Bifurcations of SDOF mechanisms using catastrophe theory.pdfVIP

International Journal of Solids and Structures 41 (2004) 559–568 /locate/ijsolstr Bifurcations of SDOF mechanisms using catastrophe theory * Andraas Lengyel, Zhong You Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK Received 30 July 2002; received in revised form 2 June 200 Abstract This paper deals with the singularities which occur on the compatibility paths of single degree of freedom finite mechanisms consisting of rigid bars and pin joints. We first examine the analogy between the bifurcations along the compatibility paths of mechanisms and those appeared in the equilibrium paths of elastic structures. Based on it, we propose that the compatibility conditions can be analysed in the same way as the equilibrium equations using the elementary catastrophe theory. A number of mechanism examples are given to illustrate that common cuspoid catastrophe types also exist in the compatibility paths of mechanisms. 200 3Elsevier Ltd. All rights reserved. Keywords: Catastrophe theory; Catastrophe types; Mechanism with one degree-of-freedom; Compatibility path; Bifurcation 1. Introduction Some of the modern structural systems are in fact mechanisms. They contain internal mobility so that their shape or geometry can be controlled to suit particular needs. Many large space deployable structures belong to this category because they need to be folded up for transportation and expanded when reaching orbit. A very important part of research into such structures involves design of the internal degree o