Inverse kinematics and dynamics of the 3-RRS parallel platform

This paper presents the formulation of the inverse kinematics and dynamics of the 3-RRS parallel platform with three degrees of freedom. For inverse kinematics, The position analysis is firstly performed. Then the differential motion constraint equations of the movable platform are established, based on which the velocity and acceleration formulae of leg actuators are derived. In inverse dynamic analysis, the parallel platform is decomposed into two parts through parting the three spherical joints, and the forces acting on the parted joints are determined according to the moment (and force) equilibrium's of the legs and the movable platform. Subsequently, the analytic expressions of the driving moments of the leg actuators are derived by means of the moment equilibrium's of the legs. Although only the 3-RRS parallel platform is analyzed in this paper, the presented method and process can also be applied to other less DOF parallel platforms.