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TECHNICAL BRIEF

Identifying and Counting the Number of Mechanisms From Kinematic Chains Subject to Design Constraints

[+] Author and Article Information
Hong-Sen Yan

Department of Mechanical Engineering, National Cheng Kung University No. 1 University Road, Tainan 70101, Taiwan, Republic of Chinahsyan@mail.ncku.edu.tw

Chih-Ching Hung

Department of Mechanical Engineering, National Cheng Kung University No. 1 University Road, Tainan 70101, Taiwan, Republic of China

J. Mech. Des 128(5), 1177-1182 (Dec 12, 2005) (6 pages) doi:10.1115/1.2218887 History: Received March 09, 2005; Revised December 12, 2005

An approach is presented, based on combinatorial theory, for the complete enumeration of nonisomorphic mechanisms precisely from kinematic chains. And, based on the permutation groups, the concept of the generating function, and Polya’s Theory, mathematical expressions are derived for counting the number of the identified mechanisms subject to the design constraints of the adjacent/incident relationship among links, joints, or links and joints. Examples are provided to illustrate the proposed approach. The results of this work can instead of the observation method to inspect the isomorphism for mechanisms; furthermore, all nonisomorphic mechanisms can be obtained exactly and systematically.

FIGURES IN THIS ARTICLE
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Copyright © 2006 by American Society of Mechanical Engineers
Topics: Chain , Design , Mechanisms
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References

Figures

Grahic Jump Location
Figure 1

The Stephenson chain and two relabeled chains

Grahic Jump Location
Figure 2

Stephenson-III mechanisms with one prismatic pair

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Figure 3

Stephenson-III mechanisms with two prismatic pairs

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Figure 4

Eight-bar mechanisms with specified types of links and joints

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