Highly Anthropomorphic Finger Design With a Novel Friction Clutch for Achieving Human-Like Reach-and-Grasp Movements

In the design of prosthetic hand fingers, achieving human-like movement while meeting anthropomorphic demands such as appearance, size, and lightweight is quite challenging. Human finger movement involves two distinct motion characters during natural reach-and-grasp tasks: consistency in the reaching stage and adaptability in the grasping stage. The former one enhances grasp stability and reduces control complexity; the latter one promotes the adaptability of finger to various objects. However, conventional tendon-driven prosthetic finger designs typically incorporate bulky actuation modules or complex tendon routes to reconcile the consistency and adaptability. In contrast, we propose a novel friction clutch consisting of a single tendon and slider, which is simple and compact enough to be configurated within the metacarpal bone. Through tactfully exploiting the friction force to balance the gravity effect on each phalanx during finger motion, this design effectively combines both consistency and adaptability. As a result, the prosthetic finger can maintain consistent motion unaffected by any spatial posture during reaching, execute adaptive motion during grasping, and automatically switch between them, resulting in human-like reach-and-grasp movements. Additionally, the proposed finger achieves a highly anthropomorphic design, weighing only 18.9 g and possessing the same size as an adult’s middle finger. Finally, a series of experiments validate the theoretical effectiveness and motion performance of the proposed design. Remarkably, the mechanical principle of the proposed friction clutch is beneficial to achieve highly anthropomorphic design, providing not only a new strategy to prosthetic hand design but also great potential in hand rehabilitation.


I. INTRODUCTION
T HE human hand is so dexterous thanks to the coordinated interaction among dozens of joints, tendons, and muscles, enabling it to execute a variety of daily activities.What is surprising is that such complex and multitudinous biomechanical components are ingeniously integrated into a limited space and weight range.Hence, anthropomorphic appearance, human size, lightweight, and motion functionality have always been the focus in the design and application of prosthetic hands [1], [2], [3], [4], [5], [6], [7].In particular, the finger is undoubtedly crucial as it could perform direct contact and interaction with objects, enabling the hand to execute various tasks.Although a single finger has three joints and four degrees of freedom, researchers have indicated that the finger often presents some specific patterns during natural reach-andgrasping tasks, owing to preset synergies or biomechanical characteristics [8], [9], [10], [11], [12].Inspired by these biological features, the tendon-driven mechanism has been wildly applied in prosthetic finger designs [13], [14], [15], [16], [17], [18].However, despite extensive research being carried out to replicate human-like movements as much as possible, existing tendon-driven finger designs generally prioritize grasping adaptability [19].For example, the most traditional way is to utilize one driving tendon threaded through all the finger joints to realize adaptive motion [20], [21], [22], [23], [24].
In the design of prosthetic hands, achieving natural finger movement to enable grasp functionality is quite importance and has been extensively studied [19], [25], [26], [27], [28], as it directly relates to the activities of daily living (ADLs) [29].Essentially, the natural reach-and-grasp task involves two distinct stages: reaching and grasping.It is well known during the grasping stage, the finger joints can automatically flex at different angles to conform to the contours of various objects, an ability referred to as adaptability.However, the grasping stage occurs after the finger makes contact with the object.However, prior to that, the finger needs to approach the object from an initial posture, known as the reaching stage.Completely different from the grasping stage, finger motion exhibit high consistency in the reaching stage.That is, the joints within a single finger not only move synchronously but also follow a specific trajectory unaffected by any spatial posture, known as the consistency [24], [30].Kamper et al. pointed out that finger motions remained highly consistent across reaching trials with varying objects in a natural manner, both within a given subject and among different subjects, regardless of how the initial finger posture changed [30].Remarkably, thanks to this consistency, our brain can reduce the control complexity [31], [32] and avoid uncertainty in multi-joint motion during reaching, which improves grasping stability as well as success rate in advance [28], [33], [34].Moreover, the consistency can help users operate prosthetics more naturally in practical use.Hence, the consistency is quite essential in the finger design.
However, effectively combining both reaching consistency and grasping adaptability in prosthetic finger design, while meeting anthropomorphic demands for appearance, size, and lightweight, remains a critical challenge.It is noteworthy that the human finger is capable of maintaining consistent motion with any initial spatial posture during reaching, which implies that it can dynamically balance the gravity effect on each phalanx in our daily activities.However, most existing traditional tendon-driven finger designs assume the phalanges to be massless rigid bodies, ignoring the gravity effect on varying finger postures.Although these designs achieve grasping adaptability, they typically incorporate high stiffness or complex tendon routes to achieve predetermined trajectories during reaching, bringing drawbacks such as excessive power consumption and bulky actuation modules [13], [14], [21], [24], [35], [36].Additionally, some designs cannot even maintain consistent motion in any spatial finger posture in practical use.In contrast, some research has aimed to enhance reaching consistency [33], [37], [38], [39], but often at the expense of grasping adaptability.
Regarding the issues mentioned above, we innovatively take gravity force into account in the finger mechanical model and propose a novel friction clutch.Based on that, we successfully combine reaching consistency (see Fig. 1(b)) and grasping adaptability (see Fig. 1(c)) together in the finger design, achieving human-like reach-and-grasp movements.Besides, because the gravity term is considered in our statics model, the proposed finger can maintain consistent motion unaffected by any spatial posture during reaching.Furthermore, the proposed finger is highly anthropomorphic in morphology, which is made in the same size as an adult's middle finger, and weighing only 18.9 g (see Fig. 1(a)).Therefore, this work realizes a highly anthropomorphic prosthetic fin- ger design that satisfies both biomimetic performance and anthropomorphism.
The rest of this article is organized as follows.Section II introduces the related work and issues.The proposed hand design is demonstrated in Sections III.The experimental results are presented in Section IV.Finally, Section V concludes this article.

