Design of a Highly Biomimetic Anthropomorphic Robotic Hand towards Artificial Limb Regeneration

  Zhe Xu and Emanuel Todorov

  "Abstract—A wide range of research areas, from te"lemanip- ulation in robotics to limb regeneration in tissu"e engineering," could benefit from an anthropomorphic robotic hand that mim- ics the salient features of the human hand. The challenges of designing such a robotic hand are mainly resultedfrom our lim- ited understanding of the human hand from engineering point of view and our ability to replicate the important biomechanical features with conventional mechanical design. Webelieve that the biomechanics of human hand is an essential component of the hand dexterity and can be replicated with highly biomimetic "design. To this end, we reinterpret the important"biomechanical advantages of the human hand from roboticist’s perspective and design a biomimetic robotic hand that closelymimics its human counterpart with artificial joint capsu"les, crocheted" "ligaments and tendons, laser-cut extensor hood, a"nd elastic pulley mechanisms. We experimentally identify theworkspaces of the fingertips and successfully demonstrate that our proof- of-concept design can be teleoperated to grasp and manipulate daily objects with a variety of natural hand postures based on hand taxonomy.

  I. I NTRODUCTION

  The significance of designing anthropomorphic robotic hands most likely originates from the expectationof using motorized prosthetic hand to restore lost hand dexterity. Although there is still no consensus about the definition "of human hand dexterity, the biological variation"s found "in length of bones, branching of tendons, and ins"ertion of muscles [1] all suggest that dexterity is a highly personal property that is not only shaped by individual’smotor control "ability, but also inherently bonded to the unique"biomechan- "ical characteristics of its very owner, and there"fore can not be generalized without considering the biologicaldifference. The conventional approach to designing anthropomorphic robotic hands often involves mechanizing biological parts "with hinges, linkages, and gimbals in order to si"mplify the seemingly complicated human counterparts. This approach is helpful for understanding and approximating the kinematics "of the human hand in general, but inevitably intr"oduces undesirable discrepancies between the human and robotic hands. The unique biomechanics of any abled humanbe- "ing, which includes complicated shapes of bones,"varied "rotational axes, and other biomechanical advantag""es, can be" seen as a validated physical system as a whole. But most of these salient features are discarded in the mechanizing process. Although significant amount of efforts have been made by researchers to solve this mismatch from the control Authors are with the Department of Computer Scien"ce & Engineering," "University of Washington, WA 98195, USA

" "e-mail: zhexu@cs.washington.edu, todorov@cs.washi"ngton.edu Fig. 1. The fully assembled biomimetic robotic hand. Left: The palmar aspect of the biomimetic robotic hand system. Topright: The dorsal view of the robotic hand. Bottom right: The laser-cutextensor hood integrated with intrinsic muscles. Note: The total weight ofour biomimetic robotic hand is less than 1 kg (942 grams) including theactuation system. "and sensing aspects, very few work has been done"to reduce the gap from the biomechanical point of view.

  The general approach of our proposed method is first to identify the important biomechanical information of the human hand and then biomimetically replicate it.This allows a close replica that shares the same kinematic and even dynamic properties of its human counterpart. Ourdesign ben- efits from several important rapid prototyping technologies: the shape of bones could be first captured with laser/MRI scanner and then 3D-printed with detailed surfacefeatures such as joint shapes and tendon insertion sites;soft tissues can be mimicked by using compliant silicone rubbers whose mechanical properties match that of the skin.

  "As shown in Fig.1, our approach resulted in a hig"hly "biomimetic anthropomorphic design, which will hav"e poten- tial impact on studies in both robotics and biology fields. Besides the obvious application in telemanipulation in which human operator can directly transfer his/her owndexterity "to the robotic hand, it could also help medical a"nd bi- ology research in terms of physically preservingpersonal biomechanical data and serving as the 3D scaffolds for limb regeneration research.

  "In the following sections, we first review relate"d work and introduce our design motivation. And then we reinterpret the important biomechanics of the human hand fromengi- "neering point of view. Meanwhile, we detail the b"iomimetic design and prototyping process of our anthropomorphic "robotic hand. After this, we experimentally inves"tigate the workspaces of each finger and the thumb. At the e"nd, we" experimentally demonstrate the efficacy of our proof-of- concept design through grasping and manipulationexperi- ments.

