Kinematic and Dynamic Analysis of a 3-PRUS Spatial Parallel Manipulator

Parallel Kinematic Machines (PKMs) are being widely used for precise applications to achieve complex motions and variable poses for the end effector tool. PKMs are found in medical, assembly and manufacturing industries where accuracy is necessary. It is often desired to have a compact and simple architecture for the robotic mechanism. In this paper, the kinematic and dynamic analysis of a novel 3- PR US (P: prismatic joint, R: revolute joint, U: universal joint, S: spherical joint) parallel manipulator with a mobile platform having 6 Degree of Freedom (DoF) is explained. The kinematic equations for the proposed spatial parallel mechanism are formulated using the Modified Denavit-Hartenberg (DH) technique considering both active and passive joints. The kinematic equations are used to derive the Jacobian matrix of the mechanism to identify the singular points within the workspace. A Jacobian based stiffness analysis is done to understand the variations in stiffness for different poses of the mobile platform and further, it is used to decide trajectories for the end effector within the singularity free region. The analytical model of the robot dynamics is presented using the Euler-Lagrangian approach with Lagrangian multipliers to include the system constraints. The gravity and inertial forces of all links are considered in the mathematical model. The analytical results of the dynamic model are compared with ADAMS simulation results for a pre-defined trajectory of the end effector.