Analysis of instantaneous motions of deficient-rank 3-RPS parallel manipulators

In this paper, the instantaneous motions of a deficient-rank 3-DOF 3-RPS parallel-actuated manipulator are studied. Firstly, the Jacobian matrix of the mechanism is established by using the imaginary-mechanism method. The principal screws of a third-order screw system are identified by means of the conic section degenerating theory. All the pitches of twists of the end-effector are discussed under three different configurations of the mechanism. It is very important to know all the feasible instantaneous motions of a deficient-rank mechanism. The work presented in this paper has great significance for robot trajectory planning and control.