  II. R ELATED WORK AND MOTIVATION

  In order to properly position our proposed biomimetic "robotic hand design, in this section we first bri"efly review "the most relevant past work in robotics, and then"explain the potential application of the highly biomimetic robotic hands "in medical and biology research, to which end we"formed our design concept.

  A. Anthropomorphic robotic/prosthetic hands

  Many advanced anthropomorphic robotic hands havebeen developed during the past decade. As thoroughly summarized "in a recent review [2], each of them possesses di"stinctive "features in terms of actuation speed, magnified f"ingertip "forces, or high degrees of freedom (DOFs), etc. H"owever they all share the same design concept of mechanizing the biological counterparts. Their design ideas can be traced back to the technologies developed for industrialassembly "robots. Equipped with joint and tactile sensors,"the motion of such a human-like robotic hand can be seen asthe coordination of five miniaturized high-precisionindustrial robots packed within a palm-sized space. The development of the anatomically corrected testbed (ACT) hand[3] was the first try towards replicating the human hand on anatomical level. However its internal mechanisms are stillbased on "hinges and gimbals, we therefore categorize it as"a spe- cial type of anthropomorphic robotic hand. The inherent mismatch between mechanisms of these robotic hands and biomechanics of human hands essentially preventsus from using natural hand motion to directly control them. Thus none of them can achieve the human-level dexterity yet. The development of prosthetic hands heavily relies on the lessons we learned from building anthropomorphicrobotic hands. State-of-the-art prosthetic hands can nowbe con- trolled with two different methods: Using non-intrusive methods such as electromyography (EMG) signals collected from the residual limb or targeted muscle reinnervation re- gions [4]; or using intrusive methods like directly implanting microelectrodes at the motor cortex of the brain[5] or cuffing peripheral nerves with miniaturized electrodes tocollect control inputs [6]. The control of prosthetic hands essentially relies on human brain. Therefore the same neuroprosthetic technologies could be more effective if the design of the prosthesis could be more similar to its biological counterpart. "In contrast to these previous designs, we propose"to use a highly biomimetic design to preserve the salientfeatures of the human hand. Our design aims to minimize the design mismatch between robot and human hands for a more efficient control and a wider application.

  B. Design tools for medicine & biology research

  We envision our biomimetic hand to become a useful tool in medicine and biology research. Transplanted hand is the only existing biological alternative for a lost human hand to date. Yet the long-waiting list and the slim chance of finding the right donor keep preventing the method to beregularly practiced at hospitals. And there are still on-going debates about the lifelong rejection side-effects. In rec"ent years," biologists start to investigate the possibility of regrowing tissues and organs through biofabrication: biocompatible materials can now be printed to form bone structu"res [7]," biodegradable artificial ligaments have been usedto replace "the torn anterior cruciate ligaments [8], human m"uscles have been successfully cultivated inside petri di"sh [9], and" peripheral nerves can also be regenerated given the right conditions [10]. All of the these promising technologies require suitable scaffolds for the growth of grafted cells. When it comes to regrowing centimeter scale limbs", such" "as the rat forelimb, decellularised cadaver parts"are required as scaffolds [11]. However even if the same techniques can "be scaled up for human trails, the limitation of"donors could "eventually become a bottleneck. Besides, in medic"al research most of the in-vivo studies conducted on cadaverhands face constantly changing conditions since the decay process of the organic tissues is irreversible. The problemof biological variations caused by individual differences couldalso result in a long lasting debate. These limitations and drawbacks motivate us to seek for an alternative form of scaffold that can reliably preserve the biomechanical information of human hand in a physical working model.

  An biomimetic anthropomorphic robotic hand that mimics the biomechanics of the human hand can be first vali- dated in robotics lab and then mass-produced withbio- compatible materials to meet the requirement of different medical/biological applications. While it is often regarded unnecessary to directly copy the bio-blueprint ofthe bi- "ological counter parts, it is possible to replica"te critical biomechanical features of the human hand step bystep. The key of success lies in a thorough understanding of the biomechanics of the human hand from the engineering point of view and the ability to materialize the findings. III. D EVELOPMENT OF THE HIGHLY BIOMIMETIC

  ROBOTIC HAND

  "In this section, we identify the important biomec"hanical features that shape the movement of human hand from "the following aspects: the bones, joints, ligamen""ts, tendons," "extensor hood, and tendon sheaths. Instead of exa"mining the human hand directly from a hand surgeon’s perspe"ctive, in" each of the following subsection we explain the essential hand biomechanics in engineering language and then discuss the ways to replicate these features with our biomimetic design.

