Proceeding of the 6th International Symposium on Artificial Intelligence and Robotics & Automation in Space: i-SAIRAS 2001, Canadian Space Agency, St-Hubert, Quebec, Canada, June 18-22, 2001.

Underactuation in Space Robotic Hands

Thierry Laliberte and Clement M. Gosselin

Departement de Genie Mecanique, Universite Laval, Quebec, Quebec, Canada, G1K 7P4thierry@gmc.ulaval.ca gosselin@gmc.ulaval.ca

Keywords Grasping, robotics, hand, gripper, un-deractuation, flexible, selfadaptive, reconfigurable,space.

Abstract

This paper presents the development of a selfadap-tive and reconfigurable robotic hand for space appli-cations which is versatile, robust and easy to con-trol. This hand has three fingers and each of thefingers has three phalanges. It will be shown thatthe selfadaptability of the hand is obtained usingunderactuation within and among the fingers of therobotic hand. Indeed, underactuation between thephalanges of a finger is realized using linkages andsprings while the underactuation among the fingersis implemented by a special one-input/three-outputdifferential. An additional degree of freedom (dof) isused to rotate two of the fingers in order to recon-figure the hand and fit the general geometry of theobject to be grasped. Overall, the hand has ten dofs,actuated by two motors, i.e., one for opening/closingof the fingers and one for orienting the fingers. In aspecific application, the robotic hand is a passive tooland the actuation is provided by the socket torqueof an ORU Tool Change Out Mechanism (OTCM).

1 Introduction

Complex tasks involving the grasping of various ob-jects in an unstructured environment are still beingperformed by human operators, even in hostile envi-ronments. One of the main obstacles to the teleoper-ation or automation of these tasks has been the lackof versatile grasping tools, i.e., of robotic hands. Inspace applications and in many other applications,the manipulation of objects with very complex me-chanical hands [1] [2] or human hands is often notessential and grasping devices are sufficient. How-ever, simple grippers [3] are not appropriate in mostcases because they are not capable of adapting to theshape of different objects. Hence, the development of

versatile robotic hands which are capable of graspinga wide variety of objects with a very simple controlstructure is of great interest for many applications,including the use of robotic devices in space. Thesehands are obtained with the help of underactuation.

2 Selfadaptation from under-

actuation

An underactuated mechanism is one which has feweractuators than degrees of freedom (dofs). When ap-plied to mechanical fingers, the concept of underac-tuation leads to selfadaptability. Selfadaptive fingerswill envelope the objects to be grasped and automati-cally adapt to their shape with only one actuator andwithout complex control strategies. In order to ob-tain a statically determined system, elastic elementsand mechanical limits must be introduced in under-actuated mechanisms. While a finger is closing onan object, the configuration of the finger at any timeis determined by the external constraints associatedwith the object. When the object is fully grasped,the force applied at the actuator is distributed amongthe phalanges.

A closing sequence of an underactuated two-doffinger is shown in Figure 1 in order to clearly illus-trate the concept of underactuation. The finger isactuated through the lower link, as shown by the ar-row in the figure. Since there are two dofs and oneactuator, one (two minus one) elastic element mustbe used. In the present example, an extension springis used which tends to maintain the finger fully ex-tended. A mechanical limit is used to keep the pha-langes aligned under the action of this spring whenno external forces are applied on the phalanges. Itshould be noted that the sequence occurs with a con-tinuous motion of the actuator. In a), the finger isin its initial configuration and no external forces arepresent. The finger behaves as a single rigid body inrotation about a fixed pivot. In b), the proximal pha-lanx makes contact with the object. In c), the secondphalanx is moving with respect to the first one and

the finger is closing on the object since the proximalphalanx is constrained by the object. During thisphase, the actuator has to produce the force whichis required to extend the spring. Finally, in d), bothphalanges are in contact with the object and the fin-ger has completed the shape adaptation phase. Theforces applied at the actuator are distributed amongthe phalanges.

b dca

Figure 1: Closing sequence of an underactuated two-dof finger.

