Research Papers

Singularity Analysis of an Extensible Kinematic Architecture: Assur Class N, Order N1

[+] Author and Article Information
David H. Myszka

 University of Dayton, Dayton, OH 45469dmyszka@udayton.edu

Andrew P. Murray

 University of Dayton, Dayton, OH 45469murray@notes.udayton.edu

James P. Schmiedeler

 The Ohio State University, Columbus, OH 43210schmiedeler.2@osu.edu

J. Mechanisms Robotics 1(1), 011009 (Aug 05, 2008) (7 pages) doi:10.1115/1.2960542 History: Received April 15, 2008; Revised June 26, 2008; Published August 05, 2008

This paper presents an analysis to create a general singularity condition for a mechanism that contains a deformable closed contour. This kinematic architecture is particularly relevant to rigid-link, shape-changing mechanisms. Closed contour shape-changing mechanisms will be shown to belong to the Assur classification because of the pattern of interconnections among the links. The general singularity equations are reduced to a condensed form, which allows geometric relationships to be readily detected. The analysis is repeated for alternative input links. A method for formulating the singularity condition for an Assur Class N, knowing the condition for a Class N1 mechanism, is given. This approach is illustrated with several examples.

Copyright © 2008 by American Society of Mechanical Engineers
Topics: Mechanisms , Equations
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Figure 1

Assur kinematic chain that becomes an Assur mechanism

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Figure 2

A singularity configuration of an Assur V/4

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Figure 3

Mechanism with three links in the closed contour

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Figure 4

Assur IV/3 mechanism

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Figure 5

Assur V/4 mechanism

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Figure 6

Assur N∕(N−1) mechanism

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Figure 7

Singularity discussed in Example 1

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Figure 8

Singularity discussed in Example 2

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Figure 9

Singularity discussed in Example 3




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