  A. The bones and joints

  "As shown in Fig. 2, the human hand has four finge"rs and one thumb and is composed of 27 bones containing 8 tightly packed small wrist bones 1 . Each fingerconsists of 1 We are interested in understanding the joint mechanism that enables "finger movement, so the wrist bones (except for t"he trapezium bone) are not in scope of our investigation at this stage.

  Fig. 2. The definition of the bones and joints ofthe human left hand (modified from [12]). Note: The trapezium bone isshown in red. three phalanges and one metacarpal bones. The thumb is an "exception, it only has two phalanges besides the"metacarpal bone. But the opposable thumb accounts for a bigportion of the entire hand function. The trapezium bone located at the base of the thumb has been found to be the critical component that enables the thumb opposition (labeled in red in Fig. 2). Together with the thumb’s metacarpal"bone, they" form the carpometacarpal (CMC) joint of the thumb. A joint is the connection between two adjacent bones whose shared contacting surfaces determine the possible motions of the joint. Different types of joints facilitate a "different set of finger motions, known as the ran"ge of motion (ROM). The metacarpophalangeal (MCP) joints are formed by the connection of phalanges to the metacarpals. Depend- "ing on the distance to the MCP joint, there exist"two more "types of joints, namely, the proximal interphalan"geal(PIP) joint and distal interphalangeal(DIP) joint. Based on this "definition, the thumb only has one DIP joint betw"een the "two thumb phalanges. During the bending motion, t"he three "finger joints work as mechanical hinges. However,"the MCP joints have one extra set of active ROM that allows the finger "to move from side to side, which are known as the"abduction "and adduction (ad/b) motions. In addition, the MC"P joints also have one passive ROM that permits twisting motion "around the axis of the finger phalanges. Thus, in"the case "of four fingers, we are only going to focus on de"scribing "the mechanism of the MCP joint, since the 1-DOF P"IP and DIP joints can be seen as a simplified case. Different from "the fingers, the complicated thumb movements are"resulted from the contact between the trapezium and firstmetacarpal bones at the CMC joint. Due to the irregular shape of the "trapezium bone (see Fig. 3), the exact locations"of its joint "axes are still under debate, but the CMC joint ha"s been commonly explained as a saddle joint that allowsthe thumb to have a wide ROM - up (adduction) and down(abdu"ction)," "bent(flexion) and straightened (extension), and t"he ability to move across the palm (opposition).

  "When designing robotic hands, robotics researcher"s often Fig. 3. Complicated bone shapes at the CMC jointof the thumb. Left: The common mechanical analogy of the first metacarpaland trapezium bones "(shown in red, modified from [12]). Right: The fi"xed joint axes used for explaining different thumb movements.

  choose 2-DOF universal joints for the MCP joints.The universal joint is good at transmitting rotary mo"tion in shafts," but lacks the 1-DOF that allows the finger to passively twist with respect to the axial direction at the MCP joint. The same problem worsens when it comes to designing the CMC joint. Because the CMC joint requires not only saddle-shaped surfaces but also curved rotation axis that suppo"rt rotation," "sliding, translation, and pivoting motions [13].""Thus, none of" the existing anthropomorphic robotic hands can restore the natural thumb motions with conventional mechanical joints "that use fixed rotation axes. In addition, the ir"regular shapes of articular surfaces are also responsible for distributing stress. It is estimated that a tip pinch of 1 kgwill generate 12 kg of joint compression at the CMC joint. Fora power "grip, the load could become as high as 120 kg [14"]. In order to maximally preserve the important surface "features of bones and joints, we 3D print artific"ial bones from the laser-scanned model of a cadaver skeleton hand [15]. As "shown in Fig. 1, all finger segments of our robot"ic hand (excluding the actuator brackets) can be printedout on a 20 "× 20 cm tray (Dimension BST 768, Stratasys). Dep"ending on the setting of the inner structure and resolution of the "parts (0.025 mm), the total printing time could b"e less than 20 hours.

