Design of a Roller-Based Dexterous Hand for Object Grasping andWithin-Hand Manipulation

Shenli Yuan1, Austin D. Epps2, Jerome B. Nowak1, J. Kenneth Salisbury3

Abstract— This paper describes the development of a novelnon-anthropomorphic robot hand with the ability to manipulateobjects by means of articulated, actively driven rollers locatedat the fingertips. An analysis is conducted and systems ofequations for two-finger and three-finger manipulation of asphere are formulated to demonstrate full six degree of freedomnonholonomic spatial motion capability. A prototype version ofthe hand was constructed and used to grasp and manipulate avariety of objects. Tests conducted with the prototype confirmedthe validity of the mathematical analysis. Unlike conventionalapproaches to within-hand manipulation using legacy robotichands, the continuous rotation capability of our rolling finger-tips allows for unbounded rotation of a grasped object withoutthe need for finger gaiting.

I. INTRODUCTION

In the pursuit of developing ever more capable roboticgraspers, researchers have sought to match the remarkabledexterity of the human hand through mechanical means. Ataxonomy for evaluating the dexterity requirements for anarray of grasping tasks is presented in [1], in which thetasks requiring the most dexterity are both prehensile andwithin-hand. These are manipulations in which contact forcesfrom the hand alone are used to grasp and stabilize theobject, and where motion of the object is generated from themodulation of the contact forces between the hand elementsand the grasped object. A robotic hand with the abilityto perform within-hand manipulation possesses the abilityto transition from the initial grasp configuration to othergrasp configurations, for example, to establish a more securegrasp by engaging object surfaces unavailable in the initialgrasp orientation. Theoretical foundations for manipulationof objects using multiple points of contact are established in[2], [3], and [4].

An extensive review of robotic hand designs in the pastcentury is presented in [5]. Only a fraction of these handshave the capacity to perform within-hand manipulation tasks.The Stanford/JPL hand [2] and Utah/MIT hand [6] areamong the earliest robotic hands possessing within-handmanipulation capabilities. Because the human hand possessesthe dexterity to perform within-hand manipulation, attemptshave been made to replicate this ability by replicating itsstructure. Anthropomorphic hands, such as [7], [8], and [9],approximate the number of degrees of freedom (DoF) of the

This research was supported, in part, by the Stanford InterdisciplinaryGraduate Fellowship.

1Department of Mechanical Engineering, Stanford University2Dexterity Systems, LLC3Department of Computer Science, Stanford Universityshenliy@stanford.edu, austin@dexterity.systems,

jerome.nowak@stanford.edu, jks@cs.stanford.edu

Fig. 1. The roller grasper prototype

human hand. The resulting robotic hands, while mechanicallycapable, have not found applications outside of the researchlab due to their cost, sophisticated sensing and controlrequirements, and the sheer complexity of programmingthem to perform within-hand manipulation.

Another approach has been to focus on achieving graspingand manipulation capabilities with fewer actuated DoF suchas [10], [11], and [12]. Many robotic hands also utilizeunder-actuated fingers in order for the hand to passivelyconform to the shape of the objects being grasped such as[13] and [14]. The use of under-actuated fingers providesincreased grasp stability at the cost of reduced controllability,making within-hand manipulation more challenging. Within-hand manipulation using under-actuated fingers is an area ofongoing research, with recent examples provided by [15] and[16].

Highly non-anthropomorphic approaches to within-handmanipulation have also been explored such as [17]. Theincorporation of actuated conveyor belts was examined in[18] in order to enhance manipulation capabilities of arobotic grasper. This concept was further explored in recentworks such as [19], [20], [21], and [22]. Conveyor surfaces(or, more generically, “active surfaces”) allow the graspers toimpart motion to grasped objects without substantial modifi-cation of the grasp pose. In these embodiments the conveyororientations are fixed, limiting object motion availability. Insome sense our work generalizes these in that we exploreimparting motion within a grasp by using active surfaces, inour case rotating cylinders, that can be placed against andoriented with respect to a grasped object.

2020 IEEE International Conference on Robotics and Automation (ICRA)31 May - 31 August, 2020. Paris, France

978-1-7281-7395-5/20/$31.00 ©2020 IEEE 8870

Fig. 2. Modular roller finger in the vertical configuration (left) andhorizontal configuration (right). Locations of joint axes are shown in red.

