,13and14while more rigid (not entirely rigid) also may rotate/bend in three axes with various spring rates that are generally higher than the join spring rates. This is a novel aspect of these gripper fingers that allow multiple modes of conformance with a grasped object.

Since the joints15,17and19may include elastic material, the spring stiffness of the joints15,17and19could be designed by selecting the thicknesses of the joints15,17and19. As shown inFIG. 2B, the smallest thickness of the joint15may be greater than the smallest thickness of the joint17, and greater than the smallest thickness of the joint19. That is, the spring stiffness of the joint15may be greater than the spring stiffness of the joint17and the spring stiffness of the joint19. In addition, the smallest thickness of the joint15may range from two times the smallest thickness of the joint17to five times the smallest thickness of the joint17, or a range from two times the smallest thickness of the joint19to five times the smallest thickness of joint19. In one embodiment, the smallest thickness of the joint15may range from 5 mm to 12.5 mm.

Referring toFIGS. 2A and 2B, the link13may have a side surface135between the ends132and133, and the side surface135may be substantially flat.

FIGS. 2C and 2Dare a right side view and a left side view respectively of a robotic finger1in accordance with some embodiments of the instant disclosure. As shown inFIGS. 2C and 2D, the finger1may be substantially tapered. Referring toFIG. 2C, the width of the link14may be substantially tapered toward the joint19, and the width of the joint19may be substantially tapered toward the link13, and the link13may be substantially tapered toward its end133. Moreover, referring toFIG. 2D, the width of the link12is substantially tapered toward the joint17and the width of the joint17is substantially tapered toward the link13. The width of the robotic finger1may range from eight times the smallest thickness of the joint17to twelve times the smallest thickness of the joint17, or range from eight times the smallest thickness of the joint19to twelve times the smallest thickness of the joint19. In one embodiment, the width of the robotic finger1may range from 20 mm to 30 mm.

The total length of the finger1, such as the distance from the right side of the link11to the left side of the link13as shown inFIG. 2D, may range from thirty times the smallest thickness of the joint17to fifty times the smallest thickness of the joint17, or range from thirty times the smallest thickness of the joint19to fifty times the smallest thickness of the third joint19. In one embodiment, the total length of the robotic finger1may range from 75 mm to 125 mm.

In addition, the length of the joint17may range from three times the smallest thickness of the joint17to six times the smallest thickness of the joint17, and the length of the joint19may range from three times the smallest thickness of the joint19to six times the smallest thickness of the joint19. In one embodiment, the length of the joint17and the length of the joint19may range from 7.5 mm to 15 mm.

FIG. 3Ais a perspective view of a robotic finger2in accordance with another embodiment of the instant disclosure. The robotic finger2may include five links21,22,23and24and five joints25,27and29. The link21may have two ends211and212which are opposite to each other. The link22may have one end221and two ends222opposite to the end221and projecting in a branch-shape. Each of two links23may have three ends231,232and233. The link24has one end242and two ends241opposite to the end242and projecting in a branch-shape. The joint25may connect the end212of the link21and the end221of the link22. Two joints27may respectively connect the ends222of the link22and the ends231of the links23. Two joints29may respectively connect the ends232of the links23and the ends241of the link24. These links21,22,23and24and these joints25,27and29may include elastic material and are formed in one piece, and thus they are configured to be compliant in three dimensions.

FIG. 3Bis a top view of a robotic finger2in accordance with some embodiments of the instant disclosure. With reference toFIG. 3B, the thickness of the end212of the link21and the thickness of the end221of the link22may be greater than the smallest thickness of the joint25. The thickness of the end222of the link22, and the thickness of the end231of the link23, may be greater than the smallest thickness of the joint27. The thickness of the end232of the link23and the thickness of the end241of the link24are greater than the smallest thickness of the joint29. That is, the thickness of the link21,22,23or24may be greater than the thickness of the joint25,27or29to which it connects. In one embodiment, the smallest thickness of the joint27or joint29may be around 2.5 mm. In particular, the largest thickness of the link22may be about 9 times greater than or equal to the smallest thickness of the joint27, and the largest thickness of the link24may be about 9 times greater than or equal to the smallest thickness of the joint29. In one embodiment, the largest thickness of the link22and the largest thickness of the link24may be greater than or equal to 22.5 mm. Further, since the smaller thickness of joint25,27,29may be substantially smaller than the thickness of the link,21,22,23,24, the joint25,27,29will be more flexible and deformable than the links21,22,23and24Referring toFIG. 3B, the joint25will act as a joint connecting the links21and22, the joint27will act as a joint connecting the links22and23, and the joint29will act as a joint connecting the links23and24.

The joints25,27and29can be considered as joints with rotation around out-of-plane axes as having a low spring rate, and rotation about in-plane axes as having a high spring rate. Further, the links21,22,23and24while more rigid (not entirely rigid) also may rotate/bend in three axes with various spring rates that are generally higher than the join spring rates. This is a novel aspect of these gripper fingers that allow multiple modes of conformance with a grasped object.