  B. The joint ligaments

  The ROM at each finger joint is restricted by thelength "of ligaments. As shown in Fig. 4, ligaments are t"ough bands of fibrous tissues inserted on both sides of the two adjacent bones. Two important branches are calledcollateral ligaments. Similar structures can be found in allthe finger joints with variations in length and thickness. Their function "is to stabilize the joint, shape the ROM, and pre"vent abnormal "sideways bending of each joint. For example, at t"he MCP "joint, the collateral ligaments originate from th"e dorsal side of the metacarpal bone and end near the palmar side of the "adjacent finger phalanx. In this way, the collate"ral ligaments "get taut when the finger bends, and become relaxe"d once the finger straightens. This is why our index fingercan easily "move from side to side when it extends, but has v"ery limited side motions once it fully bends. The thick ligament formed Fig. 4. Schematic showing the function of collateral ligaments and volar plate at the MCint. P jo

  Fig. 5. The skeleton of the 3D-printed finger connected by crocheted ligaments and laser-cut joint soft tissues. Note:All the crocheted ligaments are anchored by 1 mm screws at their biological insertion sites. on the palmar side of the finger is called volarplate. Like "the collateral ligaments, the volar plate also ha"s insertions on both sides of the bones. Its function is to prevent the occurrence of the finger deformity from hyper-extension. Together with other accessory ligaments and soft"tissues," collateral ligaments and volar plate form important structure known as the joint capsule.

  Our artificial joint capsule design allows each robotic finger to be quickly assembled as shown in Fig. 5. One pair of the crocheted ligaments is used to mimic the two collateral ligaments located on the sides of each finger joi"nt. Similarly," the function of the volar plate is replaced by two crocheted ligaments anchored across each joint. Laser-cut rubber sheet is used to mimic the soft tissues providing the human-like "compliance. Based on the ROM of each joint, the d"imension of these components varies in size and length. Compared to "our previously proposed joint design [16], our cu"rrent design greatly reduced the fabrication time.

  C. Tendons and muscles

  "Between the bones and muscles, there are two grou"ps of tendons in the human hand. The ones straightening the "fingers are called extensor tendons, the ones ben"ding the fingers are called flexor tendons. The excursionmotions of the tendons originate from the corresponding muscle groups located in the forearm. If we treat the muscles as the actuators "that output contraction forces, the tendons of th"e hand serve as the transmission system that smartly partitionthe forces and smoothly deliver torques to each finger joint. As shown "in Fig. 6(a), starting from the wrist, the extens"or tendons branch out and have multiple insertion sites on the dorsal "side of the finger bones. On the palmar side, aft"er passing "through the carpal tunnel, the flexor tendons (se"e Fig. 6(d)) travel through a series of pulley-like tendon sheaths grown onto the palmar side of the bones and eventuallyinsert at the base of the DIP and PIP joints. The collaborativemotions of the two tendon groups make fluent hand movement possible. The large muscle groups that directly connect tothe central branch of the flexor and extensor tendons are called extrinsic muscles. Most of them originate from the elbow and have muscle bellies located in the the forearm. However there also exist several small muscle groups called intrinsic muscles that are often slim enough to reside in the gap between the two adjacent metacarpal bones. The majority of these small muscles start from the wrist of hand and connect to the thin branches (the extensor hood) of the extensor tendons of each finger near the MCP joint. One importantfunction of these intrinsic muscles is to provide passive reflex-mediated stiffness at finger joints during various hand activities. We "use resilient, laser-cut rubber sheet to mimic th"ese small muscles as a joint stabilization mechanism (see Fig. 1). "In total, ten Dynamixel servos (nine MX-12W and o"ne AX-12A) are used to mimic the important large muscles and actuate our proposed robotic hand (as shown in Fig. 1). Two servos are used to control the flexion and extension of the ring and little fingers through a differential pulley transmission (see Fig. 8). The index and middle fingers are separately controlled by two pairs of servos so that each of them can bend and straighten independently. In ad"dition, they" also share an extra servo for a coupled control at their MCP joints 2 . We use three actuators to control thethumb. One of them is an AX-12A Dynamixel servo that has a larger gear ratio (254/1) than others (32/1) and is used forthe extension and abduction of the thumb. The other two servosof thumb are assigned to control the flexion and adduction"motions," respectively. The palm has one underacutated DOFthat relies on the flexion motion of the ring and little fingers. Although the wrist of the current version only serves as astatic base for "testing the fingers, its cable routing structure"closely mimics the capral tunnel of the human hand.

