Kinematic Mapping Application to Approximate Type and Dimension Synthesis of Planar Mechanisms

Kinematic mapping is used for preliminary development of an algorithm for the approximate synthesis of planar four-bar mechanisms for rigid body guidance. Both dyad type and dimensions are determined. Planar mechanism coupler motions are represented as the curves of intersection of a pair of quadric constraint surfaces, one for each of two dyads. The problem reduces to identifying the two best constraint surfaces in the pencil of quadrics containing the curve. The overdetermined synthesis equations are linear in the unknown surface shape coefficients, and their products. Non-trivial solutions exist only in the nullspace of the coefficient matrix. While the algorithm remains incomplete, results presented herein are encouraging.