Forward Kinematics and Singularities of a 3-(rR)PS Metamorphic Parallel Mechanism

摘要

A 3-(rR)PS metamorphic parallel mechanism studied in this paper has three configurations and it may switch from one configuration to another by discretely altering the reconfigurable (rR)-joint without disassembly. This paper presents the analysis of forward kinematics and singularities in one out of three configurations. Algebraic geometry approach is used to derive the constraint equations describing the motion of each kinematic chain. Groebner basis is computed over a set of constraint equations to find a univariate polynomial. Solving this univariate polynomial, the solutions of forward kinematics are obtained. Jacobian matrix is derived by taking partial derivative of the constraint equations to investigate singularities. Singularity surface is plotted in Cartesian space together with the tetrahedron, which is the workspace of moving platform.