Optimal Dimensional Synthesis of Linkages Using Exact Jacobian Determination in the SQP Algorithm

This article presents a general method for the dimensional synthesis of mechanisms. This method is based on the well-known Sequential Quadratic-Programming algorithm (SQP). However, several modifications have been introduced in order to improve the robustness and efficiency of the method. One of these modifications in the improved SQP approach is the use of the exact Jacobian instead of the finite differences (FD) methods. The article explains how to obtain the Jacobian for any structural kinematic chain. Furthermore, the method introduces several steps in order to prepare the mechanism for optimization. These steps consist in the translation, rotation, and scaling of the mechanism to be designed. The formulation implemented in the algorithm avoids singular configurations and ensures the assembly of the mechanism providing greater robustness than the conventional approach. In the article, several examples are provided to demonstrate the main characteristics of the method.