Exact Solutions of the Mixed Motion and Path Synthesis Problem for Four-Bar Linkages

An algebraic method is proposed in this work to find multiple exact solutions to the mixed motion and path synthesis problem. A system of synthesis equations is established based on Burmester theory, which is further simplified, leading to two binary quadratic equations, which are utilized for finding multiple solutions by a semigraphic searching technique. In solution searching, the orientation angle of the coupler link is utilized to generate a curve of synthesis errors, from which the real solutions are found from the points of minimum errors. Multiple exact solutions are thus found robustly and exactly. Three examples, including an actual design case, are provided to demonstrate the development method.