Type Synthesis of Non-singular Fully-isotropic Translational Parallel Mechanisms Based on Theory of Reciprocal Screw

Abstract

A systematic approach for type synthesis of non-singular fully-isotropic translational parallel mechanisms is proposed based on the theory of reciprocal screw.The matrix expression of the output motions of the end-effector of mechanism is presented firstly.According to the condition that the positive Jacobian matrix of the expression is a non-zero diagonal matrix throughout the entire workspace,the expressions of the actuated screws of each limb are determined.Then,the forms of the actuating screws of each leg are derived on the basis of the condition that the reciprocal product of actuated and actuating screws is a non-zero constant.The types and the axial directions of the actively unactuated screws are determined in light of the characteristic that the reciprocal products of the actuated screw and all other kinematic screws except the actuating screws in the identical limb are equal to zero.Type synthesis of three legs containing idle joints or not,thereby,is accomplished in terms of different co nnection degrees.Finally,the expected mechanisms are obtained by selecting three legs synthesized above to connect the platform with the base.The kinematic analysis of a novel 3-CRP parallel mechanism is performed and the result shows that the method of type synthesis for non-singular fully-isotropic parallel manipulators proposed here is correct and feasible.