II. RELATED WORK AND ISSUES
To reflect the significance of our research, in this section, we will briefly review the relevant finger designs and propose our solution based on the existing issues.

A. Adaptive Finger
The most traditional design is the adaptive finger, which utilizes one driving tendon threads through all three finger joints, as shown in Fig. 2(a).Although this kind of finger usually achieves good grasping adaptability, most of them typically incorporate high stiffness or complex tendon routes for reaching consistency, leading to issues such as excessive power consumption and bulky actuation modules.Additionally, some designs cannot even maintain consistent motion in any spatial finger posture in practical use due to ignoring the gravity term of finger phalanges.

B. Partial Consistent Finger
Some research has been conducted on improving reaching consistency [28], [33].As shown in Fig. 2(b), the distal interphalangeal (DIP) and proximal interphalangeal (PIP) joints are connected by a passive tendon, which is symmetrically distributed on each side of the joint rotation center.Thus, the DIP joint always synchronously flexes along with the PIP joint.In addition, the metacarpophalangeal (MCP) and PIP joints are connected in series by one driving tendon.Compared to the adaptive finger, the improvement is to guarantee the consistency of PIP and DIP joints, meanwhile, remain the adaptability of MCP and PIP joints.Whereas, the MCP and PIP joints cannot maintain consistent motion as the gravity term is still not considered.Thus, we named it the partial consistent finger.

C. Complete Consistent Finger
In addition, there is a finger design that ensures complete reaching consistency but sacrifices grasping adaptability [34].As shown in Fig. 2(c), two passive tendons are adopted, one coupled the PIP and MCP joints and the other coupled the DIP and PIP joints.Thus, the finger can always maintain consistent motion in any posture.Moreover, the tendon driving distance is further reduced by two thirds compared to the adaptive finger.However, the finger can only execute consistent motion, which sacrifices the grasping adaptability.
To sum up, the existing studies have not combined consistency and adaptability in the finger design, and generally ignore the gravity term.Hence, in this work, we innovatively incorporate the gravity term into the mechanical model and propose a novel friction clutch.By skillfully utilizing the equilibrium relationship between gravity and friction, we have well combined consistency and adaptability together into a highly anthropomorphic prosthetic finger design.