  D. Extensor hood

  Most of our daily tasks involving hand motions require the contraction of strong muscles connecting to the flexor "tendons. Therefore during grasping, the extensor"tendons mainly work as a breaking system that constantlyregulates the torques at finger joints. The functionality of the breaking system relies on a fibrous structure known as theextensor "hood. The extensor hood is a thin, complex, and c"ollagen- based web structure that directly wraps around the finger "2 In our current design, the abduction/adduction"motion is passively regulated by the laser-cut intrinsic muscles integrated at the MCP joints for all the fingers

  Fig. 6. The important biomechanical advantages ofthe extensor and flexor tendons of a human left hand.(a) Schematic drawing of the extensor tendons. (b) A simplified geometric representation of theextensor hood. (c) The regulation of torques at the PIP joint during finger flexion. (d) Schematic drawing of the flexor tendons. (e)The bulging process of thetendon sheaths (the pulleys) during finger flexion. (f) Mechanical analogy of the bending finger showing the increase in moment arms under the effects ofelastic pulleys. phalanges from the dorsal side. Its structure canbe geomet- rically represented by a two-layer web as shown in Fig. 6(b). The first layer of the extensor hood is called lateral bands. It has an insertion site at the base of the DIP j"oint, and" split into two small ligaments across the PIP joint. This splitting mechanism smartly regulates the breaking torques at the PIP joint based on different postures of thefinger during its bending process (see Fig. 6(c)). As shown inthe lateral "view, when the finger straightens, the two small"ligaments are above the rotation axis at the PIP joint servingas branches of the extensor tendons. When the flexor tendons keep pulling "and extensor tendons getting stretched, the finge"r starts its bending process during which the two small ligaments continue to glide off from the PIP joint and eventually "pass downwards the rotation axis. Hereinafter, al"though the extensor tendons are still transmitting forces into the two "small branches via the web structure, the two sma"ll branches are no longer behaving like extensor tendons at t"he PIP joint," but instead they begin to help flex the finger byproviding increasing flexion torques at the PIP joint. Whenthe finger "straightens, the above process repeats in the rev"erse order. The second layer of the extensor hood is known asthe central slip with a insertion point at the base of the PIP joint. Its function is to help extend/flex the PIP joint. One of its tendon branches is often connected to a small intrinsic "muscle, namely, the lumbrical muscle. It has been"reported that the lumbricals work as flexor tendons at the"MCP joints," but can help extend the PIP and DIP joints via the extensor hood mechanism. Due to its variations in size andinserting "locations, the function of the lumbricals are not"unanimously agreed yet. So we treat them as a part of the intrinsic muscles without emphasizing its uniqueness in Fig. Fig. 6"(c). In sum," "the complex, web structure of the extensor hood s"martly transmits muscle forces to finger joints throughthe gliding mechanism.

  "As shown in Fig. 1, highly resilient rubber sheet"s are first laser cut into the shape of extensor hood (with intrinsic muscles integrated) and then attached to the skeleton of the fingers (see Fig. 7) at biological insertion sites to mimic "the passive behavior of the extensor hood, leavin"g servos to achieve the active extension of the finger through the gliding mechanisms. This is an important biomechanical advantage that we incorporated into our robotic hand design. E. Tendon sheaths

  "As shown in Fig. 6(e), the tendon sheaths are fib"rous tissues that wrap around the flexor tendons and have multiple insertions on the dorsal side of finger bones. Due to their "important functions, each section of the tendon s"heaths has been named after a numbered annular pulley in nomencla- tures of hand anatomy based on their distances tothe MCP joint. Mechanical engineers design different pulley systems to apply forces and transmit power through cables. The tendon sheaths in the human hand work as a seriesof elastic pulleys to help efficiently transmit flexion forces from the muscles to the joints. Since the tendon sheaths can flatten down when the finger straightens and bulge out when the finger bends [17].

  "As illustrated in Fig. 6(e) and (f), if the flexo"r tendon starts pulling a straightened finger with constant force"and speed," the initial moment arms at joints are small and therefore can cause a fast bending motion of the finger butresult in small flexion torques at the joints. However when the "finger starts bending, the bulging effect of tend"on sheaths greatly increases the moment arms at joints leading to a slowed finger motion with rapidly magnified flexion torques. "With the elastic pulley system, the human hand ca"n keep the torques at the finger joints small when approaching "the object, but quickly deliver large torques to"the finger joints when forming a grip. Combined with the gliding "mechanisms, this is another biomechanical advanta"ge that helps the flexor tendons to dominate the finger dynamics during flexion motions.

