Loop theory and applications to some key problems of kinematic structure of kinematic chains

doi:10.1007/s11465-009-0061-6

Front Mech Eng Chin

2009, Vol. 4

Issue (3) : 276-283 https://doi.org/10.1007/s11465-009-0061-6

RESEARCH ARTICLE

Loop theory and applications to some key problems of kinematic structure of kinematic chains

Huafeng DING(

), Zhen HUANG

Robotics Research Center of Yanshan University, Qinhuangdao 066004, China

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Abstract

Structure synthesis of mechanisms is a pivotal issue in the field of mechanical innovation and mechanical conceptual design. In this paper, a new loop theory of kinematic chains is proposed. Based on this theory, some key problems that hamper computer-based automatic synthesis of mechanisms are solved. 1) The open problem of isomorphism of kinematic chains that has lasted for more than four decades is successfully solved. 2) A new rigid sub-chain detection method that is especially suitable for complex chains is proposed. 3) The characteristic representation code remains the same even if the drawing modes and labeling ways of a chain are changed, and an atlas database of kinematic chains is established. The multi-value problem for the representation of kinematic chains is solved. The results in this paper will benefit the digitization and computerization of mechanical conceptual design.

Keywords Loop theory kinematic chains isomorphism atlas database

Corresponding Author(s): DING Huafeng,Email:dhf@ysu.edu.cn

Issue Date: 05 September 2009

Cite this article:

Huafeng DING,Zhen HUANG. Loop theory and applications to some key problems of kinematic structure of kinematic chains[J]. Front Mech Eng Chin, 2009, 4(3): 276-283.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-009-0061-6
https://academic.hep.com.cn/fme/EN/Y2009/V4/I3/276

Fig.1 Kinematic chain and its topological graph

Fig.2 Example 1. (a)12-bar kinematic chain ;(b) 12-bar kinematic chain (c) CPTG of ; (d) CPTG of

Fig.3 Example 2. (a) 15-vertex graph ; (b) 15-vertex graph ; (c) CPTG of ; (d) CPTG of

Fig.4 Example 3. (a) 30-vertex graph ; (b) 30-vertex graph ; (c) their shared CPTGs

Fig.5 Comparison of computational complexity

Fig.6 20-link kinematic chain and its topological graph

Fig.7 CPTG of a l2-link kinematic chain

Fig.8 Interface of the atlas database

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