III. HIGHLY ANTHROPOMORPHIC FINGER DESIGN
As illustrated in Fig. 3, the proposed finger consists of three phalanges, one metacarpal bone, and three joints.The PIP and DIP joints are coupled by a passive tendon because their motions are highly correlated.But for the MCP and PIP joints, we propose a novel friction clutch which can provide parallel or serial transmission.In addition, extension springs are configurated on the dorsal side of finger joints for full extension.Firstly, we elaborately determine spring stiffnesses through balancing the gravity of each phalanx.Then, we detail the parallel or serial transmissions of the friction clutch respectively.

A. Stiffnesses Determination
As shown in Fig. 4, three extension springs are set on the dorsal side of finger joints, named as MCP extension spring, PIP extension spring and DIP extension spring, respectively.Each spring connects to the joint through an extension tendon.The spring stiffness should satisfy the following two demands: 1.It can provide sufficient extension torque, affording full extension of every joint in any spatial finger posture; 2. It can minimize the power consumption as much as possible.Specifically, different from the traditional approach regarding phalanges as massless rigid bodies, we consider the gravity term in the mechanical model to obtain optimal stiffnesses.
In order to cover all spatial finger postures, we establish the Cartesian coordinate with the rotation center of MCP joint as the origin.Obviously, in the III quadrant, the work done by extension springs will reach to the maximum to overcome the gravity of all phalanges for full extension, as shown in Fig. 4.Then, the equilibrium equations are as follows: where the geometric parameters are defined in Fig. 4: G n and L n denote the gravity and length of phalanx, R n expresses the distance between the barycenter to the joint rotation center, x n represents the extension torque.Furthermore, in our mechanical model, the subscript n(n = 1, 2, 3) corresponds to the phalanges and joints from proximal to distal, respectively.
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TABLE I GRAVITY PARAMETERS AND THEORETICAL TENSIONS TABLE II THE PARAMETERS OF SELECTED SPRINGS
Then, the tendon routes and geometric sketches of each joint are illustrated as shown in Fig. 5, where the subscripts n = 1, 2, and 3 are indicated as MCP, PIP, and DIP joints, respectively.θ n=1,2,3 the joint flexion angle, is in a range of 0 • ∼90 • .l f n=1,2,3 and l en=1,2,3 represent the length between the tendon insertion point and joint rotation center, r f n=1,2,3 (θ n=1,2,3 ) is the vertical distance from the tendon to the joint rotation center, and r en=1,2,3 (θ n=1,2,3 ) represents the vertical distance from the extension spring to joint rotation center, in which the subscripts f and e represent the flexion and extension sides, respectively.Thus, according to the trigonometric relationship, the lengths between two adjacent tendon insertion points on the flexion side S n=1,2,3 (θ n=1,2,3 ) and on the extension sides x n=1,2,3 (θ n=1,2,3 ) can be described as: In addition, during the process that the finger returns back to full extension from any spatial posture, the extension torque x n at each joint can be calculated as: where k n and σ n are the spring stiffness and initial tension respectively, in which the subscript n = 1, 2, 3 correspond to the MCP, PIP, and DIP joints, respectively.The volume V of each phalanx can be obtained based on the 3D modeling of the proposed finger, as shown in Fig. 3.Then, with the density value (ρ = 1.18 × 10 −6 kg/mm 3 ) of acrylic form the 3D printing company, the gravity parameters of all phalanges can be calculated by G = ρV g, as shown in Table I.By combining (1) to (3), the theoretical initial tension required for each joint can be obtained (see Table I).According to the results, we chose the springs (Accurate Inc.Japan) whose stiffnesses and initial tensions are slightly larger than but close to the theoretical values in practice.Table II shows the parameters of the practical selected springs.

