This paper proposes a kinematic model to evaluate the orientation uncertainty range of spherical linkages caused by the joint clearances. Based on the concepts of imaginary clearance link, spherical N-bar rotatability laws, and the invariant link rotatability, the uncertainty of the output angle can be treated as a mobility problem. The uncertainty region of the end-effector is treated as a workspace problem for the remodeled linkage. This paper highlights the orientation error by isolating the kinematic effects of joint clearance from other error factors. The discussion is carried out through spherical four-bar linkages and five-bar linkages. Numeric examples are presented to demonstrate the uncertainty range of the output angle and the uncertainty region of the end-effector. The result shows that, in the worst case, the error of each joint clearance will be magnified in a closed-loop structure compared with linearly adding all the clearance error. This implies that from a kinematics point of view, closed-loop spherical linkages or parallel manipulators will lead to a greater deviation on the end-effector than their open-loop counterparts. Using more passive joints in the manipulator may result in bigger error possibilities.
Journal of Mechanisms and Robotics Open Issues