The Application of General Homotopy Method on Planar Four-Bar Path Synthesis

Homotopy method is a numerical continuation method that can locate all the zeros of any given function without the specifying of initial estimates. With the assistance of proper programming technique, homotopy method can be efficient and reliable. The application of homotopy method on kinematic synthesis can resolve the inherent shortcomings that most numerical methods possess. This work presents a demonstration of homotopy method on the path synthesis of planar four-bar mechanisms. The example of nine point-path synthesis is provided. The results of all real solutions are tabulated and the corresponding mechanisms are graphically displayed so comparisons can be made with past publications. Keywords-homotopy method; four-bar mechanisms; pointpath synthesis