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Research Papers

# Workspace of Multifingered Hands Using Monte Carlo Method

[+] Author and Article Information

Department of Mechanical Engineering,
Indian Institute of Science,
Bangalore 560 012, India

Ashitava Ghosal

Professor
Department of Mechanical Engineering,
Indian Institute of Science,
Bangalore 560 012, India
e-mail: asitava@iisc.ac.in

1Corresponding author.

Manuscript received July 25, 2017; final manuscript received December 22, 2017; published online April 13, 2018. Assoc. Editor: Damien Chablat.

J. Mechanisms Robotics 10(4), 041003 (Apr 13, 2018) (12 pages) Paper No: JMR-17-1221; doi: 10.1115/1.4039001 History: Received July 25, 2017; Revised December 22, 2017

## Abstract

Multifingered hands have the capability of dexterous manipulation of grasped objects and thus significantly increase the capabilities of a robot equipped with multifingered hands. Inspired by a multijointed human finger and the hand, we propose a six degree-of-freedom (DOF) model of a three-fingered robotic hand as a parallel manipulator. Two kinds of contact, namely point contact with friction and rolling without slipping between the fingertips and the grasped object, are considered. The point contact with friction is modeled as a three DOF spherical joint, and for rolling without slipping, we use the resultant nonholonomic constraints between the grasped object and the fingers. With realistic limits on the joints in the fingers and dimensions of finger segments, we obtain the well-conditioned manipulation workspace of the parallel manipulator using a Monte Carlo-based method. Additionally, we present two new general results—it is shown that maximum position and orientation workspace is obtained when the cross-sectional area of the grasped object is approximately equal to the area of the palm of the hand and when rolling without slipping is ensured the size of the well-conditioned workspace is significantly larger ($∼1.2–1.5$ times). We also present representative experiments of manipulation by a human hand and show that the experimental results are in reasonable agreement with those obtained from simulations.

