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Research Papers

Structure Decomposition and Homomorphism Identification of Planar Variable Topology Mechanisms

[+] Author and Article Information
Chin-Hsing Kuo

Assistant Professor
Department of Mechanical Engineering,
National Taiwan University of Science and Technology,
43, Sec. 4, Keelung Road,
Taipei 106, Taiwan
e-mail: chkuo717@mail.ntust.edu.tw

Lung-Yu Chang

Department of Mechanical Engineering,
National Taiwan University of Science and Technology,
43, Sec. 4, Keelung Road,
Taipei 106, Taiwan

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received September 16, 2012; final manuscript received October 24, 2013; published online January 3, 2014. Assoc. Editor: Jian S. Dai.

J. Mechanisms Robotics 6(2), 021002 (Jan 03, 2014) (11 pages) Paper No: JMR-12-1144; doi: 10.1115/1.4026336 History: Received September 16, 2012; Revised October 24, 2013

Structural analysis of variable topology mechanisms (VTMs) is the leading task when studying the topological variability of mechanisms. Of several major concerns, structure decomposition and homomorphism identification are two dominating issues for the structural analysis of VTMs. This paper presents a systematic computational approach for the structure decomposition and homomorphism identification of planar VTMs. Along with the proposed method, a constraint matrix representation, that records the potential motion constraints and the topological structures of a VTM, is introduced for serving as the basis of the approach. In addition, a new index, namely, degrees of homomorphism (DOHs), is suggested for quantifying the topological similarity among VTMs. For illustration, an automatic steel clamping and sawing mechanism and a group of mechanisms with similar topologies are adopted, from which their structure decomposition and homomorphism identification are carried out. As shown, the method is both symbolically readable and computationally considerable. The result is helpful for the automated structural analysis and synthesis of variable topology mechanisms.

Copyright © 2014 by ASME
Topics: Topology
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Figures

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Fig. 1

An automatic steel clamping and sawing mechanism

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Fig. 2

Equivalent kinematic chains of the automatic steel clamping and sawing mechanism

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Fig. 3

Example of potential joint constraints

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Fig. 4

Procedure for the structure decomposition of variable topology mechanisms

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Fig. 5

The six digits of a numerical joint code

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Fig. 6

Schematic drawings of the decomposed mechanism

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Fig. 7

Example of spatial VTM with orthrgonal joint axes: A three-axis hozirontal machining center

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Fig. 8

Different topological similarities in two mechanism groups

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Fig. 9

Identification of topological similarity between two mechanisms

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Fig. 11

Two similar slider-crank mechanisms with variable topologies

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Fig. 12

Topological variations of the six-bar mechanism

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Fig. 13

Topological variation of the five-bar mechanism

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Fig. 14

The topology graphs of the mechanism in Fig. 3

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Fig. 15

The topology graph of the mechanism in Fig. 11

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