B. Parallel Transmission of the Friction Clutch
The friction clutch consists of one slider and one connecting tendon.As shown in Fig. 3, the connecting tendon threads through the slider with two ends fixed on the proximal and intermediate phalanges respectively.The slider is embedded inside the metacarpal bone, with a driving tendon fixed its lower end.In the static friction state, the friction clutch forms parallel transmission to provide consistent finger motion.Fig. 6 illustrates the mechanism of parallel transmission during reaching, showing the consistent finger motion in the process of approaching but without contacting the object.Fig. 6(a) exhibits the initial posture, in which the finger is fully extended.At this point, the slider is located on the top of the straight groove inside the metacarpal bone.Assuming that the connecting tendon would not slide relative to the slider, forming a static friction state.Thus, the connecting tendon can be taken as two separate tendons attached to the slider without interfering.The driving force T will be equivalently transferred to both sides of the connecting tendon, enabling the MCP and PIP joints to generate synchronous flexion, as shown in Fig. 6 (b) and (c).In addition, the DIP joint will always flex synchronously with the PIP joint by the passive tendon.Hence, in the static friction state, the friction clutch forms a parallel transmission to ensure consistent finger motion.Thus, the friction coefficient µ of the friction clutch is the critical factor to counterpoise the ever-changing work done by spring force and gravity during motion.
As shown in Fig. 7, we simplified the friction clutch and extension springs in the mechanical model to facilitate the statics analysis.Fig. 7(a) represents the initial finger posture of full extension, where T is the driving force, T 1 and T 2 are tensions on both sides of the connecting tendon respectively.Assuming that T 1 acts on the MCP joint, the MCP extension Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.spring acts on the ipsilateral connecting tendon.Similarly, the connecting tendon on the side of T 2 corresponds to the PIP and DIP extension springs.Fig. 7(b) illustrates the displacement S of the slider under the action of T , the displacements of the connecting tendon are x 1 (θ 1 ) and x 2 (θ 2 ) respectively.Due to parallel transmission, the following equation can be obtained: where x 1 (θ 1 ) and x 2 (θ 2 ) are defined in Fig. 5.According to (4), the MCP and PIP joints will flex synchronously at the same speed.Moreover, the DIP joint always passively flexes synchronously with the PIP joint.Therefore, in static friction, all the finger joints will rotate synchronously, resulting in consistent finger motion.Then, by using (3) and the geometric parameters of each joint (see Fig. 5), the following equilibrium equations can be obtained: Furthermore, to facilitate the analysis of static friction, we magnify the contact part of the connecting tendon and slide (see Fig. 8).T 1 and T 2 are tensions, N is supporting force, and f s is static friction force.The following equations can be obtained: In addition, assuming that: T = N .
As mentioned above, the varying work done by gravity along with the changed finger posture will affect the joint trajectories in real-time.Therefore, the gravity term needs to be considered covering all four quadrants in space.According to the coordinate definition (see Fig. 4), take Q n=I,I I,I I I,I V as the coefficient of gravity term corresponding to each quadrant.Then, the corresponding gravity term can be expressed as: where L n , R n , and G n are defined in Fig. 4. C n and S n represent cos θ n and sin θ n respectively.The subscript n (n + 1) means θ n + θ (n+1) , and n (n + 1) (n + 2) denotes θ n + θ (n+1) + θ (n+2) .Therefore, N and f s can be solved through ( 5) to (7).
For instance, in the I quadrant, N and f s during the whole finger motion can be calculated as: By substituting the parameters of gravity and spring stiffness (see Table I and II) into (8), T 1 , T 2 , N , f s can be obtained.Thus, the theoretical calculation results of T 1 , T 2 , N , f s in each quadrant can be obtained in the same way, which are plotted in Fig. 9. Thereinto, the maximum theoretical static friction force f s(max) =1.6085N exists in the IV quadrant.Then, the theoretical static friction coefficient µ can be calculated as: In the implementation, all tendons adopted belong to one kind of wire (UXITIKD Ltd., diameter 0.8 mm, breaking strength 370 N), and all rigid frames are made by 3D printing.The 3D printer (Stratasys Co., resolution 0.1 mm) can support four printing materials: nylon, glass fiber, acrylic, and ABS (acrylonitrile butadiene styrene).Thus, it is necessary to choose a suitable material for the slider to satisfy the theoretical µ (see (9)), guaranteeing that the friction clutch can work in the static friction state.Assuming that µ m is the material friction coefficient, thus, the following equation should be satisfied: Then, we conducted experimental measurements with all kinds of materials to find the most optimal one.As shown in Fig. 10, four sliders were made with different materials.Each of them was threaded through a wire, constituting the proposed friction clutch.Specifically, the measuring procedure is as follows: first, clamp the slider with a vise and let both sides of the wire hang naturally; next, attach the same weight Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

