Research Papers

Realization of an Arbitrary Planar Stiffness With a Simple Symmetric Parallel Mechanism

[+] Author and Article Information
Shuguang Huang1

Joseph M. Schimmels

Department of Mechanical Engineering,  Marquette University, Milwaukee, WI 53201-1881j.schimmels@marquette.edu


Corresponding author.

J. Mechanisms Robotics 3(4), 041006 (Sep 27, 2011) (8 pages) doi:10.1115/1.4004894 History: Received November 22, 2010; Revised June 15, 2011; Published September 27, 2011; Online September 27, 2011

This paper presents a new method for the realization of a planar compliant behavior with an elastic mechanism. The mechanisms considered are parallel with symmetric geometry. We show that any planar stiffness matrix can be realized using a parallel mechanism with four line springs connected symmetrically. Among the four springs, two are identical parallel springs equidistant from the stiffness center, and the other two identical springs intersect at the stiffness center. A synthesis procedure based on geometry is presented and mechanism compactness is discussed.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

Two springs having the same direction but opposite d. They are symmetric about the y-axis.

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Figure 2

A realization of a stiffness based on the stiffness center (a) requires two line springs and one torsional springs (b) requires three line springs.

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Figure 3

A pair of line springs intersecting at one point

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Figure 4

Symmetric elastic mechanism with four line springs. (a) The mechanism is symmetric about the y-axis. (b) The mechanism is symmetric about the x-axis.

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Figure 5

Mechanism compactness. (a) Mechanism synthesized with the procedure. The mechanism is not necessarily compact in size. (b) Compact mechanism with d = s and h = hmin .

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Figure 6

Screw interpretation of the result. A and B are the instantaneous centers associated with twists t1 and t2 , respectively.

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Figure 7

Realization of a planar stiffness with a symmetric mechanism. (a) Mechanism with geometry d = 2, s = 5.34, and θ = 25.91 deg. (b) Mechanism with geometry d = 4, s = 3.07, and θ = 15.61 deg. (c) Compact mechanism with geometry d = s = 2.95 and θ = 18.13 deg.

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Figure 8

L-d curve for different values of h




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