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## References

Ritter, H. , and Haschke, R. , 2014, “ Hands, Dexterity, and the Brain,” Humanoid Robotics and Neuroscience: Science, Engineering and Society, CRC Press, Boca Raton, FL, pp. 49–77.
Balasubramanian, R. , and Santos, V. J. , 2014, The Human Hand as an Inspiration for Robot Hand Development, Vol. 95, Springer, Cham, Switzerland.
Okamura, A. M. , Smaby, N. , and Cutkosky, M. R. , “ An Overview of Dexterous Manipulation,” IEEE International Conference on Robotics and Automation (ICRA), San Francisco, CA, Apr. 24–28, pp. 255–262.
Hanafusa, H. , and Asada, H. , 1977, “ A Robot Hand With Elastic Fingers and Its Application to Assembly Process,” IFAC Symposium on Information Control Problems in Manufacturing Technology, Tokyo, Japan, Oct. 17–20, pp. 127–134.
Salisbury, J. K. , and Craig, J. J. , 1982, “ Articulated Hands: Force Control and Kinematic Issues,” Int. J. Rob. Res., 1(1), pp. 4–17.
Jacobsen, S. , Iversen, E. , Knutti, D. , Johnson, R. , and Biggers, K. , 1986, “ Design of the Utah/MIT Dextrous Hand,” IEEE International Conference on Robotics and Automation (ICRA), San Francisco, CA, Apr. 7–10, pp. 1520–1532.
Murray, R. M. , and Sastry, S. S. , 1989, “ Control Experiments in Planar Manipulation and Grasping,” IEEE International Conference on Robotics and Automation (ICRA), Scottsdale, AZ, May 14–19, pp. 624–629.
Butterfaß, J. , Grebenstein, M. , Liu, H. , and Hirzinger, G. , 2001, “ DLR-Hand II: Next Generation of a Dextrous Robot Hand,” IEEE International Conference on Robotics and Automation (ICRA), Seoul, South Korea, May 21–26, pp. 109–114.
Deimel, R. , and Brock, O. , 2016, “ A Novel Type of Compliant and Underactuated Robotic Hand for Dexterous Grasping,” Int. J. Rob. Res., 35(1–3), pp. 161–185.
Deshpande, A. D. , and Matsuoka, Y. , 2014, “ Development of an Anatomically Correct Testbed (ACT) Hand,” The Human Hand as an Inspiration for Robot Hand Development, Springer, Cham, Switzerland, pp. 453–475.
Lin, J. , Wu, Y. , and Huang, T. S. , 2000, “ Modeling the Constraints of Human Hand Motion,” IEEE Workshop on Human Motion, Los Alamitos, CA, Dec. 7–8, pp. 121–126.
Dizioğlu, B. , and Lakshiminarayana, K. , 1984, “ Mechanics of Form Closure,” Acta Mech., 52(1), pp. 107–118.
Nguyen, V.-D. , 1987, “ Constructing Stable Grasps in 3D,” IEEE International Conference on Robotics and Automation (ICRA), Raleigh, NC, Mar. 31–Apr. 3, pp. 234–239.
Montana, D. J. , 1988, “ The Kinematics of Contact and Grasp,” Int. J. Rob. Res., 7(3), pp. 17–32.
Cai, C. S. , and Roth, B. , 1986, “ On the Planar Motion of Rigid Bodies With Point Contact,” Mech. Mach. Theory, 21(6), pp. 453–466.
Kerr, J. , and Roth, B. , 1986, “ Analysis of Multifingered Hands,” Int. J. Rob. Res., 4(4), pp. 3–17.
Borràs, J. , and Dollar, A. M. , 2015, “ Dimensional Synthesis of Three-Fingered Robot Hands for Maximal Precision Manipulation Workspace,” Int. J. Rob. Res., 34(14), pp. 1731–1746.
Cobos, S. , Ferre, M. , Uran, M. S. , Ortego, J. , and Pena, C. , 2008, “ Efficient Human Hand Kinematics for Manipulation Tasks,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2008), Nice, France, Sept. 22–26, pp. 2246–2251.
Dunn, W. L. , and Shultis, J. K. , 2011, Exploring Monte Carlo Methods, Elsevier, Amsterdam, The Netherlands. [PubMed] [PubMed]
Stamper, R. E. , Tsai, L.-W. , and Walsh, G. C. , 1997, “ Optimization of a Three DOF Translational Platform for Well-Conditioned Workspace,” IEEE International Conference on Robotics and Automation (ICRA), Albuquerque, NM, Apr. 20–25, pp. 3250–3255.
Chaudhury, A. N. , and Ghosal, A. , 2017, “ Optimum Design of Multi-Degree-of-Freedom Closed-Loop Mechanisms and Parallel Manipulators for a Prescribed Workspace Using Monte Carlo Method,” Mech. Mach. Theory, 118, pp. 115–138.
Fishman, G. , 2013, Monte Carlo: Concepts, Algorithms, and Applications, Springer Science & Business Media, New York.
Selig, J. M. , 2004, Geometric Fundamentals of Robotics, Springer Science & Business Media, New York.
Edelsbrunner, H. , and Mücke, E. P. , 1994, “ Three-Dimensional Alpha Shapes,” ACM Trans. Graph., 13(1), pp. 43–72.
Lee, D.-T. , and Schachter, B. J. , 1980, “ Two Algorithms for Constructing a Delaunay Triangulation,” Int. J. Comput. Inf. Sci., 9(3), pp. 219–242.
Artec3D, 2018, “Artec Eva Scanner,” Artec Europe, Luxembourg, UK, accessed Mar. 15, 2017,
Nakamura, M. , Miyawaki, C. , Matsushita, N. , Yagi, R. , and Handa, Y. , 1998, “ Analysis of Voluntary Finger Movements During Hand Tasks by a Motion Analyzer,” J. Electromyography Kinesiology, 8(5), pp. 295–303.
Chaudhury, A. N. , and Ghosal, A. , 2017, “ Determination of Workspace Volume of Parallel Manipulators Using Monte Carlo Method,” Computational Kinematics, Springer, Cham, Switzerland, pp. 323–330.
Degeorges, R. , and Oberlin, C. , 2003, “ Measurement of Three-Joint-Finger Motions: Reality or Fancy? A Three-Dimensional Anatomical Approach,” Surg. Radiol. Anat., 25(2), pp. 105–112. [PubMed]
Degeorges, R. , Laporte, S. , Pessis, E. , Mitton, D. , Goubier, J.-N. , and Lavaste, F. , 2004, “ Rotations of Three-Joint Fingers: A Radiological Study,” Surg. Radiol. Anat., 26(5), pp. 392–398. [PubMed]
Autodesk, 2013, “Autodesk-Netfabb Version 7.4.0 532(2013),” Autodesk, Mill Valley, CA.
Cole, A. B. , Hauser, J. E. , and Sastry, S. S. , 1989, “ Kinematics and Control of Multifingered Hands With Rolling Contact,” IEEE Trans. Autom. Control, 34(4), pp. 398–404.
Murray, R. M. , Li, Z. , and Sastry, S. S. , 1994, A Mathematical Introduction to Robotic Manipulation, CRC Press, Boca Raton, FL.
Ghosal, A. , 2006, Robotics: Fundamental Concepts and Analysis, Oxford University Press, New Delhi.
Ghosal, A. , and Ravani, B. , 2001, “ A Differential-Geometric Analysis of Singularities of Point Trajectories of Serial and Parallel Manipulators,” ASME J. Mech. Des., 123(1), pp. 80–89.
Bardinet, E. , Ayache, N. , and Cohen, L. , 1994, “ Fitting of Iso-Surfaces Using Super-Quadrics and Free-Form Deformations,” IEEE Workshop on Biomedical Image Analysis (BIA), Seattle, WA, June 24–25, pp. 184–193.
Solina, F. , and Bajcsy, R. , 1990, “ Recovery of Parametric Models From Range Images: The Case for Super-Quadrics With Global Deformations,” IEEE Trans. Pattern Anal. Mach. Intell., 12(2), pp. 131–147.
Menon, M. S. , Ravi, V. , and Ghosal, A. , 2017, “ Trajectory Planning and Obstacle Avoidance for Hyper-Redundant Serial Robots,” ASME J. Mech. Rob., 9(4), p. 041010.
Barr, A. H. , 1992, “Rigid Physically Based Super-Quadrics,” Graphics Gems III (IBM Version), D. Kirk, ed., Academic Press, San Diego, CA, pp. 137–159.
Taubin, G. , 1993, “ An Improved Algorithm for Algebraic Curve and Surface Fitting,” IEEE Fourth International Conference on Computer Vision (ICCV), Berlin, May 11–14, pp. 658–665.
Boyd, S. , and Vandenberghe, L. , 2004, Convex Optimization, Cambridge University Press, New York.
Agarwal, S. , Srivatsan, R. A. , and Bandyopadhyay, S. , 2016, “ Analytical Determination of the Proximity of Two Right-Circular Cylinders in Space,” ASME J. Mech. Rob., 8(4), p. 041010.
Moore, M. , and Wilhelms, J. , 1988, “ Collision Detection and Response for Computer Animation,” ACM Siggraph Computer Graphics, Vol. 22, ACM, New York, pp. 289–298.
Wellmann, C. , Lillie, C. , and Wriggers, P. , 2008, “ A Contact Detection Algorithm for Super-Ellipsoids Based on the Common-Normal Concept,” Eng. Comput., 25(5), pp. 432–442.
Howe, R. D. , Kao, I. , and Cutkosky, M. R. , 1988, “ The Sliding of Robot Fingers Under Combined Torsion and Shear Loading,” IEEE International Conference on Robotics and Automation (ICRA), Philadelphia, PA, Apr. 24–29, pp. 103–105.
MathWorks, 2015, “MATLAB Version 8.5.0.197613 (R2015a),” The MathWorks Inc., Natick, MA.
Polhemus-Liberty, 2018, “Polhemus-Liberty Wired Electromagnetic Position and Orientation Tracker,” Polhemus-Liberty, Colchester, VT, accessed Apr. 22, 2017,
Tracey, B. H. , and Miller, E. L. , 2012, “ Nonlocal Means Denoising of ECG Signals,” IEEE Trans. Biomed. Eng., 59(9), pp. 2383–2386. [PubMed]
White, R. M. , 1980, “Comparative Anthropometry of the Hand,” DTIC Document, Natick, MA, Technical Report No. NATICK/TR-81/010.
Manning, J. T. , 2012, “ Sex Differences and Age Changes in Digit Ratios: Implications for the Use of Digit Ratios in Medicine and Biology,” Handbook of Anthropometry, Springer, New York, pp. 841–851.
Arora, J. , 2004, Introduction to Optimum Design, Academic Press, San Diego, CA, pp. 154–157.