TABLE III MATERIAL FRICTION COEFFICIENT
to both sides of the wire; then, gradually add weight on one side until the wire just starts to slide relative to the slider and record the weight changes.The items used in the experiment are shown in Fig. 10.In order to reduce the measurement error, the experiment was repeated five times for each slider.According to the measurement data, µ m can be calculated through (6) and (9).The calculation results of µ m are shown in Table III: According to the results, the µ m of acrylic is closest to the theoretical value µ and satisfies (10).Thus, we chose acrylic material to make the slider.The friction coefficient of the practically applied friction clutch is:

C. Serial Transmission of the Friction Clutch
On the other hand, in the dynamic friction state, the friction clutch forms serial transmission to provide adaptive finger  motion.Fig. 11 illustrates the mechanism of serial transmission under dynamic friction during the grasping stage, showing adaptive motion after the finger contacting with the object.Fig. 11(a) and (b) show the process that the finger has been blocked at the MCP joint due to contact with an object, from the initial full extension posture.Then, if keep increasing the driving force T, the tension acted on the connecting tendon will increase correspondingly.Once the tension becomes large enough to overcome the maximum static friction force of the friction clutch, the connecting tendon will slide relative to the slider.At this moment, the friction state will become to dynamic friction, forming serial transmission.As shown in Fig. 11(b) and (c), the unblocked PIP and DIP joints will be driven in series and continue to flex until adapt the object, resulting in adaptive motion.
To investigate the serial transmission in dynamic friction state, we simplify the corresponding mechanical components into the mechanical model (Fig. 12).Firstly, as the MCP joint is blocked due to the contact with the object, the MCP extension spring can no longer be stretched.Thus, the side related to the tension T 1 can be taken as a fixed end, as shown in Fig. 12(a).Then, the driving force T will be transferred to the other side via the slider, namely the tension T 2 .With the action of T 2 , the unblocked PIP and DIP joints will continue to flex, resulting in the displacement x 2 (θ 2 ), as shown in Fig. 12(b).Here, the displacement x 2 (θ 2 ) will be evenly divided to two sides via the slider.Thus, the displacement S should satisfy x 2 (θ 2 ) = 2 s.Then, the equilibrium equations among tensions T 1 , T 2 , support force N , and dynamic friction force f d can be described as (see Fig. 12 (b)): where µ m is assigned in (11).Since the theoretical static friction coefficient has the maximum value in the IV quadrant (Fig. 9), substituting the gravity term (see (7) and ( 8)) of the IV quadrant into (13), the following equations can be obtained: Equation ( 13) describes the f d and N , in the process that the PIP joint continues to flex after the MCP joint is blocked at a certain angle.Thus, by combing ( 12) and ( 13), the theoretical values of f d , N , and T 2 can be calculated.The calculation results are plotted in Fig. 13, which assumes that when the MCP joint is blocked at angle θ 1 .Here, θ 1 has a range of 0 • ∼90 • .However, as the friction clutch is embedded in the metacarpal bone, the above theoretical calculation cannot be verified by actual measurement.Thus, we will carry out statics analysis on the proposed finger for further verifying the theoretical correctness, as shown in Fig. 14.According to the D-H method, the following equations can be obtained: n−1  n−1 1 where n−1 1 P n and n 1 F n denote the contact point and contact force, respectively.The subscript n(n = 1, 2, 3) corresponds to the proximal, intermediate, and distal phalanx in turn.τ is the output torque at each contact point, and J T is the Jacobi transposed matrix.Then, τ can be calculated as follows: where M n=1,2,3 denotes the actuation torque of each joint.As assumed, the friction clutch will form a serial transmission in the dynamic friction state, allowing the PIP joint continue to flex even when the MCP joint is blocked.And, the DIP joint will always flex synchronously with the PIP joint via the passive tendon.Thus, θ 2 = θ 3 can be taken as a boundary condition.Then, the contact forces F 2 and F 3 can be calculated.Assuming that the MCP joint is blocked at θ 1 , then, the theoretical values of F 2 and F 3 during the entire flexion process from 0 • to 90 • can be plotted in Fig. 15.IV.EXPERIMENTS AND DISCUSSION A series of experiments were conducted to verify the theoretical effectiveness and motion performance of the proposed finger (Fig. 16(a)) from the aspects of force verification, reaching consistency, and grasping adaptability, including three other competitors (Fig. 16(b)-(d)).