Fig. 3. Motorized roller assembly exploded view. Parts 3-5 and the outerrace of 2 and 8 rotate with Ci, the others are fixed with Bi (Bi and Cidefined in Fig. 4)

In this work, we developed a grasper with articulatedactive rollers at the fingertips, which provide steerable activesurfaces. This allows unbounded rotation of a grasped objectwithout the need for finger gaiting in ways not seen inthe state of the art. The design of the grasper is describedin section II. Section III provides analysis of within-handmanipulation in different configurations. Section IV showsvarious experiments conducted for manipulation and grasp-ing and discusses experimental results. Conclusions andfuture work are presented in section V.

II. DESIGN

The grasper assembly consists of three kinematicallysimilar fingers (Fig. 2), each consisting of three actuatedDoF. The proximal DoF is a revolute joint directly drivenby a Robotis Dynamixel XM430-W350 smart actuator. Theintermediate DoF is orthogonal to the proximal DoF, andis based on a parallelogram mechanism similar to [23]with the input and ground links anchored on the centerlineof the parallelogram. The intermediate DoF controls theorientation of the fingertip roller, and is actuated by a microdigital servomotor (Savox SW0250MG). Structural parts aremade of machined aluminium, 3D printed resin and lasercut acrylic. Neoprene strips are adhered to the faces ofthe two vertical links of the parallelogram mechanism so

Fig. 4. 3D Kinematics. Relevant notations are given Table II. Joint anglesfor fingers 2 and 3 are defined similarly to finger 1, relative to local frames.Frame G is fixed to the wrist, and Ai,Bi, Ci are the frames of the links infinger i. Here θB1/A1

= −θB2/A2= θB3/A3

= 90.

that they may be used as secondary grasping surfaces. Theparallelogram configuration was selected in order to place theactuator further from the roller so as to maximize the area ofthe roller’s surface that is available for grasping and within-hand manipulation. The fingertip roller (Fig. 3) is actuated bya micro DC gearmotor equipped with a quadrature encoder,and is capable of continuous rotation. The roller is fitted witha stack of square cross-section neoprene O-rings to providea high-friction surface for grasping and manipulation. Thecomplete grasper weighs 800 g, and each finger can provide20 N of normal force at the roller center.

The kinematic configuration and parameterization of thegrasper assembly are shown in Fig. 4. Fingers 1 and 2are arranged symmetrically and have parallel proximal jointaxes. The parallelogram mechanisms of these two fingers areassembled in mirrored fashion such that when the roller isoriented vertically the vertical links connected to the topsof each roller assembly (parallelogram link 2 in Fig. 2) arelocated on the same side of the grasper. Finger 3 is placedsuch that its proximal joint axis is orthogonal to the proximaljoint axes of fingers 1 and 2, and this axis is offset from theshared midplane of fingers 1 and 2. It is placed such thatwhen finger 3’s roller is oriented vertically (θB2/A2

= −90),the axis of the roller lies on the symmetry plane of fingers 1and 2. Finger 3 has a parallelogram mechanism configurationidentical to finger 1. Roller pivoting is constrained such thatθB1/A1

∈ [0, 90], θB2/A2∈ [−90, 0] and θB3/A3

∈[0, 90]. The configuration described here allows for severalgrasp and within-hand manipulation modalities which will bediscussed in the following sections. The physical dimensionsof the prototype grasper are given in Table I.

III. ANALYSIS

The hand’s multiple degrees of freedom and contact sur-faces result in a wide range of manipulation and grasping

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TABLE IPHYSICAL DIMENSIONS

Link a b c r d1 d2 d3Dimension [mm] 186 20 10 15 28 48 83

TABLE IINOTATION

Symbol(s) MeaningA Point A.A Vector giving the coordinates of A.XA Unit vector defining the X axis of frame A. If no frame

is specified, frame G is used.AU Vector U expressed in frame A. If no frame is specified,

frame G is used.RX , TX Classes of translations and rotations, respectively, around

vector X .RXA (θ) 3 × 3 rotation matrix around vector XA of a positive

angle θ using the right hand rule, expressed in frame A.ΩB/A Rotation velocity vector of frame B relative to frame A.θB/A Angle of rotation of frame B relative to frame A.

capabilities. To better understand the extent thereof, wepresent a kinematic analysis in the simplified case of 6-DoFspatial manipulation of a spherical object in contact with therollers, with considerations on how further parametrizationand computation could extend our analysis to other objectclasses (e.g. the ones manipulated experimentally). See TableII and Fig. 4 for notations and parameters used in this section.Here frame G is fixed with ZG pointing vertically up.

