Jacobian formulation for a novel 6-DOF parallel manipulator

The derivation of the Jacobian matrix for a novel six degree of freedom parallel manipulator is presented in this paper. A force decomposition approach is used to compute the Jacobian. The parallel manipulator consists of a base plate, a top plate, and three connecting legs with all revolute joints. The key to the Jacobian formulation presented here is the derivation of a mapping from the applied end-effector force and torque to two force components at each spherical joint. Each leg of the manipulator can then be treated separately and the actuated joint torques can easily be computed from these spherical joint forces