Kinematic sensitivity analysis of linkage with joint clearance based on transmission quality

This paper presents an effective method to analyze the transmission performance of linkages that have joint clearance. Joint clearance was treated as virtual link to simplify the study. Equivalent kinematical pairs were used to model the motion freedoms caused by the joint clearances. With joint clearance presented, the number of unknown joint parameters is greater than the number of loop closure equations obtained in position analysis. Under kine-static and dynamic analysis, a mechanism should be in equilibrium at any configuration. The joint transmission wrench should equilibrate all externally applied wrenches for each link member. An extra set of constraint equations can be obtained since the joint transmission wrench screw should be reciprocal to the joint twist screw of the member. Then the mechanism positions can be solved with the loop closure and reciprocal equations simultaneously.