A few underactuated fingers have been proposed inthe literature. Some of them are based on linkageswhile others are based on tendon-actuated mecha-nisms. Examples of underactuated hands based ontendons are given in [4], [5] and [6]. Tendon sys-tems are generally limited to rather small graspingforces and they lead to friction and elasticity. Hence,for applications in which large grasping forces areexpected, linkage mechanisms are usually preferredand the present work is limited to the study of thelatter mechanisms. One of the only studies on thestatics of underactuated grippers is presented in [7].In the latter reference, the static analysis of a sys-tem composed of two fingers, each having two dofs,is performed and some results are given to presentthe advantages of underactuated fingers over a sim-ple parallel gripper. In [8], an underactuated handwith three fingers is presented. Each of the fingers isbased on a two-dof mechanism having two phalangesand one actuator. Additionally, a special mechanismis introduced in order to allow the distal phalangesto be maintained orthogonal to the palm when preci-sion grasps are performed. In [9], a mechanical handresembling the human hand is presented. Each ofthe fingers is composed of three phalanges but hasonly two dofs since the motion of the last phalanxis directly coupled to the motion of the second pha-lanx. Another type of underactuation can also befound in the literature [10] [11]. It consists in usingbrakes or clutches in order to sequentially drive thedifferent dofs with a single actuator. Such systemsare different from the underactuated mechanisms de-scribed above in behaviour and implementation. Fi-

nally, it should be clearly understood that robotic orprosthetic hands in which the motion of the fingersis mechanically coupled [12] are not underactuated.Indeed, they are designed to mimic the motion of hu-man fingers but the relative motion of the phalangesis determined at the design stage and therefore noshape adaptation is possible.

3 Three-dof underactuated fin-

ger

As presented in the literature review, the existingunderactuated fingers based on linkages have twophalanges or three coupled phalanges with two dofs.However, it is desirable to design an underactuatedfinger with three phalanges and three dofs since itleads to more stable grasps and more efficient shapeadaptation. The result is a behaviour similar to thatof human fingers. This finger mechanism has beenintroduced in [13] and is illustrated in Figure 2. Inorder to obtain a three-dof finger with three pha-langes, a four-bar mechanism is added to the five-bar mechanism of a two-dof finger. It is important

Fk

jF

Fl

F

xF

y

Fmotor

b2

c 2

b1

a2

ψ2

2β ψ

1α

1

k

l

j

α2

c 1

a1

β1

Figure 2: Three-dof shape adaptation mechanism inan average configuration.

to notice that the behaviour of the finger is deter-mined by its geometry, dimensioned at the designstage, since the different dofs cannot be controlledindependently. Hence, the choice of the design pa-rameters is a crucial issue in order to obtain stablegrasps and a proper distribution of the forces amongthe fingers.

The different parameters involved in the design, il-lustrated in Figure 2, are now discussed. The lengthof the phalanges, i.e., l, k, j are fixed from compar-

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ison with other existing fingers and experimentationwith a finger model on objects to be grasped. Theremaining design variables are ai, bi, ci and ψi. In or-der to introduce design constraints and to reduce thenumber of independant variables, some relationshipsbetween these parameters are imposed, reducing thenumber of variables to two. In [14], it has been shownthat the behaviour of the fingers is mainly dictatedby the ratios Ri = ai/ci. In order to minimize the‘thickness’ of the finger, the length ci should be assmall as possible but is limited by mechanical inter-ference considerations. Therefore, ci is fixed, andthen ai is fixed for a given ratio. The performanceof the finger regarding the stability of behaviour, themechanical interferences and the internal forces iscorrect if the transmission angle is close to 90 de-grees when the finger is in an average configuration,as illustrated in Figure 2. The parameters bi andψi can be computed from this criterion. First, theaverage configuration of the finger is defined as theconfiguration in which angles α1 and α2 are given by

αi =αi,min + αi,max

2, i = 1, 2 (1)

where αi,min is the minimum value of angle αi andαi,max is its maximum value. Then, the average an-gles β1 and β2, as defined in Figure 2, are given by

β1 = arcsin

(

a1 − c1l

)

, β2 = arcsin

(

a2 − c2k

)

(2)

which leads to values of bi given by

b1 = l cosβ1, b2 = k cosβ2 (3)

and to the values of ψi given by

ψ1 = π − α1 + β2 − β1, ψ2 =3π

2− α2 − β2 (4)

Using the above equations as design constraints, theparameters can be computed as functions of the ra-tios R1 and R2.