Since the joints25,27and29may include elastic material, the spring stiffness of the joints25,27and29could be designed by selecting the thicknesses of the joints25,27and29. As shown inFIG. 3B, the smallest thickness of the joint25may be greater than the smallest thickness of the joint27, and greater than the smallest thickness of the joint29. That is, the spring stiffness of the joint25may be greater than the spring stiffness of the joint27and the spring stiffness of the joint29. In addition, the smallest thickness of the joint25may range from two times the smallest thickness of the joint27to five times the smallest thickness of the joint27, or may range from two times the smallest thickness of the joint29to five times the smallest thickness of the third joint29. In one embodiment, the smallest thickness of the joint25may range from 5 mm to 12.5 mm.

Referring toFIGS. 3A and 3B, each of the links23may have a side surface235between the ends232and233, and the side surface235is substantially flat. The side surfaces235and the links23thereof and the joints29and27which connect to the links23can deform independently of the links22and24. That is, the surfaces235of the links23can accommodate to the irregular surface of the object which will be grasped.

In addition, in some embodiments, the surfaces235may not be made the same shape, nor have the same surface material. Further, the surfaces235may have different geometries, widths, lengths, stiffnesses to allow a wider range of grasping modes. They may even have different numbers of links and joints.

FIGS. 3C and 3Dare a left side view and a right side view of a robotic finger2in accordance with some embodiments of the instant disclosure. As shown inFIG. 3C, the link24may have two ends241projecting in a branch-shape and connecting to the joints29respectively. Moreover, each of joints29may connect the end232of the link23. As shown onFIG. 3D, the link22may have two ends222projecting in a branch-shape and connecting to the joints27respectively. Moreover, each of the joints27may connect the end231of the link23. Referring toFIGS. 3C and 3D, the distance between the joints29, the distances between the joints27, and the distances between the links23are narrowed from the links22,24to the tips of the links23.

The total length of the finger2, such as the distance from the right side of the link21to the left side of the link23as shown inFIG. 3D, may range from thirty times the smallest thickness of the joint27to fifty times the smallest thickness of the joint27, or range from thirty times the smallest thickness of the joint29to fifty times the smallest thickness of the third joint29. In one embodiment, the total length of the robotic finger2may range from 75 mm to 125 mm.

In addition, the length of the joint27may range from three times the smallest thickness of the joint27to six times the smallest thickness of the joint27, and the length of the joint29may range from three times the smallest thickness of the joint29to six times the smallest thickness of the joint29. In one embodiment, the length of the joint27and the length of the joint29may range from 7.5 mm to 15 mm.

In order to analytically study the subject finger, it is reduced to an approximation of a 5-bar pin-link mechanism. The three joints areas of the finger are approximated as pins with associated spring stiffnesses. The four link areas of the finger are approximated as rigid links, as is the ground link.

Birglen and Gosselin in their paper ‘Kinetostatic Analysis of Underactuated Fingers’ (2004) propose a method for designing and analyzing the stability of a 5-bar linkage-driven finger similar to our finger. The paper concludes that a pinch grasp is stable if a linear contact is made on both sides of what it also defines as the ‘equilibrium point,’ which we will not elaborate on here.

However, the analysis only holds if the spring stiffness of the second and third joints is zero. In our case, the spring constants of the second and third joints, while much less than the stiffness of the first joint, are non-negligible. Therefore, the motion of the finger should be corrected so that the gripping area of the third link remains substantially parallel to the Y-Z plane.

The aforesaid correction can be done by, for example but is not limited to, ‘superimposing’ a linkage with the desired motion onto our original linkage. Without any modification, the third link will rotate too much with respect to the world frame, or, in other words, not rotate enough with respect to the rest of the finger. With the modifications we describe below, the third link will rotate the appropriate amount to keep its face parallel to the opposite gripper finger.

Because the spring strength of the first joint is much greater than those of the second and third joints, we can approximate the linkage as a 4-bar linkage when it is not contacting any object. Instead of designing a parallel linkage, a linkage is designed where the coupler (the third link, in the case of our finger) rotates clockwise whenever the driver (the first link, in the case of our finger) rotates counterclockwise.

Practically, implementing this modification is as simple as making sure the distance from the end111of the link11to the end142of the fourth link14is greater than the distance from the joint17to the joint19.

FIG. 4Ais a top schematic view of a robotic gripper100in accordance with some embodiments of the instant disclosure. As shown inFIG. 4A, the robotic gripper100may have a body3and two robotic fingers1and2mounted to the body3. The body may have two drivers and two idle ground joints, wherein one of the elements31and32is a driver and the other one is an idle ground joint, and wherein one of the elements33and34is a driver and the other one is an idle ground joint. The end111of the link11of the robotic finger1is mounted to the element31(not shown), and the end142of the link14of the robotic finger1is mounted to the element32, and thereby the robotic finger1is mounted to the body3. It means that the robotic finger1will be driven by a single driver. When the driver drives the end111to rotate around the element31or drives the end142to rotate around the element32, the robotic finger1will move relative to the body3. Moreover, the end242of the link24of the robotic finger2is mounted to the element33, and the end211of the link21of the robotic finger2is mounted to the element34, and thereby the robotic finger2is mounted to the body3. It means that the robotic finger2will be driven by a single driver. When the driver drives the end242to rotate around the element33or drives the end211to rotate around the element34, the robotic finger2will move relative to the body3. In addition, referring toFIG. 4A, the position of the element31is lower than the position of the element32, and the position of the element34is lower than the position of the element33such that the line between the elements31and32, and the line between the joints17and19are not parallel to each other, and the line between the elements33and34and the line between the joints27and29are not parallel to each other. Further, the distance between the elements31and32is larger than the distance between the joints17and19of the robotic finger1, and the distance between the elements33and34is larger than the distance between the joints27and29of the robotic finger2. Moreover, the face135of robotic finger1and the line between joints17and19of robotic finger1form an angle that is greater than 90 degrees. Further, the surface135of the robotic finger1and the surface235of the robotic finger2are substantially parallel to each other.

