Social Cognitive Optimization Algorithm for Approximate Path Generation Synthesis of Spherical 4R Linkage

Abstract

Using the coordinate transformation principle，the parametric equation for the trajectory generated is derived by the coupler point of spherical 4R linkage. On this basis，a constrained optimization model is constructed to formulate the approximate synthesis problem of spherical 4R linkage for the path generation without prescribed timing. The model takes the minimizing sum of squares for path errors as the objective function， and the existing crank，length coordination，and transmission angle restriction as the constraints. Combining the self-adaptive penalty function method，this study employs the social cognitive optimization (SCO) algorithm to solve the aforementioned problem. In order to enhance the convergence speed and accuracy of SCO algorithm，a novel accelerating social cognitive optimization (ASCO) algorithm is proposed in which the differential evolution (DE) operators are used to local search. Numerical examples of mechanism synthesis are given，and trajectory analysis results show that the established model and presented ASCO algorithm are feasible and effective. Furthermore，comparative tests on computational performance to address the examples are implemented with SCO，DE，and ASCO algorithm，and the numerical experiments indicate that ASCO outperforms SCO and DE in terms of robustness，convergence speed and accuracy.

Keywords

• Spherical 4R linkage