A study is performed on fingers with different com-binations of ratios Ri, giving an overview of possiblefingers. To perform the study, a series of grasps areperformed on circular objects of different sizes andat different positions, in order to simulate differentsizes and shapes of objects, using a simulation toolpresented in [14]. The main criteria used to estimatethe performance of the fingers are:

a) The sum of the forces applied by each fingeron the object must be directed towards the palm(Fy) and the opposite finger (Fx) in order to obtaina stable grasp. Also, the forces Fx should be largerthan the forces Fy in order to obtain balanced grasps,

since the forces Fy work in cooperation (towards thepalm) and the forces Fx work in opposition (againsteach other). That is, Fx = EFy , where the valueof E depends on the type of grasp and is generallyapproximately equal to 2. The performance indexassociated with the resulting forces is given by thesum of the smallest force for each of the m objectsgrasped.

Ixy =

∑m

i=1 min(Fx,i, EFy,i)

m(5)

b) The forces should be well distributed amongthe phalanges in order to avoid large local forces onthe object. The corresponding index is defined asthe ratio of the total force on the three phalangesdivided by the largest force.

Ilkj =

∑m

i=1Fl,i+Fk,i+Fj,i

max(Fl,i,Fk,i,Fj,i)

m(6)

c) An equilibrium point should exist on the lastphalanx in all configurations in order to ensure fea-sible grasps. The equilibrium point is defined as thepoint of contact on a phalanx which leads to staticequilibrium, for a given configuration, when no con-tact occurs at the preceding phalanx (see [14] for de-tails). If the equilibrium point is not located on thelast physical phalanx, then the grasp is not possi-ble and the object will be ejected. If the equilib-rium point is on the last physical phalanx, the indexIep = 1; if it is not, the index Iep = 0.

d) The finger mechanism should be as compactas possible. If the finger is sufficiently compact, theindex Ic = 1. Otherwise, the index is between 0 and1.

The performance indices are combined in order toobtain a global index IG = I2

xyIlkjIepIc for each ofthe fingers. The index Ixy is squared since it is a moreimportant criterion. A graph of IG as a function ofR1 and R2 is presented in Figure 3. An effectivefinger can then be chosen among the best values ofIG. For example, R1 = 2 and R2 = 2.5.

3.1 Parallel precision grasp mecha-

nism

Underactuated fingers cannot perform precisiongrasps while maintaining the distal phalanges paral-lel to each other, for objects of different sizes. How-ever, this feature allows more stable grasps when onlythe tips of the fingers are used and is very often fea-sible with simple grippers. A mechanism has beenproposed in order to achieve this behaviour for a two-dof underactuated finger [8]. A mechanism achiev-ing a similar behaviour with the third phalanx of a

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1.41.6

1.82

2.22.4

2.62.8

1.8

2

2.2

2.4

2.6

2.8

3

0

0.5

1

R1

R2

I G

Figure 3: Global performance index.

three-dof underactuated finger has been developedhere [13] and is shown in Figure 4. It is composed oftwo parallelograms mounted in series. This mecha-nism is coupled to the phalanges of the finger but notto the other links of the shape adaptation mechanism(it is moving on a parallel plane). Two mechanicallimits with springs at the top and bottom ends of themechanism allow precision grasps to be performedand the adaptation to power grasps if necessary. Thisis illustrated in Figure 4. In configurations (a), fromdashed lines to full lines, a parallel motion of thedistal phalanx is accomplished, by maintaining theparallelogram mechanism on its mechanical limits.In (b), a power grasp is performed, with contacts onall phalanges. In this case, the parallelogram mech-anism is moved away from its mechanical limits andthe distal phalanx is no longer maintained parallel.

(a) (b)

Figure 4: The parallel precision grasp mechanism(dark lines). (a) parallel precision grasps. (b) powergrasp.