A. Sphere Manipulation Configurations

Controlling object motion relies on controlling the velocityvector applied at each contact point, which requires carefullysteering the rollers. For simplicity, constraining each rolleri to a vertical (|θBi/Ai

| = 0, abbreviated V ) or horizontal(|θBi/Ai

| = 90, abbreviated H) position, results in eightpossible three-finger sphere manipulation configurations, andtwelve possible two-finger ones. Considering the symmetri-cal combinations to be the same, this leaves six distinct three-finger and seven two-finger combinations. Of the thirteencombinations, five were deemed particularly useful for theirversatility and/or ease of use. The associated DoF of thesphere when actuating the joints at Ai and Bi are presentedTable III, assuming no slip. A manipulation configuration isdescribed e.g. by HHV when rollers 1 and 2 are horizontaland roller 3 is vertical, and HV× when roller 1 is horizontal,2 is vertical and 3 is unused. In addition, there exists auseful two-finger manipulation where fingers 1 and 2 pivotin sync between H and V (abbreviated P ), as it providespure X-rotation and is suitable for switching manipulationconfiguration, e.g. as an intermediate step from V V V toHH×. These configurations are illustrated Fig. 5.

Table III demonstrates that sequentially combining thosesix configurations enables full 6-DoF spatial motion of asphere. While two-finger cases locally cover all DoF, three-finger manipulation is required for unrestricted X rotationand better stability. As some DoF are coupled, certain puremotions are not instantaneously achievable, but may be

TABLE IIISPHERE MANIPULATION DOF VS. ROLLER PIVOT ANGLE

Roller Config. Translation Rotation1 2 3 TX TY TZ RX RY RZ

H H × X X XV V × XRY

X XTXX

P P × XV V H X XRX

XTZ

V V V X XH H H XNotes: (1) All directions are relative to frame G. (2) V means|θBi/Ai

| = 0; H means |θBi/Ai| = 90; P means synchronously

pivoting between H and V ; and × means the finger is not used. (3)Subscripts of Xindicate coupled motion and specify its nature.

(a) V V H (b) V V V (c) HHH

(d) HH× (e) V V× (f) PP×

Fig. 5. Roller configurations for spherical object manipulation

replicated using a succession of coupled motions. This is dueto the nonholonomic nature of the grasper, much like a carindirectly achieves a lateral translation by moving in forwardand reverse while adjusting steering during parallel parking.Other examples include uses of nonholonomic dextroushands such as [24] and [25].

One should note that V V× is potentially unstable, as thesphere could roll out due to gravity e.g. during TY , thoughthis is less of a concern for flat-faced objects, or for smallobjects and large forces thanks to roller surface compliance.A support contact with finger 3 can also aid in stabilizingthe grasp.

Other manipulation configurations not considered hereyield unstable, more complex or redundant motions, e.g.HV× (unstable) or HV V (couples TY with RZ). Caseswhere θBi/Ai

have intermediate values are also possiblebut beyond the scope of this paper. Furthermore, thesemotions can analogously be applied to other convex objectsas demonstrated in section IV with a six-sided die, thoughdepending on their geometry slip might occur or motionavailability may be restricted.

As a demonstration of how one would control a sphere,we present an in-depth analysis of three-finger V V H ma-nipulation and two-finger HH× manipulation.

