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Algorithm for topological design of multi-loop hybrid mechanisms via logical proposition

Published online by Cambridge University Press:  26 July 2011

Qiang Zeng  and
Yuefa Fang
Qiang Zeng*
Affiliation:
Robotics Research Lab., School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, 100044, PR China
Yuefa Fang
Affiliation:
Robotics Research Lab., School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, 100044, PR China
*
*Corresponding author. E-mail: [email protected]
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Summary

This paper introduces the mathematical logical proposition into kinematics and presents a novel method for topological design and representation of mechanisms. The six-value non-classical logical matrix in three orders is proposed to represent spatial basic motions, relations, and selection of moving reference frame. The combinatorial logical sets of mechanisms are built and axiomatized to analyze serial–parallel hybrid mechanisms. In accordance to the logical relations, the mapping between topological arrangement and topological geometry is developed, and algorithm of decomposition synthesis is presented. Furthermore, the higher dimensional topological arrangement of multi-loop hybrid mechanism can be obtained by mapping of higher dimensional geometry. At last, four typical examples are developed to illustrate application of method of logical proposition in topological design of mechanisms. The method is helpful for topological design and analysis of multi-loop hybrid mechanisms.

Keywords

Logical propositionLogical matrixTopological designMulti-loop kinematic chainsHybrid mechanisms
Type
Articles
Information
Robotica , Volume 30 , Issue 4 , July 2012 , pp. 599 - 612
Copyright
Copyright © Cambridge University Press 2011

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