FIG. 4Bis a top schematic view of a robotic gripper100in accordance with some embodiments of the instant disclosure, wherein the robotic fingers1and2are opened. As shown inFIG. 4B, the robotic fingers1and2are actuated to move away from each other. The robotic finger1is driven by one of the elements31and32. Since the robotic finger1includes elastic material and is formed in one piece and has the flexible and deformable joints15,17, and19, the robotic finger1will act as a five-bar linkage mechanism when the driver drives the robotic finger1. Referring toFIG. 4B, when the robotic finger1is moved outwardly by the driver, the joints15,17, and19are deformed, and the links11,12and13are rotated around the joints15,17, and19. Likewise, the robotic finger2is driven by one of the elements33and34. Since the robotic finger2includes elastic material and is formed in one piece and has the flexible and deformable joints25,27, and29, the robotic finger2will act as a five-bar linkage mechanism when the driver drives the robotic finger2. Referring toFIG. 4B, when the robotic finger2is moved outwardly by the driver, the joints25,27and29are deformed, and the links21,22and23are rotated around the joints25,27and29.

In addition, since the line between the elements31and32and the line between the joints17and19are not parallel to each other, and the line between the elements33and34and the line between the joints27and29are not parallel to each other, and the distance between the elements31and32is substantially larger than the distance between the joints17and19of the robotic finger1and the distance between the elements33and34is substantially larger than the distance between the joints27and29of the robotic finger2, the side surface135of the robotic finger1and the side surface235of the robotic finger2will be kept to be substantially parallel to each other during the process of opening the robotic fingers1and2.

FIG. 4Cis a top schematic view of a robotic gripper100in accordance with some embodiments of the instant disclosure, wherein the robotic fingers1and2are nearly closed. As shown inFIG. 4C, the robotic fingers1and2are actuated to move close to each other. As mentioned above, since the robotic finger1includes elastic material and is formed in one piece and has the flexible and deformable joints15,17and19, the robotic finger1will act as a five-bar linkage mechanism when the driver drives the robotic finger1. Referring toFIG. 4C, when the robotic finger1is moved inwardly by the driver, the joints15,17and19are deformed and the links11,12and13are rotated around the joints15,17and19. Further, since the robotic finger2includes elastic material and is formed in one piece and has the flexible and deformable joints25,27and29, the robotic finger2will act as a five-bar linkage mechanism when the driver drives the robotic finger2. Referring toFIG. 4C, when the robotic finger2is moved inwardly by the driver, the joints25,27and29are deformed and the links21,22and23are rotated around the joints25,27and29.

In addition, since the line between the elements31and32and the line between the joints17and19are not parallel to each other, and the line between the elements33and34and the line between the joints27and29are not parallel to each other and the distance between the elements31and32is substantially larger than the distance between the joints17and19of the robotic finger1, and the distance between the elements33and34is substantially larger than the distance between the joints27and29of the robotic finger2, the side surface135of the robotic finger1and the side surface235of the robotic finger2will be kept to be substantially parallel to each other during the process of closing the robotic fingers1and2.

FIG. 5Ais a top schematic view of a robotic gripper100′ in accordance with another embodiment of the instant disclosure. As shown inFIG. 5A, the robotic gripper100′ may have a body3′ and two robotic fingers1′ and2′ mounted to the body3′. The body3′ may have two drivers and two idle ground joints, wherein one of the elements31′ and32′ is a driver and the other one is an idle ground joint, and wherein one of the elements33′ and34′ is a driver and the other one is an idle ground joint. The end111′ of the link11′ of the robotic finger1′ is mounted to the element31′ and the end142′ of the link14′ of the robotic finger1′ is mounted to the element32′, and thereby the robotic finger1′ is mounted to the body3′. It means that the robotic finger1′ will be driven by a single driver. When the driver drives the end111′ to rotate around the element31′ or drives the end142′ to rotate around the element32′, the robotic finger1′ will move relative to the body3′. Moreover, the end242′ of the link24′ of the robotic finger2′ is mounted to the element33′ and the end211′ of the link21′ of the robotic finger2′ is mounted to the element34′, and the robotic finger2′ is thereby mounted to the body3′. It means that the robotic finger2′ will be driven by a single driver. When the driver drives the end242′ to rotate around the element33′ or drives the end211′ to rotate around the element34′, the robotic finger2′ will move relative to the body3′. In addition, referring toFIG. 5A, the elements31′,32′,33′ and34′ are positioned such that the line between the elements31′ and32′ and the line between the joints17′ and19′ are parallel to each other, and the line between the elements33′ and34′ and the line between the joints27′ and29′ are parallel to each other. Further, the distance between the elements31′ and32′ is substantially equal to the distance between the joints17′ and19′ of the robotic finger1′, and the distance between the elements33′ and34′ is substantially equal to the distance between the joints27′ and29′ of the robotic finger2′. Thus, in this state, the surfaces135′ and235′ of the robotic fingers1and2may not be kept to be substantially parallel to each other. As shown inFIG. 5A, the surfaces135′ and235′ may be inclined outwardly.

