Data-driven kinematics: Unifying synthesis of planar four-bar linkages via motion analysis

This paper presents a novel data-driven approach for kinematic synthesis of planar four-bar linkages consisting of revolute (R) or prismatic (P) joints by extracting the geometric constraints of a motion. The approach unifies the often elusive type synthesis problem with dimensional synthesis and for a given motion determines the best combinations of R- and P-joints in a four-bar linkage and their dimensions by analyzing a given motion. The underlying formulation is based on concepts of planar quaternions, kinematic mapping, and data-fitting. By formulating the kinematic constraints of planar four-bar linkages in a unified form and then fitting the constraints with the given motion data in the image space of planar displacements, we obtain the best type and the dimensions of the linkages. The results will be demonstrated via MotionGen, an intuitive iOS and Android app that implements this approach and allows designers to synthesize linkages for the motion generation problem.