  "As shown in Fig. 7, three patches of laser-cut ru"bber sheets are used to mimic the elastic pulley mechanism. The flexor tendon made of high strength Spectra

  R ?

  strings

  Fig. 7. Snapshots of an assembled finger showingboth the gliding mechanism of the extensor hood and the bulging effect of the tendon sheaths during finger flexion.

  (200 N yield strength) is routed through the rubber tendon sheaths via several rivet reinforced ports. The flexor tendons of our robotic hand mimic the flexor digitorum profundus (FDP) tendon of human hand. Although the human finger has another flexor tendon - the flexor digitorumsuperficialis (FDS) tendon - inserted to the base of the PIP jo"int, we" choose not to incorporate the FDS in this versionof the "robotic hand, because it is reported that the FDP"tendon generates greater fingertip forces than the FDS tendon during isometric tasks [18].

  IV. P ERFORMANCE OF THE BIOMIMETIC ROBOTIC HAND

  In order to evaluate the efficacy of our proof-of#NAME? "design, in this section, we first quantitatively"investigate "the fingertip trajectories, and then qualitativel"y conduct the telemanipulation experiments. The experimental se"tup, pro-" "cedures, and results are reported in following su"bsections. A. Fingertip trajectories

  "As we briefly mentioned, the ring and little fing"ers are coupled considering their collaborative relationship as the grasping fingers. Their flexion and extension motions are controlled by a pair of Dynamixel servos througha differ- ential pulley transmission as shown in Fig. 8. The benefit of using such a pulley structure is to provide an extra source of hand compliance in addition to the build-in compliance at "each finger joint, since it allows the two graspi"ng fingers to conform to the contour of an object by automatically adjusting the shared string length between the two insertion sites. But the drawback is that the underactuatedmechanism could also become a source of uncertainty bringing the two fingers into certain unknown postures when they bend and straighten between the two extreme postures. Thusit is important to first investigate the repeatabilityof our proposed "mechanism, especially when the finger’s ROM is c"ontrolled in between full flexion and extension postures.

  "Compared to the ring and little fingers, the inde""x, middle," and thumb are each actuated by more than two serv"os," therefore they can be better controlled in this case. In "the fingertip tracking experiment, we chose two e"xtreme positions for the coupled ring and little fingers", and then" controlled the two servos to bend and straightenthe coupled fingers approximately once every two seconds. Thecoor- dinates of the reflective markers attached to thefingertip are recorded by a motion capture system (Vicon Bonita) Fig. 8. Labeled pictures showing the differentialpulley transmission for ring and little fingers and the locations of thereflective makers. Note: All the marker coordinates were recorded with restiveto the forearm frame. pec Fig. 9. The displacement of the ring’s fingertipduring 20 repetition of flexion and extension motions. Note: Similar tracking data were recorded and observed for the litter finger.

  composed of 7 infrared cameras at 240 Hz VGA resolution. "The Vicon system was calibrated, and is able to d"etect 0.5 mm displacement in all directions.

  In order to avoid the marker occlusion and confusion "issues, we attached a forearm frame (see Fig. 8)"near the "wrist of our robotic hand, so that we could recor"d the marker "trajectories for one fingertip at a time, and the"n transform their coordinates from the default world frame tothis forearm frame when processing the data. The use of this forearm frame also allows us to constantly change the orientation of our robotic hand during hand motions in order toachieve good visibility for the reflective markers.

  The Cartesian coordinates of the fingertips fromthe ring "and little fingers are very similar, and therefor"e only the ones from the ring finger are plotted in Fig. 9. The data of 20 repetitions of the full flexion and extension motions show a highly repeatable pattern suggesting that our biomimetic finger design and the differential pulley systemcan be successfully combined to build reliable robotic hand. "After being projected onto the X-Z plane, the fle"xion and extension trajectories of the ring finger’stip can be clearly observed in Fig. 10(b). Our experiments show that the flexion and extension motions of our biomimetic robotic finger were not following the same trajectory. The area bounded by the two trajectories covers a big portion of the reachable workspace of the ring finger [19]. Theflexion trajectory closely resembles that of the logarithmic spiral curve observed from human finger’s flexion motion [20]. The (a)

  (b) (c)

  Fig. 10. The trajectories of the fingertips of our biomimetic robotic hand. (a) 3D scatter plot of fingertip trajectories. (b) The ring fingertip’s trajectories projected onto the X-Z plane. (Note:The scatter plot is from the 20 repetitions of the full flexion and extensionmotions.) (c) The trajectories of the fingertips projected onto the X-Z plane.

  difference between the flexion and extension fingertip trajec- tories results from the sequential joint movements shaped by "joint stiffness. As shown in Fig. 7, the variable"joint stiffness is regulated by the gliding mechanism of the extensor hood and the elastic pulleys of the tendon sheaths.