FIG. 5Bis a top schematic view of a robotic gripper100′ in accordance with some embodiments of the instant disclosure, wherein the robotic fingers1′ and2′ are opened. As shown inFIG. 5B, the robotic fingers1′ and2′ are actuated to move away from each other. The robotic finger1′ is driven by one of the elements31′ and32′. Since the robotic finger1′ includes elastic material and is formed in one piece and has the flexible and deformable joints15′,17′ and19′, the robotic finger1′ will act as a five-bar linkage mechanism when the driver drives the robotic finger1′. Referring toFIG. 5B, when the robotic finger1′ is moved outwardly by the driver, the joints15′,17′ and19′ are deformed and the links11′,12′ and13′ are rotated around the joints15′,17′ and19′. Likewise, the robotic finger2′ is driven by one of the elements33′ and34′. Since the robotic finger2′ includes elastic material and is formed in one piece, and has the flexible and deformable joints25′,27′ and29′, the robotic finger2′ will act as a five-bar linkage mechanism when the driver drives the robotic finger2′. Referring toFIG. 5B, when the robotic finger2′ is moved outwardly by the driver, the joints25′,27′ and29′ are deformed and the links21′,22′ and23′ are rotated around the joints25′,27′ and29′.

In addition, since the line between the elements31′ and32′ and the line between the joints17′ and19′ are substantially parallel to each other, and the line between the elements33′ and34′ and the line between the joints27′ and29′ are substantially parallel to each other and the distance between the elements31′ and32′ is substantially equal to the distance between the joints17′ and19′ of the robotic finger1′, and the distance between the elements33′ and34′ is substantially equal to the distance between the joints27′ and29′ of the robotic finger2′, the side surface135′ of the robotic finger1′ and the side surface235′ of the robotic finger2′ will not be kept to be substantially parallel to each other during the process of opening the robotic fingers1′ and2′. As shown inFIG. 5B, the surfaces135′ and235′ are inclined outwardly.

FIG. 5Cis a top schematic view of a robotic gripper100′ in accordance with some embodiments of the instant disclosure, wherein the robotic fingers1′ and2′ are in a substantially closed state. As shown inFIG. 5C, the robotic fingers1′ and2′ are actuated to move close to each other. As mentioned above, since the robotic finger1′ includes elastic material and is formed in one piece and has the flexible and deformable joints15′,17′ and19′, the robotic finger1′ will act as a five-bar linkage mechanism when the driver drives the robotic finger1′. Referring toFIG. 5C, when the robotic finger1′ is moved inwardly by the driver, the joints15′,17′ and19′ are deformed and the links11′,12′ and13′ are rotated around the joints15′,17′ and19′. Further, since the robotic finger2′ includes elastic material and is formed in one piece and has the flexible and deformable joints25′,27′ and29′, the robotic finger2′ will act as a five-bar linkage mechanism when the driver drives the robotic finger2′. Referring toFIG. 5C, when the robotic finger2′ is moved inwardly by the driver, the joints25′,27′ and29′ are deformed and the links21′,22′ and23′ are rotated around the joints25′,27′ and29′.

In addition, since the line between the elements31′ and32′ and the line between the joints17′ and19′ are substantially parallel to each other, and the line between the elements33′ and34′ and the line between the joints27′ and29′ are substantially parallel to each other, and the distance between the elements31′ and32′ is substantially equal to the distance between the joints17′ and19′ of the robotic finger1′, and the distance between the elements33′ and34′ is substantially equal to the distance between the joints27′ and29′ of the robotic finger2′ (referring toFIG. 5A), the side surface135′ of the robotic finger1′ and the side surface235′ of the robotic finger2′ will not be kept to be substantially parallel to each other during the process of closing the robotic fingers1′ and2′. As shown inFIG. 5C, the side surfaces135′ and235′ are inclined inwardly.

Given the above, as shown inFIG. 5A, if the line between the elements31′ and32′ and the line between the joints17′ and19′ are substantially parallel to each other, and the line between the elements33′ and34′ and the line between the joints27′ and29′ are substantially parallel to each other, and the distance between the elements31′ and32′ is substantially equal to the distance between the joints17′ and19′ of the robotic finger1′ and the distance between the elements33′ and34′ is substantially equal to the distance between the joints27′ and29′ of the robotic finger2′, the side surface135′ of the robotic finger1′ and the side surface235′ of the robotic finger2′ will not be kept to be substantially parallel to each other during the processes of opening and closing the robotic fingers1′ and2′. As shown inFIGS. 5B and 5C, the surfaces135′ and235′ are inclined outwardly when the robotic fingers1′ and2′ are opened and the side surfaces135′ and235′ are inclined inwardly when the robotic fingers1′ and2′ are closed. Since the side surface135′ of the robotic finger1′ and the side surface235′ of the robotic finger2′ will not be kept to be substantially parallel to each other during the processes of opening and closing the robotic fingers1′ and2, the robotic gripper100′ cannot accurately and smoothly pinch an object. Especially, the robotic gripper100′ will hardly pinch a small object or an object with a small diameter, such as a pen.