B. Example Three-Finger Manipulation

Using the homogeneous transformation matrices spec-ified in Table IV, a point designated by a vector CiU

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TABLE IVREFERENCE FRAME TRANSFORMATIONS

From To Homogeneousframe frame transformation matrix

G A1GA1M =

[RYG (θA1/G) −d1 GXG0 0 0 1

]G A2

GA2M =

[RZG (π)RYG (θA2/G) d2 GXG

0 0 0 1

]G A3

GA3M =

[RZG (−π/2)RYG (θA3/G) d3 GYG

0 0 0 1

]Ai Bi Ai

Bi M =

[RXAi

(θBi/Ai) aAiZAi

0 0 0 1

]Bi Ci Bi

CiM =

[RZBi

(θCi/Bi ) bBiXBi + cBiYBi0 0 0 1

]

in frame Ci can be expressed in frame G:[GU

1

]=

GAiMAi

BiMBi

CiM

[CiU1

]. Let D be a spherical object of radius

R and center D contained within the workspace. AssumingD is within the grasper workspace, contact between D androller Ci is expressed as:

‖ZBi× (Ci −D)‖ = r +R (1)

where [Ci

1

]= GAi

MAi

BiMBi

CiM[0 0 0 1

]T(2)

Furthermore, assuming there is no slip, the angles of rollerCi and object D can be computed using the no-slip conditionat their point of contact I:

d

dtID∈Ci −

d

dtICi∈D = 0 (3)

where ID∈Ci is the point of Ci that is momentarily coincidentwith D, and ICi∈D is the point of D that is momentarilycoincident with Ci, and we choose to compute the derivativesin the center-of-momentum frame of D (where we assumeG is inertial).

When θAi/G and θBi/Aiare known, (1) gives a 2D solution

space of possible ball positions for each finger, and innondegenerate cases the intersection of all three spaces givesa unique ball position for that configuration. When D isknown, (1) gives a 1D inverse kinematic solution space forθAi/G and θBi/Ai

, which can be reduced to one or twodiscrete joint positions by e.g. imposing θBi/Ai

. We furtherdiscuss the existence of multiple solutions in the case oftwo fingers in III-C. Solving (1) and (3) for all fingersallows us to numerically determine joint positions for within-hand translation and rotation of a ball, and determine whichmovements will result in slip so as to avoid them. General-izing to manipulating an arbitrary convex shape leaves (3)unchanged, and requires a 3D parametric equation of saidshape to adapt (1) as well as considering object orientation.

A 3D kinematic simulation showing the manipulationconfiguration V V H was performed in MATLAB in the case

of a sphere. A sequence from this simulation is shown inFig. 6. If the no-slip condition is maintained at the contactsurfaces of fingers 1 and 2, the only translation modalityavailable for TZ movement is rolling up and down. Torestrict rolling motion to be around X , the contact points offingers 1 and 2 are always symmetrical about the Y -Z plane.Therefore, a translation TZ induces a rotation RX . Themagnitude of RX is inversely proportional to the effectiverolling motion radius, i.e. the distance between the contactpoint with finger 1 or 2, and the axis going through D andparallel to X . Thus a smaller effective radius results in morerotation RX per unit translation TZ .

In the simulated sequence shown Fig. 6, the rollers offingers 1 and 2 translate the sphere from its initial pose (Fig.6a) a distance of +∆y along Y while finger 3 providesstabilization (Fig. 6b). The roller of finger 3 is then used toroll the sphere up along the surfaces of fingers 1 and 2 adistance of +∆z and an angle ∆θx,1 (Fig. 6c). The effectiveradius R1 of this rolling motion is displayed on the figureas an orange circle. The rollers of fingers 1 and 2 are onceagain used to translate the sphere a distance of −∆y alongY (Fig. 6d). Finally, the roller of finger 3 is used to rollthe sphere a distance of −∆z along Z, with effective radiusR2 < R1 and angle −∆θx,2 (Fig. 6e). All throughout thismotion, θAi/G,i∈[1,3] are adjusted accordingly. The sphere’scenter has returned to its original position, but has turned anangle of ∆θx,final = (1/R1 − 1/R2)∆z < 0. This allowsthe effective rolling radius for TZ movement to be changedindependent of TY for successive up/down motions, therebycreating a nonholonomic circuit where the sphere may betranslated from its initial pose through the circuit, arrivingback at the initial cartesian position but with a net change inrotation RX .

C. Example Two-Finger Manipulation

In the HH× configuration, 3-DoF manipulation of aconvex object in the X-Z plane is possible using the jointsat A1, A2, C1 and C2. This can be described using (1) and(3), though the case of a spherical or cylindrical object D canbe regarded as a 5-bar linkage, whose forward and inversekinematics have been explicitly solved in [26] (see Fig. 7).In the interest of implementing these explicit kinematics inour controller, we adapt the results in [26] to our vector-based notations and to the added symmetry of our design.For known joint angles θA1/G and θA2/G we have the forwardkinematics equation:

D =1

2(C1 + C2)± (C2 −C1)× YG

√(r +R)2

‖C2 −C1‖2− 1

4(4)

A positive sign in (4) has the ball resting on top of the rollers,while a negative sign has it below, held only by friction.