  The fingertip trajectories of other digits were also recorded. Unlike the pre-determined inputs for the ring and "little fingers, the repetitive movements of the i""ndex, middle," and thumb were teleoperated by the human operatorthrough our custom-made data glove 3 . As shown in Fig. 1"0, the" "two principal components of the thumb motions, na"mely the flexion/extension and the abduction/adductionwere tested separately. The teleoperation results in more scattered data points compared to the ones collected from the prepro- grammed motions of ring and little fingers (see Fig. 9). B. Object grasping and manipulation

  In order to further evaluate the overall performance of "our robotic hand, we conducted grasping and manip"ulation experiments using 31 objects from the prioritizedlist [21]. During the test a human operator hands differentobjects to "the robotic hand with his right hand, meanwhile,"used his left hand to teleoperate the digits of the robotic hand to grasp/manipulate the object via the data glove (see Fig. 11). This process is known as the tele-manipulation during which 3 Details about the data glove can be found in [1"5], but is out of the scope" of this paper.

  Fig. 11. Snapshots showing the teleoperation process of our biomimetic robotic hand.

  Fig. 12. The hand taxonomy realized by our biomimetic robotic hand (Note: see the taxonomy figure in [22] for comparison). the movement of the robotic hand is both controlled and guided by the same human operator’s hand motionand visual feedback. This experiment can be seen as aseries of cooperative grasping tasks between the human operator and the robotic hand in which the former could clearly monitor the status of the grasped object without the occlusion issue at the grasping site (see our video submission for details). "During the object grasping task, we observed that"different grasping postures can be naturally transferred from the "human operator to our biomimetic robotic hand, pa"rticu- larly from the motion of the thumb. This is because our biomimetic robotic hand successfully preserves the important biomechanics of the human hand that essentially determines the hand kinematics. The resulting grasps cover most of the grasping types defined by human hand taxonomy [22"], except" for the ones that require independent control ofthe ring and little fingers (see Fig. 12).

  "Last but not least, we tested the in-hand manipul"ation ability of our biomimetic robotic hand. As shown"in Fig. 13," the whiteboard eraser was successfully regraspedfrom hori- zontal to vertical position through a series of continuous hand motions involving the use of all the digits. It is interesting Fig. 13. Snapshots of our biomimetic robotic handperforming in-hand manipulation of a whiteboard eraser.

  to observe that complicated in-hand manipulationtasks can be accomplished without any force feedback. Thisagain suggests that matching the kinematics of the robotic hand to its human counterpart is important for the success of teleoperation tasks.

  V. C ONCLUSION AND FUTURE WORK

  We have designed and prototyped a highly biomimetic anthropomorphic robotic hand that closely mimicsthe im- portant biomechanics of the human hand with artificial joints "and ligaments. During this process, we first iden"tified two crucial constraints that have been limiting the development of anthropomorphic robotic hands: the lack of properly translated engineering knowledge of the human hand and the restrictions caused by conventional mechanical joints. And then we reinterpreted and detailed the ways to replicate important biomechanical advantages of the human hand with the language and methods that roboticists can easily under- stand. We experimentally demonstrated that our proposed robotic hand design has good repeatability in finger motions and can be teleoperated to grasp and manipulate awide selection of daily objects within the fingertip workspaces under current design.

  "In future work, we are planning to incorporate bi"omimetic wrist design and already-developed fingertip sensors [23] into our robotic hand so that we can further improve its "telemanipulation performance. In addition, due to"the in- herent similarity between our robotic hand and its human "counterpart, we are going to collaborate with res"earchers from biology and tissue engineering to further explore its potential to serve as a bio-fabricated device/scaffold in the emerging fields of neuroprosthetics and limb regeneration. VI. A CKNOWLEDGMENTS

  This work was supported by the US National Science Foundation. The authors would like to thank Dr. Christopher Allan at the HarborView Medical Center for his help on "guiding the cadaver hand dissection, and thank Sv"etoslav Kolev for his help on setting up Vicon experiments. R EFERENCES

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