A. Experiment I: Force Verification
Firstly, a prototype of the proposed finger (Fig. 16(a)) was implemented by a 3D printer (Stratasys Co., resolution 0.1 mm).Thereinto, all rigid frames were made of acrylic material and tendons employed were made of the same wire (UXITIKD Ltd., diameter 0.8 mm, breaking strength 370 N).The purpose of this experiment is to verify the validity of the statics model proposed in section III.For the proposed finger, we measured the forces F 2 and F 3 of the intermediate and distal phalanges in the IV quadrant as assumed in the statics model (see Fig. 14), and then made a comparison with the corresponding theoretical results (see Fig. 15).To facilitate the measurement, blocks with varying angles were used to fix the MCP joint at certain angles, mimicking different blocked situations caused by contacting with an object.The experimental procedure was demonstrated in Fig. 17(a), (b), and (c) in sequence, as follows: 1. Clamp the finger by a vise and fix the MCP joint at a preset angle with a block.Then, attach 1 kg load on the driving tendon to fully flex the finger (Fig. 17(a)).2. Use a force gauge (SanLiang Co., Ltd., SL-50) to measure the forces F 2 and F 3 when pushing back the corresponding phalanx till it stopped at a certain angle (Fig. 17  In order to better compare with the theoretical values, as shown in Fig. 17     substituting 1 kg load into (17) and (18).The blue curve is the theoretical value without extension force.It is clear that the measured values are mainly distributed closer to the theoretical curve with a similar tendency.Thus, the experiments verified the correctness of the proposed statics model.