[An Exemplary Embodiment of Pinch Mode]

FIGS. 6A and 6Bshow that the robotic gripper100can perform a pinch grasp of a square object. Referring toFIG. 6A, the robotic gripper100will pinch an object51which has two substantially flat and substantially parallel surfaces511and512. The drivers31,32,33and34drive the robotic fingers1and2such that they move inwardly. As mentioned above, the side surface135of the robotic finger1and the side surface235of the robotic finger2will be kept to be substantially parallel to each other during the process of closing the robotic fingers1and2. Thus, the side surface135and the side surface235will be substantially parallel to each other until they contact the side surfaces511and512of the object51. As shown inFIG. 6B, since the side surfaces511and512of the object51are parallel to each other, the parallel surfaces135and235can directly pinch the object51. Then the robotic fingers1and2have grasped and can lift the object51.

As mentioned above, the spring stiffness of the joint15is substantially greater than the spring stiffness of the joint17and the spring stiffness of the joint19, and the spring stiffness of the joint25is substantially greater than the spring stiffness of the joint27and the spring stiffness of the joint29. The greater spring stiffness of the joints15and25will be helpful for keeping the side surfaces135and235to be substantially parallel to each other during the process of closing the robotic fingers1and2, and cause the robotic fingers1and2to be strong enough to pinch the object51tightly. If the spring stiffness of the joints15and25are too weak, the side surfaces135and235may not remain substantially parallel to each other during the process of closing the robotic fingers1and2, and then the robotic fingers1and2cannot pinch the object51. Even if such robotic fingers1and2with weak spring stiffness of the joints15and25can pinch the object51, the robotic fingers1and2will not be strong enough to pinch the object51tightly. Thus, preferably, the smallest thickness of the joint15is at least two times greater than the smallest thickness of the joint17and at least two times greater than the smallest thickness of the joint19, and the smallest thickness of the joint25is at least two times greater than the smallest thickness of the joint27and at least two times greater than the smallest thickness of the joint29.

[An Exemplary Embodiment of Conforming Mode]

FIGS. 7A, 7B and 7Cshow that the robotic gripper100grasps an oddly-shaped object. Referring toFIG. 7A, the robotic gripper100will grasp an oddly-shaped object, such as a ball52. The drivers31,32,33and34drive the robotic fingers1and2such that they move inwardly. As mentioned above, the side surface135of the robotic finger1and the side surface235of the robotic finger2will be kept to be substantially parallel to each other during the process of closing the robotic fingers1and2. Thus, the side surface135and the side surface235will be substantially parallel to each other until the robotic fingers1and2contact the outer surface of the ball52. As shown in FIG.7B, the robotic fingers1and2contact the outer surface of the ball52and the side surfaces135and235are substantially parallel to each other.

After the robotic fingers1and2contact the outer surface of the ball52, the drivers31,32,33and34still drive the robotic fingers1and2to move inwardly. However, since the ball52is grasped between the link14of the robotic finger1and the link24of the robotic finger2, the links14and24will not continue to move inwardly. Thus, the drivers31,32,33and34will cause the joints15,17,19,25,27and29to be further deformed. In this way, as shown inFIG. 7C, the links13and23will further rotate around the joints19and29respectively and thus still move inwardly. Finally, the robotic fingers1and2will conform to the ball52, and then the robotic gripper can grasp and lift the ball52.

In addition, as mentioned above, the spring stiffness of the joints15,25should be strong enough such that the robotic fingers1and2are tough enough to pinch an object tightly. However, if the spring stiffness of the joints15,25is too strong, the joints15and25will not be further deformed after the robotic fingers1and2contact the ball52and the drivers31,32,33and34still drive the robotic fingers1and2to move inwardly. That is, the links13and23will not further rotate around the joints19and29respectively and will not move inwardly. Therefore, the robotic fingers1and2will ultimately not conform to the ball52.

[Another Exemplary Embodiment of Conforming Mode]

Firstly, the X, Y and Z axes shown inFIGS. 8A and 8Buse a three-dimensional Cartesian coordinate system. The positive Z-axis may extend in the general direction from the end111of the link11to the end133of the link13and can be interpreted to be vertical in the primary linkage plane. The positive X-axis extends in the general direction from the end142of the link14to the end112of the link11and can be interpreted to be horizontal in the primary linkage plane. The remaining Y axis is defined the right-hand rule.