For a given ball position D, there are two possible jointangles at A1 and A2, given by the law of cosines:

θAi/G =π

2± αi(D)− βi(D)− γ (5)

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(a) Original pose (b) Step 1: +TY (c) Step 2: +TZ , +RX (d) Step 3: -TY (e) Step 4: -TZ , -RX

Fig. 6. Side view of 3D kinematic simulation demonstrating within-hand manipulation of a sphere. The path of the sphere center is shown by the redline segments, and the purple axes are fixed in C3. The effective radius of the rolling motion involving RX and TZ is given by the orange circle, and isdifferent between steps 2 and 4, resulting in a net rotation.

Fig. 7. 2D Kinematics

where, with i in 1, 2,

αi(D) = arccos

(‖Ci −Ai‖2 − (r +R)2 + ‖D −Ai‖2

2‖Ci −Ai‖‖D −Ai‖

)(6)

βi(D) = | atan2 ((D −Ai) ·ZG , (D −Ai) ·XG)| (7)

γ = atan2 (b, a+ c) (8)

‖Ci −Ai‖ =√

(a+ c)2 + b2 (9)

Only one set of finger positions provides the most securegrasp with continuous manipulation capabilities. The follow-ing constraints narrow down the solutions to a negative signin (5) for both fingers, and reduce the workspace D can bein:• viewed from above, the center of gravity of the sphere

should be between rollers 1 and 2;• the fingers should be applying forces toward each other

in order to maintain a secure grasp.Equations (4) and (5) give forward and inverse kinematic

relationships between the positions of the fingers and that ofthe center of the ball. To take into account the rotations ofD, C1 and C2, we need only write the no-slip condition (3)in this simplified case:

R θD/G = r(θC1/B1− θA1/G) + (r +R)θDC1 (10)

R θD/G = r(−θC2/B2+ θA2/G) + (r +R)θDC2 (11)

where θDCi is the angle between the vectors XG and Ci−D,counted positively towards YG .

We now have explicitly formulated 3-DoF planar forwardkinematics with (4), (10) and (11), and inverse kinematics

with (5), (10) and (11), which allows full 3-DoF planarmotion.

IV. EXPERIMENTS AND DISCUSSION

A proof-of-concept modular prototype (Fig. 1) was madeto validate the analysis in section III and further exploremanipulation and grasping capabilities. We mounted threeroller finger modules (Fig. 2) on two different bases inidentical finger configurations. Base types were a benchtopvariant with ZG pointing up, and a variant designed to bemounted on a Universal Robots UR5 robotic arm.

A. Manipulation

All manipulation configurations referenced in Table IIIand Fig. 5 were experimentally validated with a rangeof sphere sizes, thus demonstrating fully controlled 6-DoFmanipulation by transitioning between said configurations.Furthermore, we successfully applied these capabilities tononspherical objects of varying size, hardness and aspectratio, such as a six-sided die (Fig. 9), a sheet of paper,the interior surface of a ring (Fig. 8a) or an open topbox (Fig. 8b). The V V V configuration was also used tounscrew a bottle cap, with the threading pushing the capup so it slipped vertically along the inside of the rollers.This pushes the fingers apart while maintaining contact viaforce control. Generally speaking, the hand can achievecontrolled manipulation of objects with simple geometricfeatures (further demonstrated in the complementary video).

For fingertips without continuous rolling capabilities, mo-tions like rotating a ball or turning a threaded object (e.g.a screw or bottle cap) are typically done by gaiting, whichinvolves breaking and re-establishing contact between thefingers and the object. This motion can be complex tocontrol, especially in the case of prehensile manipulation.In comparison, the grasper described here is particularlyefficient for this. Manipulation from inside an object is alsoa less common modality, which is enabled here by havingmost of the roller perimeter exposed, allowing the grasper tofurther extend its manipulation capabilities beyond its sizelimitations by fitting large objects around the outside of thefingers (e.g. in the case of an open top box).