B. Experiment II: Reaching Consistency
As elucidated in section III, the proposed finger can realize consistent motion in any spatial posture during reaching, owing to the parallel transmission brought by the novel friction clutch for tactfully balancing the gravity effect with the friction force.To better verify this remarkable function, we conducted reaching trials by comparison with other three kinds of relevant tendon-driven fingers mentioned in section II.For accurate comparison, the dimension, fabrication method, extension springs, and tendon materials of the three competitors were all implemented the same as the proposed finger, except for the different internal tendon transmission corresponding to the respective mechanism (Fig. 2).Accordingly, the adaptive finger, partial consistent finger, and complete consistent finger were employed here as presented in Fig. 16(b) to (d).
Angle sensor was installed at each joint, and a servo motor (POWER HD, Ltd., LF-20MG, torque 20kgcm) was used to actuate the finger to flex from 0 • to 90 • .Based on the microcontroller (STM32F767IGT6), joint angles were recorded real-timely.The sampling period was 1 ms, and the serial transmission frequency was 115200 bit/s.To cover every spatial posture, we tested each finger in four quadrants respectively, according to the Cartesian coordinate established in section III. 5 trials were repeated in each quadrant, and the average measurement results have been plotted in Fig. 19.Obviously, the proposed finger in Fig. 19  driving tendon.Similarly, as shown in Fig. 19(c), the partial consistent finger exhibits approximate motion patterns in the I, II, and IV quadrants, except that its DIP and PIP joints flex synchronously rather than sequentially.This is because the passive tendon couples these two distal joints and results in good synchronism.Even so, this kind of coupling cannot ensure the motion being consistent in all quadrants, like the one in the III quadrant, due to the varied gravity effect.Last, the complete consistent finger (Fig. 19(d)) exhibits highly synchronism and consistency across all four quadrants, because the DIP and PIP joints are fully coupled to the MCP joint through two passive tendons.However, this kind of tendon mechanism sacrifices adaptability because all three joints can only move together, resulting in a lack of compliance when interacting with various objects.
Consequently, the experiment results indicated that the proposed finger can remain highly consistency across all four quadrants during reaching, owing to the parallel transmission brought by the friction clutch for the MCP and PIP joints instead of simple coupling.Specifically, the proposed friction clutch can effectively balance the ever-changing gravity effect during finger motion, ensuring consistent motion in any spatial posture while still preserving the adaptability of finger.The

C. Experiment III: Grasping Adaptability
Furthermore, the proposed finger can automatically realize adaptive motion during grasping owing to the serial Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
transmission brought by the friction clutch in the dynamic friction state.To investigate this adaptability, grasping tasks were carried out on different objects.Some daily objects were employed: a foam ball (6 cm diameter), a rubber ball (4.5 cm diameter), a cylindrical lipstick (1.8 cm diameter), an eye drop box (1.1 cm thick), and a square lipstick (1×1 cm of crosssection).An assistant was employed to hold an object in the front of the finger, then, drive the finger to flex via a servo motor until it adapts to the object.Fig. 20 are the experimental video snapshots.It is observed that the proposed finger can well adapt to objects with different contours and dimensions.Firstly, for typical columnar objects [40] with varying diameters, the finger presents good adaptability (Fig. 20(a), (b) and (c)).Significantly, the finger can continue to flex until adapt to the object even when the MCP joint are almost fully blocked by the object.Secondly, the finger also exhibits good adaptability to regular and irregular quadrilateral objects (Fig. 20(d) and (e)).It can be attributed to the benefit that the proposed friction clutch can provide serial transmission during grasping, allowing adaptive finger motion.
The numerical results of the joint angle changes of each task are illustrated in Fig. 21.Specifically, when grasping a foam ball and a rubber ball, as shown in Fig. 21(a) and (b), the MCP joint angle was always maintained between 0 • ∼10 • because it was blocked by the spherical object.In contrast, the PIP and DIP joints were not affected and continued to flex, then briefly paused at around 20 • ∼25 • when initially in contact with the object.Subsequently, the two joints continued to flex until they reached nearly 45 • , resulting in an adaptive grasp.Similarly, when grasping a grasp an eye drop box, as shown in Fig. 21(d), the MCP joint angle stayed between 0 • ∼15 • due to the obstruction caused by the object throughout the task.Meanwhile, the PIP and DIP joints kept flexing and ultimately fully adapted to the object when they reached approximately 75 • .In addition, when grasping a cylindrical lipstick and a square lipstick, Fig. 21(c) and (e) clearly illustrated the angle changes of joints before and after contact with irregular shaped objects, transitioning from consistent motion to adaptive grasp.
Consequently, the experimental results clearly verified the adaptability of the proposed finger, which can be attributed to the advantages of serial transmission in proposed friction clutch, enabling the finger joints to automatically adapt to the object during grasping.