FIG. 8Ashows that the robotic gripper100lifts a heavy object53. When the robotic gripper100lifts a heavy object53, it may deflect in undesirable ways. As shown inFIG. 8A, the object may exert a frictional force on the surfaces of the robotic fingers1and2. The bending of the robotic fingers1and2due to gravity is negative in the Y-axis or about the X-axis. Thus, the robotic fingers1,2should be designed as a cantilevered beam with force acting on it at some distance from the body member3. In order to design the robotic fingers1and2as a cantilevered beam, the width of the fingers1and2should be increased in the Y-axis. Moreover, referring toFIG. 2C, the ratio of the distance between the end133of the link13and the111end of the link11to the width of the first link11ranges substantially, from 3.5 to 6.

FIG. 8Bshows that another robotic gripper100″ lifts a heavy object53. The robotic fingers1″,2″ are not designed as a cantilevered beam with force acting on it at some distance from the body member3″. That is, the width of the fingers1″ and2″ are not varied along the longitudinal axis of the robotic fingers1″ and2″, and thus the fingers1″ and2″ are not configured to be tapered. In such a situation, the fingers1″ and2″ may bend and/or deform in the normal direction (in the Z-axis) when the robotic gripper100″ lifts a heavy object53.

[Another Exemplary Embodiment of Conforming Mode]

With regard to this embodiment, it shows the torsion of the finger about the Z-axis. The X, Y and Z axes shown inFIG. 9Ause a three-dimensional Cartesian coordinate system. The positive Z-axis may extend in the general direction from the end111of the link11to the end133of the link13and can be interpreted to be vertical in the primary linkage plane. The positive X-axis extends in the general direction from the end142of the link14to the end112of the link11and can be interpreted to be horizontal in the primary linkage plane. The remaining Y axis is defined using the right-hand rule.

Since the robotic fingers1and2include elastic material, they can conform to most shapes with ease. The robotic fingers1and2can be twisted along their longitudinal axes such that the contact surfaces of the robotic fingers1and2can be deformed to be substantially perpendicular to the normal of the outer surface of the object they grasp. Referring toFIG. 9A, the robotic fingers1and2can deform by twisting about their Z-axes. In particular, the joints15,17,19,25,27,29are configured to be twisted along their longitudinal axis. The length of the joint17may range from three times the smallest thickness of the joint17to six times the smallest thickness of the joint17, and the length of the joint19may range from three times the smallest thickness of the joint19to six times the smallest thickness of the joint19, and the length of the joint27may range from three times the smallest thickness of the joint27to six times the smallest thickness of the joint27, and the length of the joint29may range from three times the smallest thickness of the joint29to six times the smallest thickness of the joint29. As shown inFIG. 9A, when the robotic gripper100grasps the mug54with the cylindrical surface, the robotic fingers1and2will twist such that the surface135of the link13of the robotic finger1and the surfaces235of the links23of the robotic finger2will be returned to be perpendicular to the normal of the outer surface of the mug54. In this way, the robotic fingers1and2conform to the outer surface of the mug54, and thus the robotic gripper100can grasp the mug54in a stable manner.

FIGS. 9B and 9Care top schematic views showing grasping movement of the robotic gripper100.

Referring toFIG. 9B, before grasping the mug54, the surface235of the robotic finger2can be substantially flat. The surface235of one the robotic finger2can be substantially aligned with the surface235of another robotic finger2. The surface235of one the robotic finger2can be substantially in parallel to the surface235of another robotic finger2. The surface135of the robotic finger1can be substantially parallel to the surface235of the robotic finger2. The side surface237of the robotic finger2can substantially flat. The surface237of one the robotic finger2can be substantially aligned with the surface237of another robotic finger2. The surface237of one the robotic finger2can be substantially in parallel to the surface237of another robotic finger2.

Referring toFIG. 9C, when grasping the mug54, the robotic finger1, which may include elastic or flexible material(s), can be twisted with respect to a longitudinal axis (e.g. the Z axis as shown inFIG. 9A). The side surface or lateral surface135of the robotic finger1can be deformed to conform to the inner surface of the mug54during grasp operation of the robotic gripper100. The side surface or lateral surface135of the robotic finger1can be tightly pressed on the inner surface of the mug54during grasp operation of the robotic gripper100. Part of the side surface or lateral surface135of the robotic finger1can be tightly pressed on the inner surface of the mug54during grasp operation of the robotic gripper100.

The surface235of one the robotic finger2may not be substantially aligned with the surface235of another robotic finger2. The surface235of one the robotic finger2may not be substantially in parallel to the surface235of another robotic finger2. The surface135of the robotic finger1may not be substantially parallel to the surface235of the robotic finger2. The side surface237of the robotic finger2may not be substantially flat. The surface237of one the robotic finger2may not be substantially aligned with the surface237of another robotic finger2. The surface237of one the robotic finger2may not be substantially in parallel to the surface237of another robotic finger2.

Further, the robotic finger2, which can include elastic or flexible material(s), can be twisted with respect to a longitudinal axis (e.g. the Z axis as shown inFIG. 9A). The side surface or lateral surface235of the robotic finger2can be deformed to conform to the outer surface of the mug54during grasp operation of the robotic gripper100. Part of the side surface or lateral surface235of the robotic finger2can be conform to the outer surface of the mug54during grasp operation of the robotic gripper100. The side surface or lateral surface235of the robotic finger2can be tightly pressed on the outer surface of the mug54during grasp operation of the robotic gripper100. The side surface or lateral surface235of the robotic finger2can be tightly pressed on the outer surface of the mug54during grasp operation of the robotic gripper100. Part of the side surface or lateral surface235of the robotic finger2can be tightly pressed on the outer surface of the mug54during grasp operation of the robotic gripper100.

