A novel objective function for path generation synthesis of the four-bar mechanism with prescribed timing

Dimensional Design of four-bar mechanisms, as the simplest and most widely used linkage, is always one of the main issues raised in the field of mechanism design. In the past, geometric and graphical analysis methods were used to design these mechanisms, but with the advancement of technology, numerical optimization methods, and meta-heuristic algorithms, it is possible to solve problems more precisely and consider a higher number of precision points. The path generation synthesis problem of this mechanism has been solved using different algorithms and in different design modes, including with and without prescribed timing, which the synthesis problem with prescribed timing is more difficult and has a higher path generation error. In this research, to solve the synthesis problem of four-bar mechanism path generation with prescribed timing, a novel objective function is utilized, which includes two terms, path error and angle error. This new objective function leads to a lower error for path generation with prescribed timing. Four different designs are considered and their results, where extracted by the PSO algorithm, are compared. The results of solving this problem for three numerical examples show that the design in the fourth state, which uses the new objective function, has fewer path generation errors.