V. CONCLUSION
This study proposes a highly anthropomorphic finger, which realizes human-like reach-and-grasp movements by well combining both consistency and adaptability.A prototype is built based on the theoretical design, and a series of experiments are conducted to verify the effectiveness and performance.The highlight of this work is the proposed friction clutch, which not only ingeniously utilizes the friction to form the parallel and serial transmissions, but also can automatically switch between them.Specifically, in the static friction state, the friction clutch forms the parallel transmission to realize consistent finger motion; in the dynamic friction state, it forms the serial transmission to realize adaptive finger motion.Of particular emphasis is the use of gravity term in our mechanical model, which is not only crucial for determining appropriate spring stiffness but also guaranteeing consistent motion unaffected by any spatial postures.Moreover, the friction clutch is simple and compact, which can be embedded in the metacarpal bone.Hence, the proposed finger satisfies both biomimetic and anthropomorphic demands.
Essentially, the proposed design principle based on the friction clutch can be expanded to a broader scope than prosthetic hands, as the friction force can be adjusted through simple parameters like contact area, states and so on.Particularly, for anthropomorphic demands in prosthetic designs or rehabilitation applications for mimicking human-like movement, it more benefits for realizing miniaturization, lightness, and multi-motion function.Firstly, the proposed friction clutch can function a parallel or a serial transmission, so that it can be extended to the mechanism with super-multi-joint linkage such as a bionic spine.At the same time, given that the friction clutch has the characteristics of combining consistency with adaptive function, which can highly mimic bionic motion of the human hand, the proposed design concept can be applied to the exoskeleton for hand rehabilitation.Secondly, because the parallel transmission enables multiple joints move along a predetermined trajectory, the control complexity and the number of actuators are greatly reduced, resulting in saving energy consumption and the cost.Therefore, the mechanism of the proposed friction clutch is more conducive to realize the anthropomorphic design, which not only provides a new method for prosthetic hand design, but also can be actually used for rehabilitation fields.Next, we plan to apply the proposed design to a prosthetic hand.Further consideration will be given to the grasp performance and motion stability of a whole hand to better leverage the advantages of the proposed mechanism.

Fig. 1 .
Fig. 1.The proposed finger: (a) size, appearance, and weight of the proposed finger, (b) consistent motion in the reaching stage, and (b) adaptive motion in the grasping stage.

Fig. 3 .
Fig. 3.The three-dimensional model of the proposed finger.

Fig. 5 .
Fig. 5. Tendon route and of geometric sketch of each joint.
(b) and (c)).Meanwhile, record joint angles via an angle sensor (Alps Electric Co., Ltd.RDC506018A).3. Measure 5 arbitrary angles for each trial and repeat 5 times for each phalanx with different blocks.
(d), some blocks with different angles of 90 • , 75 • , and 60 • were used to fix the MCP joint respectively, mimicking different locked angles caused by contacting with an object.Fig. 18 shows the experiment results, in which 5 circles on the dashed lines indicate 5 measurements of each trial.The red curve represents the theoretical value by
Fig. 17.The experimental setup: (a) load with 1 kg, (b) force measurement of F 2 , (c) force measurement of F 3 , and (d) blocks.
(a) presents highly consistency during flexion across all four quadrants.All finger joints (MCP, PIP, and DIP) flex synchronously and remain an approximate slope in any spatial finger posture, demonstrating good repeatability and consistency.By contrast, curves of MCP joint in both the adaptive (Fig. 19(b)) and partial consistent finger (Fig. 19(c)) are quite different in the III quadrant, although they can be consistent in the I, II, and IV quadrants.As shown in Fig. 19(b), in the I, II, and IV quadrants, all joints of the adaptive finger flex sequentially from the DIP to MCP joints with an approximate slope.It is worth noting that the proximal joints always begin to flex only after the distal joints have fully flexed to 90 • .This occurs because the gravity parameters decrease sequentially from the proximal to distal phalanges, resulting in the lightest one always reaching full flexion first under the actuation of the Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

Fig. 21 .
Fig. 21.Joint angle changes of each task: (a) grasp a foam ball, (b) grasp a rubber ball, (c) grasp a cylindrical lipstick, (d) grasp an eye drop box, and (e) grasp a square lipstick.