Unified kinematics modeling of variable topologies of a 3rTPS metamorphic parallel mechanism

This paper investigates the mobility analysis and forward kinematics of 4 different configurations of 3(rt)PS parallel manipulators in which the moving platform and the base are two arbitrarily chosen platforms. After proposing mathematical model, multivariate polynomials describing the position and orientation of the moving platform are constructed in which the input data are the limb lengths, angels and design parameters. Based on the multivariate polynomials, a code was developed through Matlab Programming language utilizing the symbolic toolbox. It is shown that a maximum number of complete analytic solutions in complex and real domain for any input data is equal to 16. Numerical examples of forward displacement analysis of the 2 different configurations of the 3(rt)PS parallel mechanism are demonstrated to verify the analytic solutions. This special type of parallel mechanism paves the ground for the workspace, path planning and control of this special metamorphic mechanism.