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RESEARCH PAPERS

Geometric Design of Three-Phalanx Underactuated Fingers

[+] Author and Article Information
Lionel Birglen

Department of Mechanical Engineering, Ecole Plytechnique, Montreal, QC, H3T LI4, Canadabirgleu@polymtl.ca

Clément M. Gosselin

Department of Mechanical Engineering, Laval University, Québec, QC, G1K 7P4, Canada

J. Mech. Des 128(2), 356-364 (Apr 13, 2005) (9 pages) doi:10.1115/1.2159029 History: Received November 03, 2004; Revised April 13, 2005

This paper studies the grasp stability of two classes of three-phalanx underactuated fingers with transmission mechanisms based on either linkages or tendons and pulleys. The concept of underactuation in robotic fingers—with fewer actuators than degrees of freedom—allows the hand to adjust itself to an irregularly shaped object without complex control strategy and sensors. With a n-phalanx finger, n contacts (one for each phalanx) are normally required to statically constrain the finger. However, some contact forces may be lacking due to either the transmission mechanism, or simply the object size and position. Thus, one may define an ith order equilibrium, when the finger is in static equilibrium with i missing contacts. In this paper, the case for which n=3 is studied with a particular emphasis on the cases for which i=1 and i=2. The fact that some contact forces do not appear or are negative, can lead in some cases to the ejection of the object from the hand, when no equilibrium configuration is achieved.

Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Two-phalanx underactuated finger: closing sequence

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Figure 2

(a) Ideal grasping sequence and (b) degenerating into ejection

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Figure 3

Two-phalanx fingers

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Figure 4

Final stability of the grasp with one phalanx contact

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Figure 5

Three-phalanx finger using linkages (springs not indicated for legibility purposes)

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Figure 6

Three-phalanx finger using tendons (springs not indicated for legibility purposes)

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Figure 7

Cases studied for ejection

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Figure 8

Equilibrium configuration with no contact on the distal phalanx

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Figure 9

Grasp-state trajectory and equilibrium surface for initial configuration (θ2i,θ3i,k3i)=(π∕4,π∕4,0.16)—parameter set 2

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Figure 10

Grasp-state trajectory and equilibrium surface for the same initial configuration as Fig. 9—parameter set 1

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Figure 11

Case 3: Example of equilibrium surface with initial configuration (θ2i,θ3i,k2i,k3i)=(10deg,70deg,0.33,0.31)—parameter set 2.

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Figure 12

Case 3: state trajectory with initial configuration (θ2i,θ3i,k2i,k3i)=(10deg,70deg,0.33,0.31)—parameter set 2.

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Figure 13

Equilibrium surfaces with different initial values of k2 (other parameters are unchanged from Fig. 1)

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Figure 14

Case 3 degeneracy analysis

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Figure 15

Case 3 stability regions with respect to design parameters

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