[Another Exemplary Embodiment of Conforming Mode]

FIGS. 10A and 10Bshow that the robotic gripper100grasps a rod-like object55with relatively less diameter or width (e.g. a broom handle). The link22of the robotic finger2may have two ends222connecting to two links23respectively. Further, the link13of the robotic finger1may be configured to correspond to the space between the links23of the robotic finger2. Thus, when the robotic gripper100grasps a long, small diameter, rod-like object55, the link13of the robotic finger1may pass through the space between the links23of the robotic finger2such that the long small diameter rod-like object55could be fixedly grasped by the robotic gripper100.

As shown inFIG. 10A, when the robotic gripper100grasps the rod-like object55, the end133of the link13of the robotic finger1may be pass through a space between the ends233of the link23of the robotic finger2.

Referring toFIG. 10B, the link13of the robotic finger1and the links23of the robotic finger2may be interlaced with each other such that the rod-like object55could be held by the robotic fingers1and2.

FIG. 11is a perspective view of a robotic finger6in accordance with some other embodiments of the instant disclosure. The robotic finger6may include five links61,62,63,64and65and four joints661,662,663and664. The link61may have two ends611and612which are opposite to each other. The link62may have two ends621and622which are opposite to each other. The link63may have three ends,631,632and633. The link64may have two ends641and642, which are opposite to each other. The link65may have two ends651and652which are opposite to each other. The joint661may connect the end612of the link61and the end621of the link62, and the joint662may connect the end622of the link62and the end631of the link63, the joint663may connect the end632of the link63and the end641of the link64, and the joint664may connect the end642of the link64and the end651of the link65. These links61,62,63,64and65and these joints661,662,663and664may include elastic material and are formed in one piece, and thus they are configured to be compliant in three dimensions.

Further, the thickness of the end612of the link61and the thickness of the end621of the link62may be greater than the smallest thickness of the joint661. The thickness of the end622of the link62and the thickness of the end631of the link63may be greater than the smallest thickness of the joint662. The thickness of the end632of the link63and the thickness of the end641of the link64may be greater than the smallest thickness of the joint663. The thickness of the end642of the link64and the thickness of the end651of the link65may be greater than the smallest thickness of the joint664. That is, the thickness of the link61,62,63,64,65may be greater than the thickness of the joint661,662,663,664to which it connects. Since the joint661,662,663,664may have the smaller thickness, the joint661,662,663,664will be more flexible and deformable than the link61,62,63,64,65. Accordingly, the joints661,662,663,664will act as joints connecting the links61,62,63,64and65. That is, the links61,62,63,64and65can rotate around the joints661,662,663and664.

FIG. 12is a perspective view of a robotic finger7in accordance with some other embodiments of the instant disclosure. The robotic finger7may include six links71,72,73,74,75and76and six joints771,772,773,774,775and776. The joint771may connect the end711of the link71. The joint772may connect the end722of the link72and the end731of the link73. The joint773may connect the end732of the link73and the end741of the link74. The joint774may connect the end742of the link74and the end751of the link75. The joint775may connect the end752of the link75and the end762of the link76. The joint776may connect the end723of the link72and the end761of the link76. These links71,72,73,74,75and76and these joints771,772,773,774,775and776may include elastic material and are formed in one piece, and thus they are configured to be compliant in three dimensions.

Further, the thickness of the end711of the link71and the thickness of the end721of the link72may be greater than the smallest thickness of the joint771. The thickness of the end722of the link72and the thickness of the end731of the link73may be greater than the smallest thickness of the joint772. The thickness of the end732of the link73and the thickness of the end741of the link74may be greater than the smallest thickness of the joint773. The thickness of the end742of the link74and the thickness of the end751of the link75may be greater than the smallest thickness of the joint774. The thickness of the end752of the link75and the thickness of the end762of the link76may be greater than the smallest thickness of the joint775. The thickness of the end723of the link72and the thickness of the end761of the link76may be greater than the smallest thickness of the joint776. That is, the thickness of the link71,72,73,74,75,76may be greater than the thickness of the joint771,772,773,774,775,776to which it connects. Since the joint771,772,773,774,775,776may have the smaller thickness, the joint771,772,773,774,775,776will be more flexible and deformable than the link71,72,73,74,75and76. Accordingly, the joints771,772,773,774,775and776will be act as joints connecting the links71,72,73,74,75and76. That is, the links71,72,73,74,75and76can rotate around the joints771,772,773,774,775and776.

FIG. 13is a perspective view of a robotic finger8in accordance with some embodiments of the instant disclosure. The robotic finger8may include seven links81,82,83,84,85,86and87and seven joints881,882,883,884,885,886and887. The joint881may connect the end811of the link81. The joint882may connect the end822of the link82and the end831of the link83. The joint883may connect the end832of the link83and the end841of the link84. The joint884may connect the end842of the link84and the end851of the link85. The joint885may connect the end852of the link85and the end861of the link86. The joint886may connect the joint882and the end871of the link87. The joint887may connect the joint885and the end872of the link87. These links81,82,83,84,85,86and87and these joints881,882,883,884,885,886and887may include elastic material and are formed in one piece, and thus they are configured to be compliant in three dimensions.

