Optimal Synthesis of Mechanisms for Path Generation Using Fourier Descriptors and Global Search Methods

[+] Author and Article Information
Irfan Ullah

Department of Mechanical Engineering, NWFP University of Engineering & Technology, Peshawar, Pakistan

Sridhar Kota

Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, Michigan 48109

J. Mech. Des 119(4), 504-510 (Dec 01, 1997) (7 pages) doi:10.1115/1.2826396 History: Received July 01, 1996; Revised July 01, 1997; Online December 11, 2007


Generally, success in synthesis of mechanisms for path generation is limited to finding a reasonable local optima at best in spite of a very good initial guess. The most widely used Structural Error objective function is not effective in leading to practical solutions as it misrepresents the nature of the design problem by requiring the shape, size, orientation and position of the coupler curve to be optimized all at once. In this paper, we present an effective objective function based on Fourier descriptors that evaluates only the shape differences between two curves. This function is first minimized using a stochastic global search method derived from simulated annealing followed by Powell’s method. The size, orientation and position of the desired curve are addressed in a later stage by determining analogous points on the desired and candidate curves. In spite of highly non-linear mechanisms design space, our method discovers near-global and practical solutions consistently without requiring any initial guess.

Copyright © 1997 by The American Society of Mechanical Engineers
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