Research Papers

Workspace of Multifingered Hands Using Monte Carlo Method

[+] Author and Article Information
Arkadeep Narayan Chaudhury

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

Ashitava Ghosal

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

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 (1.21.5 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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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

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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.

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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

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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

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Fig. 7

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

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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)

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Fig. 4

Schematic of the parallel manipulator

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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)

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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

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Fig. 10

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

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Fig. 11

Typical velocities encountered during manipulation of grasped object

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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

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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

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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)

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Fig. 15

Scaled plot showing effects of constraints on hand workspace



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