4 Underactuation among fin-

gers

In addition to underactuation in fingers, it is possibleto include underactuation among fingers. The prin-ciple of underactuation among fingers has been usedin the literature for the actuation of a few coupled-motion fingers [15] [16], each mechanism adding onedegree of underactuation. In the present hand, aone-input/three-output differential is used, addingtwo degrees of underactuation. Therefore, if somefingers are blocked, the remaining fingers will con-tinue to close until they properly grasp the object.The force is fully applied only when all the fingershave properly made contact with the object. Thesystem is illustrated in figure 5. The differential is

Figure 5: One-input/three-output differential andtransmission screws.

composed of two planetary gear trains. The firstplanetary gear train has the carrier as input and thesun gear and internal gear as outputs. The secondplanetary gear train has the internal gear of the firstplanetary gear train as input and the sun gear andinternal gear as outputs. Therefore, the three gen-eral outputs are the sun gear of the first planetarygear train, the sun gear of the second planetary geartrain and the internal gear of the second planetarygear train. In order to obtain proper distribution ofthe power, the three outputs should have the same orclose to the same output torque. This torque distri-

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bution is obtained by a proper selection of the gearratios. The three outputs of the differential are cou-pled to transmission screws through gears. Thesescrews transform the rotational movement in trans-lational movement and allow selflocking of each ofthe fingers for proper stability. The force is trans-mitted to the fingers through an actuation bar. Tosynchronize the closing of the fingers, the fingers areopened until they all reach their maximum openinglimit. When no external force is exerted on the fin-gers, the outputs of the differential stay synchronizedwith the help of internal friction.

5 Reconfiguration

In order to adapt to the general geometry of the ob-ject to be grasped, the hand can be reconfigured bymodifying the orientation of the fingers. Note thatthis feature is widely used in the literature, in severaldifferent versions. In the proposed hand, two of thefingers can be oriented. The orientation of the twofingers is coupled by a geared mechanism, shown infigure 6. The fingers are placed on the vertices ofan equilateral triangle. The required grasping orien-tations of the fingers can be reduced to three maingrasping configurations : cylindrical, spherical andplanar, as illustrated in figure 7. In the cylindricalconfiguration, two fingers point in the same directionwhile the third one points in the opposite directionand moves between the other two. In the sphericalconfiguration, the three fingers are oriented towardsthe center of the triangle. In the planar configura-tion, two fingers are directly facing each other andthe third finger is not used. In the planar configura-tion, where the third finger is not used, its closing isblocked at an output of the differential by a stopperactivated by the orientation mechanism.

6 Robotic grasping hand

The combination of the preceding features leads toa robotic hand with ten dofs and two degrees ofactuation, illustrated in figure 8. One actuator isused to drive the differential which drives the open-ing/closing of each of the three fingers via a trans-mission screw. The second actuator is used to drivethe orientation of the fingers. To the knowledge ofthe authors, the hand includes the combination ofthe underactuation of the phalanges of a finger andthe fingers of a hand for the first time.

Figure 6: The orientation mechanism. The two sec-tions of gear are attached to the two orientable fin-gers. When appropriate, the teeth of the stopper willengage with one of the outputs of the differential.

Cylindrical Spherical Planar

Figure 7: Main configurations of fingers.

Figure 8: CAD model of the hand with motors.

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7 ISS implementation

In a ISS (International Space Station) specific imple-mentation, the hand, called SARAH (Self-AdaptingRobotic Auxilary Hand) is driven and handled byan OTCM (ORU Tool Change Out Mechanism), theend effector placed at the end of the SPDM (Spe-cial Purpose Dextrous Manipulator) arms. There-fore, SARAH is considered as a tool. In this case,the power is provided by the socket torque and ad-vance of the OTCM. The socket advance has onlylimited power and control possibilities, therefore thetwo tasks (open/close and orientation) must be actu-ated by the powerful and controlable socket torque.