Further, the thickness of the end811of the link81and the thickness of the end821of the link82may be greater than the smallest thickness of the joint881. The thickness of the end822of the link82and the thickness of the end831of the link83may be greater than the smallest thickness of the joint882. The thickness of the end832of the link83and the thickness of the end841of the link84may be greater than the smallest thickness of the joint883. The thickness of the end842of the link84and the thickness of the end851of the link85may be greater than the smallest thickness of the joint884. The thickness of the end852of the link85and the thickness of the end861of the link86may be greater than the smallest thickness of the joint885. The thickness of the end871of the link87may be greater than the smallest thickness of the joint886. The thickness of the end872of the link87may be greater than the smallest thickness of the joint887. That is, the thickness of the link81,82,83,84,85,86,87may be greater than the thickness of the joint881,882,883,884,885,886,887to which it connects. Since the joint881,882,883,884,885,886,887may have the smaller thickness, the joint881,882,883,884,885,886,887will be more flexible and deformable than the link links81,82,83,84,85,86,87. Accordingly, the joints881,882,883,884,885,886,887will act as joints connecting the links81,82,83,84,85,86and87. That is, the links81,82,83,84,85,86and87can rotate around the joints881,882,883,884,885,886and887.

FIG. 14is a top schematic view of a robotic finger9in accordance with some embodiments of the instant disclosure. The robotic finger9may include four links91,92,93, and94. The link91is pivotally connected to the link92with the connection joint95. The link92is pivotally connected to the link93with the connection joint96. The link94is pivotally connected to the link93with the connection joint97. The links91,92,93,94and the joints95,96,97are not formed in one piece and can be made by different materials. Thus, the robotic finger9cannot be made by one-time injection molding and the cost for manufacturing the robotic finger9will be higher.

As used herein, the terms “approximately”, “substantially”, “substantial” and “about” are used to describe and account for small variations. When used in conduction with an event or circumstance, the terms can refer to instances in which the event of circumstance occurs precisely as well as instances in which the event or circumstance occurs to a close approximation. As used herein with respect to a given value or range, the terms “approximately”, “substantially”, “substantial” and “about” generally mean within ±10%, ±5%, ±1%, or ±0.5% of the given value or range. Ranges can be expressed herein as from one endpoint to another endpoint or between two endpoints. All ranges disclosed herein are inclusive of the endpoints, unless specified otherwise. When used in conjunction with an event or circumstance, the terms can refer to instances in which the event or circumstance occurs precisely as well as instances in which the event or circumstance occurs to a close approximation. For example, when used in conjunction with a numerical value, the terms can refer to a range of variation less than or equal to ±10% of that numerical value, such as less than or equal to ±5%, less than or equal to ±4%, less than or equal to ±3%, less than or equal to ±2%, less than or equal to ±1%, less than or equal to ±0.5%, less than or equal to ±0.1%, or less than or equal to ±0.05%. For example, a first numerical value can be deemed to be “substantially” the same or equal to a second numerical value if the first numerical value is within a range of variation of less than or equal to ±10% of the second numerical value, such as less than or equal to ±5%, less than or equal to ±4%, less than or equal to ±3%, less than or equal to ±2%, less than or equal to ±1%, less than or equal to ±0.5%, less than or equal to ±0.1%, or less than or equal to ±0.05%. For example, “substantially” perpendicular can refer to a range of angular variation relative to 90° that is less than or equal to ±10°, such as less than or equal to ±5°, less than or equal to ±4°, less than or equal to ±3°, less than or equal to ±2°, less than or equal to ±1°, less than or equal to ±0.5°, less than or equal to ±0.1°, or less than or equal to ±0.05°.

In addition, if the robotic gripper of the instant disclosure is at much larger or smaller scale, the ratios of the thickness of links and joints, and the finger lengths and widths may be substantially different depending on the elastomeric materials used, and the fact that the cross section of the joints vary as a square (affecting both the spring rates and stiffnesses) while the volume of the links vary as a cube (affecting their mass).

The foregoing outlines feature several embodiments and detailed aspects of the present disclosure. The embodiments described in the present disclosure may be readily used as a basis for designing or modifying other processes and structures for carrying out the same or similar purposes and/or achieving the same or similar advantages of the embodiments introduced herein. For example, numerical values, ratios, geometric description (e.g. shape or contour) as discussed above can be readily used as a basis for designing or modifying other processes and structures for carrying out the same or similar purposes and/or achieving the same or similar advantages of the embodiments introduced herein. Such equivalent constructions do not depart from the spirit and scope of the present disclosure, and various changes, substitutions, and alterations may be made without departing from the spirit and scope of the present disclosure.

The above embodiments merely describe the principle and effects of the present disclosure, instead of limiting the present disclosure. Therefore, persons skilled in the art can make modifications to and variations of the above embodiments without departing from the spirit of the present disclosure. The scope of the present disclosure should be defined by the appended claims.