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and
Machine Theory
Mechanism and Machine Theory 43 (2008) 1596–1609
ate/mechmt
Computer-aided structure position theory
of kinematic chains and its applications
Huafeng Ding *, Zhen Huang, Dejun Mu
Robotics Research Center, Yanshan University, Qinhuangdao, Hebei 066004, China
Received 2 November 2006; received in revised form 19 December 2007; accepted 23 December 2007
Available online 14 February 2008
Abstract
Rigid sub-chain detection and isomorphism identification are two of the most difficult problems in puter-aided
structure synthesis of kinematic chains. This paper aims to find an efficient solution which can be fulfilled within -
puter itself to the problem of rigid sub-chain detection of planar kinematic chains, especially plex planar mecha-
nisms. Based on the array representation of the loops of kinematic chains, this paper first introduces two operations of
loops, the ‘‘H” and ‘‘È” operations. Then a new theory of structure position of kinematic chains is proposed on
the basis of the concept of the independent loop set. After that a new method grounded on the theory is proposed for rigid
sub-chain detection. Finally, the optimized algorithm for structure position is presented and the corresponding pro-
gram for rigid sub-chain detection is developed as well.
Ó 2008 Elsevier Ltd. All rights reserved.
Keywords: Kinematic chain; Topological graph; Loop operation; Structure position; Rigid sub-chain detection
1. Introduction
In the process of mechanism creative design, the structure synthesis is the primary and the most important
issue [1,2]. It can not only optimize nearly all kinds of existing mechanisms, but also invent or create novel
mechanisms. However, a key problem in mechanism structural synthesis is automatic synthesizing of kine-
matic chains in a systematical way [3–5]. In the 1960s, to represent the kinematic chain, the topological graph
was introduced whose vertices correspond to links of