Decomposition of planar burmester problems using kinematic mapping

In this paper, we revisit the classical Burmester problem of the exact synthesis of a planar four-bar mechanism with up to five task positions. Instead of assuming the joint type (revolute or prismatic) a priori, we seek to extract both the dimensions and joint types of a four-bar linkage from the given tasks. Kinematic mapping of plane kinematics has been used to formulate the Burmester problem as a manifold fitting problem in the image space. Instead of finding the design parameters of planar dyads directly, this paper seeks to determine a set of eight homogeneous coefficients for the constraint manifold in the null space associated with the five given tasks. Two additional constraints on these coefficients are then applied to finalize the synthesis process. The result is a novel algorithm that is simple and efficient and allows for task driven design of four-bar linkages with revolute and prismatic joints.