Optimization of scale-rotation-translation synthesis after shape synthesis for path generation of planar mechanisms

Abstract

Two-phase synthesis methods for path generation have been proposed in the literature. The first is shape synthesis and the second may be termed scale-rotation-translation synthesis. The second synthesis approaches discussed in the literature using geometric-based approaches, including the properties of a curve or mean distance and orientation of radial lines are feasible. In this study, the method of determination of analogous points after shape optimization discussed in the literature is rebuilt. Moreover, an objective and intuitional standard using the mean nearest distance between target points and the corresponding coupler points is proposed to estimate the accuracy of the second synthesis approaches. To further understand whether the approaches are sufficiently accurate, a scale-rotation-translation synthesis optimization is utilized to find the optimum solution using the mean nearest distance as the objective function, which does not need input angles as design variables. The genetic algorithm–differential evolution (GA-DE) evolutionary algorithm is applied, with the results of the two approaches as initial guesses, to solve the optimum problem. Two representative examples of path generation of four-bar mechanisms are studied. It can be concluded that scale-rotation-translation synthesis optimization should be used to obtain more accurate solutions.

Keywords:

• coupler curve
• two-phase synthesis
• mechanism synthesis
• mechanism optimization

Acknowledgment

This work was supported by the National Science Council of the Republic of China (Taiwan) under the Contract NSC 100-2221-E-237-004.