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Research Papers

Multistable Behaviors of Compliant Sarrus Mechanisms

[+] Author and Article Information
Guimin Chen

e-mail: guimin.chen@gmail.com

Geng Li

Key Laboratory of Electronic Equipment Structure
Design of Ministry of Education,
School of Electro-Mechanical Engineering,
Xidian University,
Xi'an Shaanxi 710071, China

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the Journal of Mechanisms and Robotics. Manuscript received July 14, 2012; final manuscript received December 19, 2012; published online March 26, 2013. Assoc. Editor: Anupam Saxena.

J. Mechanisms Robotics 5(2), 021005 (Mar 26, 2013) (10 pages) Paper No: JMR-12-1100; doi: 10.1115/1.4023557 History: Received July 14, 2012; Revised December 19, 2012

Multistable mechanisms providing spatial motion could be useful in numerous applications; this paper explores the multistable behavior of the overconstrained spatial Sarrus mechanisms with compliant joints (CSMs). The mechanism analysis is simplified by considering it as two submechanisms. The kinetostatics of CSMs have been formulated based on the pseudorigid-body method for compliant members at any combination of joints. The kinetostatic results show that a CSM is capable of exhibiting bistability, tristability, and quadristability. The type of behavior is found to depend on the initial (as-fabricated) position and the relative limit positions of the two submechanisms. Possible applications of multistable CSMs include deployable structures, static balancing of human/robot bodies, and weight compensators.

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Figures

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Fig. 1

A Sarrus mechanism illustrated in its three different positions

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Fig. 2

An example compliant Sarrus mechanism with a wide small-length flexure used for joint 5. The equations in this paper apply to this example and to cases with compliant joints at any combination of joints.

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Fig. 3

Three typical compliant joints of high off-axis stiffness (with respect to the compliant axis): (a) a wide small-length flexure hinge, (b) a cross-type torsion joint, and (c) a cross-spring pivot

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Fig. 4

The pseudorigid-body models of the two slider-crank mechanisms extracted from a compliant Sarrus mechanism: (a) one lies in the XY plane with link a1 as the input link and (b) the other lies in the XZ plane

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Fig. 5

The initial assembled position and the limit positions of points A and B in the two slider-crank mechanisms, respectively

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Fig. 6

The input torque versus θ1 of a bistable Sarrus mechanism (K3≠0)

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Fig. 7

The strain energy curve of a tristable Sarrus mechanism (K3≠0)

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Fig. 8

The three stable configurations of the tristable Sarrus mechanism whose strain energy curve is shown in Fig. 7

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Fig. 9

The input torque versus θ1 of a bistable Sarrus mechanism (K5≠0)

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Fig. 10

The input torque versus θ1 of a tristable Sarrus mechanism (K5≠0)

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Fig. 11

The strain energy curve of a quadristable Sarrus mechanism (K5≠0). The curve starts from θ1=θ10=63.8 deg (the first stable position) and ends at θ1=63.8 deg+360 deg (again the first stable position), thus forming a closed curve.

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Fig. 12

The input torque versus θ1 of a quadristable Sarrus mechanism (K5≠0)

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Fig. 13

A quadristable Sarrus mechanism with its four stable configurations (with both the top and front views being shown)

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Fig. 14

The potential energy versus θ1 of a bistable CSM of Type 2 (K5≠0)

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Fig. 15

The potential energy versus θ1 of a tristable CSM of Type 3 (K5≠0)

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Fig. 16

The potential energy versus θ1 of a quadristable CSM of Type 4

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Fig. 17

The strain energy versus θ1 of a tristable Sarrus mechanism (K3≠0 and K5≠0)

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Fig. 18

The strain energy versus θ1 of the tristable Sarrus mechanism (K3≠0 and K5≠0)

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