7.1 Indexing mechanism

The switching of the power of the socket torque be-tween the two tasks is performed by the socket ad-vance with the help of an indexing mechanism, illus-trated in figure 9. The power of the socket torque istransmitted to the sockets of the differential or ori-entation mechanism through the main shaft. It isfree to rotate and translate in the hole of the bottomplate, and includes nuts at its ends. An indexingring is free to rotate but fixed in translation on themain shaft. Indexing pins are attached to the mi-cro interface and are inserted in the grooves of theindexing ring in order to guide the motion of the in-dexing ring. A compression spring is inserted on themain shaft, between the bottom plate and a shoulderon the main shaft, in order to keep the main shaftbackwards. In this position, no mechanism socketsare engaged. When the OTCM socket pushes on themain shaft, it advances against the spring. This ad-vance is stopped by the indexing pins up to a positionthat engages the main shaft on one of the two mech-anism sockets, depending on the length of the grooveengaged. Then, if the socket torque is activated, thecorresponding mechanism is activated. Each timethe socket of the OTCM is releasead and advanced,the power is switched between the two mechanismsockets.

7.2 Orientation

In order to obtain predefined self-locked configura-tions, the orientation of the fingers is driven via aGeneva mechanism. The input is provided via asocket on the Geneva driver. When the Genevamechanism is in the moving phase, the pin of theGeneva driver is in one of the slots of the Genevawheel. During this phase, the Geneva driver movesthe Geneva wheel by 90 degrees. When the Geneva

Figure 9: The indexing mechanism.

mechanism is in the dwell phase, the Geneva wheelis locked by the locking disk of the Geneva driver.Also, the Geneva driver is free to rotate, allowingplay for easy insertion of the nut of the main shaft inthe socket if they are not properly aligned. Duringthis phase, the fingers are locked in their orientationeven if they are not driven. To restrain the orienta-tion of the fingers in the appropriate range, one ofthe four slots of the Geneva wheel is filled to stopthe rotation of the Geneva mechanism.

8 Prototypes and experimen-

tation

A plastic (P1) and a metal (M1) prototypes ofSARAH have been built. The fingers are 5.5 incheslong and placed on a circle of 3.75 inches diameter.SARAH P1 has been tested manually with a mo-torized screwdriver. Some grasps are illustrated inFigure 10. SARAH M1, illustrated in Figure 11,has been tested with the help of an apparatus de-veloped to emulate the OTCM, named Laval OTCM(LOTCM). In order to measure the forces that areapplied, a force/torque sensor is used. It is placedbetween half cylinders to emulate a cylindrical ob-ject of 3.5 inches of diameter.

The main results of the validation and character-ization of SARAH M1 are summarized here. Thegrasping characteristics of SARAH M1 have beenmeasured in four different configurations coveringthree different grasps, i.e., cylindrical power grasp(opposing fingers and palm-finger opposition), cylin-

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drical precision grasp and planar precision grasp.The grasping force vs input torque relationship ofSARAH M1 has been obtained experimentally forthe previous grasps and is presented in Figure 12.The curves result from the application of linear re-gression on the measured data. The tests show thatSARAH M1 is able to grasp more than 50 lbs in acylindrical power grasp of a 3.5 inches cylinder. Theforce could be larger with a smaller cylinder. Also,the tests show that SARAH M1 is able to grasp morethan 25 lbs in a cylindrical precision grasp and morethan 15 lbs in a planar precision grasp. This is fora socket torque of 60 lb-in. The above results showthe grasping force that can be applied on an object.However, since the fingers of SARAH are self-locking,the external forces that can be resisted by SARAHare higher than the motorized grasping forces. In-deed, external forces of more than 60 lbs were appliedand SARAH M1 resisted properly.

(a) (b)

(c) (d)

Figure 10: Examples of grasps with SARAH P1: (a)Cylindrical power grasp. (b) Cylindrical precisiongrasp. (c) Spherical precision grasp. (d) Planar pre-cision grasp, note that one of the fingers is blockedopen to allow an effective grasp.

Figure 11: The SARAH prototype M1.

0 10 20 30 40 50 600

5

10

15

20

25

30

35

40

45

50

Overview of the grasp types for combined load types

Socket torque (lb−in)

Gra

spin

g fo

rce

(lb)

Cylindrical power, opposing fingers Cylindrical power, palm−finger oppositionCylindrical tip Planar tip

Figure 12: The grasping force vs input torque rela-tionship of SARAH M1.

