Robotica
- Robotica / Volume 30 / Issue 04 / July 2012, pp 599-612
- Copyright © Cambridge University Press 2011
- DOI: http://dx.doi.org/10.1017/S0263574711000865 (About DOI), Published online: 26 July 2011
Articles
Algorithm for topological design of multi-loop hybrid mechanisms via logical proposition
Qiang Zenga1 c1 and Yuefa Fanga1
a1 Robotics Research Lab., School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, 100044, PR China
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.
(Accepted June 25 2011)
(Online publication July 26 2011)
KEYWORDS:
- Logical proposition;
- Logical matrix;
- Topological design;
- Multi-loop kinematic chains;
- Hybrid mechanisms
Correspondence:
c1 Corresponding author. E-mail: 07116302@bjtu.edu.cn