B. Grasping

In addition to performing within-hand manipulation tasks,the presence of actively driven rolling fingertips offers ben-efits for grasping objects of different sizes, shapes, andproperties. Several of the grasp techniques explored involve

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(a) V V× (b) HH×(box) (c) HH×(regular) (d) HH×(thin) (e) HH×(soft) (f) PPH(regular) (g) PPH(box) (h) HHH

Fig. 8. Other roller configurations (Fig. 8a for manipulation; 8b for manipulation and grasping; the rest for grasping)

Fig. 9. Manipulation of a six-sided die to show all faces of a cube.Transitions are, in sequence from left to right, top to bottom: V V H(RX

& TZ), V V V (RZ), V V V (RZ), V V V (RZ), PP × (RX))

operating the rollers in a counter-rotating manner such thatthe grasped object is drawn into the grasper, allowing anobject to be picked up without the assistance of externalmotion provided by a robot arm.

Figure 8 includes a list of grasp modalities we were ableto perform successfully. These include:• Picking up and manipulating a box via its inner faces

using two fingers in the horizontal orientation (Fig. 8b).• Picking up a box via its exterior faces (Fig. 8c).• Utilizing one roller for pre-grasp sliding manipulation

[27] to direct a thin object to the edge of a constrainingsurface where a second fingertip may establish a pinchgrasp on the object (Fig. 8d).

• Grasping a flexible object, such as a piece of fabric,by taking advantage of its capacity for deformation. Byoperating the rollers in a counter-rotating manner whileengaged with the flexible item, it is possible to drawthe item into the rollers (Fig. 8e).

• Using the interior surfaces of the parallelogram mech-anism vertical members of fingers 1 and 2 to providemotion on one side of an item, and the roller of finger3 to provide motion on the opposite surface (Fig. 8f).

• Using the exterior surfaces of the parallelogram mecha-nism vertical members of fingers 1 and 2 and the rollerof finger 3 to manipulate a box via its interior faces(Fig. 8g).

• Grasping and manipulating a box via its interior facesusing all three fingers for a more stable grasp (Fig. 8h).

C. Limitations

1) Nonholonomic Nature: The system is nonholonomic,as the grasped object cannot be moved in an arbitrarydirection instantaneously. The object may need to go through

a series of motions before a certain pose can be achieved(e.g. rolling an object in the Z direction in the HH×configuration).

2) Slipping: The object might slip when there is notenough contact area or contact points with the rollers,causing inaccuracy in the manipulation. This can happen forobjects with sharp edges, or inherently unstable grasps suchas the V H× configuration.

3) Power Grasping: Although each finger has three DoF,two of them are dedicated to controlling roller motions, andonly one controls general finger pose. While the grasperperforms well in pinch grasp (especially with the addedhelp of rollers), this makes conforming to an object’s shapedifficult, hence power grasp is not possible except for a smallsubset of objects (e.g. thin and long shapes which can beconstrained between straight fingers).

V. CONCLUSIONS & FUTURE WORK

This paper describes the preliminary design and controlof a robot hand that can manipulate objects by using therolling motion of reorientable powered cylindrical fingertips.With three modular 3-DoF fingers, we demonstrate full 6-DoF spatial manipulation of objects with simple geometrysuch as a sphere, a cube or a marker, as well as variousgrasping modalities. The system however is nonholonomic,in that it cannot move an object in an arbitrary directioninstantaneously - the cylinders must be aligned correctlybefore we can proceed with arbitrary motion. This constraintcould be removed by using spherical fingertips able to rotatein two independent directions. While analysis involving theJacobian (or more properly, the Grasp Matrix [2]) is requiredfor controlling grasp forces and object differential motions,it is beyond the scope of this preliminary study. The hand wepresented takes a decidedly non-anthropomorphic approachto within-hand manipulation. It raises interesting questionsabout control and planning, as well as mechanism design.Future work includes developing various control schemes forcontrolled slipping during three-finger manipulation, analysisof the roller grasper workspace and dynamics, and redesignof the finger and roller mechanism.

ACKNOWLEDGMENT

The authors would like to express their appreciation toKeven Wang and UnitX, Inc. for use of their robot andfacilities during our experimental validations.

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