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

TLDR

Success in synthesizing mechanisms for path generation is typically limited to local optima, and the widely used Structural Error objective is ineffective because it forces simultaneous optimization of shape, size, orientation, and position. The study introduces a Fourier‑descriptor–based objective function that evaluates only shape differences between curves. The objective is first minimized by a simulated‑annealing–derived stochastic global search followed by Powell’s method, after which size, orientation, and position are adjusted by matching analogous points on the curves. The method consistently finds near‑global, practical solutions across a highly nonlinear design space without requiring an initial guess.

Abstract

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.