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9 Conclusion

In this paper, it has been shown that the combina-tion of underactuation into and among fingers canbe used to design a ten-dof hand driven by onlytwo motors. This selfadaptive and reconfigurablehand is covered by a pending patent. The robotichand developed in this project is especially usefulwhere various sizes and shapes of objects are to begrasped, and where simplicity of use and controlis important. In this sense, SARAH is especiallywell suited for the context of the ISS. Addition-ally, its interface is already compatible with theOTCM of the SPDM arms. Although it has greatgrasping flexibility, SARAH is not able to performmanipulation. Therefore, SARAH is intendedto help the astronauts and not to replace them.Experimentation has demonstrated the capabilityof a prototype to grasp various shapes and sizesof objects with sufficient force and appropriatestability. Current work includes the development ofother versions of the hand for industrial use or otherspace applications, as well as the development andcontrol of a hand equiped with tactile sensors.

Acknowledgements The work reported here hasbeen performed under a research grant from NSERCand MDRobotics.

References

[1] S.C. Jacobsen, J.E. Wood, D.F. Knutti, andK.B. Biggers, “The UTAH/M.I.T. DextrousHand: Work in Progress”, The InternationalJournal of Robotics Research, Vol. 3, No. 4,pp. 21–50, 1984.

[2] M.T. Mason, J.K. Salisbury, Robot Handsand the Mechanics of Manipulation, The MITPress, Cambridge, 1985.

[3] F.Y. Chen, “Gripping Mechanisms for Indus-trial Robots: An Overview”, Mechanism andMachine Theory, Vol. 17, No. 5, pp. 299–311,1982.

[4] J.D. Crisman, C. Kanojia and I. Zeid, “Gras-par : A Flexible, Easily Controllable RoboticHand”, IEEE Robotics and Automation Mag-

azine, pp. 32–38, June 1996.

[5] D.F. Graham, “Artificial Hand and DigitTherefor”, US Patent 5200679, 1993.

[6] S. Hirose and Y. Umetani, “The Developmentof Soft Gripper for the Versatile Robot Hand”,

Mechanism and Machine Theory, Vol. 13, pp.351–359, 1978.

[7] H. Shimojima, K. Yamamoto and K.Kawawita, “A Study of Grippers withMultiple Degrees of Mobility”, JSME Interna-tional Journal, Vol. 30, No. 261, pp. 515–522,1987.

[8] S.J. Bartholet, “Reconfigurable End Effector”,US Patent 5108140, 1992.

[9] R.M. Crowder and D.R. Whatley, “RoboticGripping Device Having Linkage ActuatedFinger Sections”, US Patent 4834443, 1989.

[10] N. Ulrich and V. Kumar, “Grasping Using Fin-gers with Coupled Joints”, Proceedings of theASME Mechanisms Conference, Vol. 15-3, pp.201–207, 1988.

[11] S. Lee, “Artificial Dexterous Hand”, US Patent4946380, 1990.

[12] J. Zhang, G. Guo and W.A. Gruver, “Opti-mal Design of a Six-Bar Linkage for an Anthro-pomorphic Three-Jointed Finger Mechanism”,Proceedings of the ASME Mechanisms Confer-ence, Phoenix, vol. DE-45, pp. 299–304, 1992.

[13] C.M. Gosselin and T. Lalib-erte,“Underactuated Mechanical Fingerwith Return Actuation”, US patent 5 762 390,1998.

[14] T. Laliberte and C.M. Gosselin, “Simula-tion and Design of Underactuated MechanicalHands”, Mechanism and Machine Theory, Vol.33, No. 1/2, pp. 39–57, 1998.

[15] M. Rakik, “Multifingered Robot Hand withSelfadaptability”, Robotics and Computer-Integrated Manufacturing, Vol. 5, No. 2-3, pp.269–276, 1989.

[16] G. Guo, X. Qian and W.A. Gruver, “A Single-DOF Multi-Function Prosthetic Hand Mecha-nism With an Automatically Variable SpeedTransmission”, Proceedings of the ASMEMechanisms Conference, Phoenix, vol. DE-45,pp. 149–154, 1992.

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