## Figures

Fig. 1

Anatomical and schematic representation of the human hand: (a) a three-dimensional (3D) scanned model of the and (b) anatomy of human hand3

Fig. 2

Super-ellipsoid approximations of human fingertips. The approximations for the female subject are better due to the higher resolution of the available 3D scan. (a) Super-ellipsoid approximation of a male subject's fingertips and (b) super-ellipsoid approximation of a female subject's fingertips.

Fig. 3

Spherical joint approximation of the fingertips with object: (a) schematic of the spherical joint and (b) interaction of the finger with the object

Fig. 4

Schematic of the parallel manipulator

Fig. 5

Representation of two cases of interaction between super-ellipsoids and their intersection volumes: (a) impossible intersection of two super-ellipsoids, (b) representation of the intersection volume of Fig. 5(a), (c) possible intersection of two super-ellipsoids, and (d) representation of the intersection volume of Fig. 5(c)

Fig. 6

Description of two bodies in contact and permissible contact zone on fingertip: (a) contact between the finger and the object and (b) allowable contact zone on the index finger

Fig. 7

Flowchart of the proposed algorithm to obtain workspace. [θl,θh] is the permissible range for the spherical joints.

Fig. 8

Dexterous manipulation using a three-fingered grasp: (a) human hand manipulating a ball and (b) snapshot of the computer simulation of the scenario in Fig. 8(a)

Fig. 9

Location of sensors on the hand and a known ill conditioned pose: (a) location of sensors in the experiment and (b) frequently encountered ill-conditioned pose

Fig. 10

Experimental results on human hand workspaces: (a) comparison of the theoretically and experimentally obtained workspaces and (b) orientations achieved in experiments

Fig. 11

Typical velocities encountered during manipulation of grasped object

Fig. 12

Convergence of the algorithm and variation of WR/WS with change in object size: (a) convergence of the algorithm across four different trials and (b) WR/WS with change in object size

Fig. 13

Workspaces of hand described in Tables 1 and 2 manipulating a ball of radius 17.5 mm: (a) possible positional workspace and (b) possible orientation workspace

Fig. 14

Comparison of workspaces of hand considering two different models of contact across different hands: (a) rolling workspace, (b) S-joint workspace, and (c) independence of the result in Table 4 to choice of condition number in Eq. (17)

Fig. 15

Scaled plot showing effects of constraints on hand workspace

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