Synthesis of spherical four-bar mechanisms using spherical kinematic mapping

Abstract

Designing a spherical four-bar mechanism that guides a coupler system through five given orientations is an old and well known problem. Here we use kinematic mapping to solve the problem. We investigate the constraint surface belonging to a spherical RR-chain and solve the problem in the newly defined kinematic design space. The algorithm results in RR-chains which pairwise combined give the synthesized four-bars. It is remarkable that with this method the univariate polynomial can be computed completely general without specifying the parameters of the problem with numerical values. Furthermore for the first time an example with six real RR-chains is given. These can be combined to 30 real four-bars that move the coupler system through the five given precision points.