Finding All Solutions to Approximate Synthesis of Planar Linkages for Function Generation, Rigid-Body Guidance and Path Generation

Generally, approximate kinematic synthesis of planar linkage is studied using optimization method. But this method has two defects: i) the initial guesses are hard to determine and ii) the global optimum solution is difficult to find. In this paper, a new method which can find all solutions to approximate kinematic synthesis of planar linkage is proposed. Firstly, we reduce the approximate synthesis problem to finding all solutions to polynomial equations. Polynomial continuation method is then used to find all solutions. Finally, all possible linkages can be obtained. Approximate syntheses of planar four-bar linkage for function generation, rigid-body guidance and path generation are studied in detail and 3 examples are given to illustrate the advantages of the proposed method.