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Research Papers

Structural Synthesis of Serial-Parallel Hybrid Mechanisms Based on Representation and Operation of Logical Matrix

[+] Author and Article Information
Qiang Zeng

Robotics Research Laboratory, School of Mechanical and Electrical Control Engineering, Beijing Jiaotong University, Beijing 100044, P.R.C.07116302@bjtu.edu.cn

Yuefa Fang

Robotics Research Laboratory, School of Mechanical and Electrical Control Engineering, Beijing Jiaotong University, Beijing 100044, P.R.C.yffang@bjtu.edu.cn

J. Mechanisms Robotics 1(4), 041003 (Sep 17, 2009) (10 pages) doi:10.1115/1.3204253 History: Received August 23, 2008; Revised June 13, 2009; Published September 17, 2009

This paper presents a systematic approach on structural synthesis of serial-parallel hybrid mechanisms from the point of displacement group theory and mathematical logic. The hybrid mechanisms can be represented by binary 12 bit string matrix, where the lower 4 bits represents the universal set of spatial displacement subsets, while the higher 8 bits represents the two-order adjacent relations of spatial displacement subsets. Meanwhile, the concept of an arrangement matrix and three types of fractal operations can be developed. Utilizing the novel representational approach of mechanisms, the displacement subsets and spatial adjacent relations can be operated in logical matrices based on the given mapping of logical matrix operation. The binary logical mirror coordinate system of mechanisms is developed by logical representations. Finally, an example of structural synthesis of hybrid mechanism (two-order hybrid mechanism) is introduced using the proposed approach. The approach is helpful for the processing of serial-parallel hybrid mechanism designs.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Examples of combinations of the three types of fractal arrangement

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Figure 2

4 bit representation of displacement subsets

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Figure 3

Two-order adjacent relations

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Figure 4

4 bit representation of relative relations

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Figure 5

PRRP and 3−RP̱S

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Figure 6

3−ṞRR/3−ṞRR

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Figure 7

Logical status of displacement subsets and adjacent relations in four-dimensional mirror coordinates

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Figure 8

Graphic representation of kinematical chain PCR in four-dimensional mirror coordinates

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Figure 9

Representation and simplification of combined chain G1 and G2 in four-dimensional mirror coordinates

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Figure 10

Mirror coordinates and mechanical structure of 3−GG

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Figure 11

Procedure of structural synthesis of serial-parallel hybrid mechanisms

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Figure 12

Displacement subsets and adjacent relations of hybrid mechanism with 3DOF

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Figure 13

Hybrid mechanical structure with spatial translation of 3DOF

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