Kinetostatic Performance Comparison of Spherical Parallel Mechanisms Extracted from Type Synthesis with Modeling Clearance in Passive Joints

A Spherical Parallel Mechanism (SPM) is used to rotate a body around a fixed point. Using type synthesis, different kinematic arrangements can be obtained for the robot with three degrees of rotational freedom. The most commonly used structure for this robot is the 3-RRR kinematic architecture which is an overconstrained parallel mechanism and causes several problems of mounting the mechanism, but has the advantage of having high rigidity thus a good accuracy. In this paper two non-overconstrained architectures 3-RRS and 3-RSR that are extracted from the type synthesis are compared with overconstrained one from accuracy point of view based on joint clearance. First, a method to obtain a model of moving platform pose (position and orientation) error based on joint clearance is introduced which leads to a standard convex optimization problem. Then maximum values of six components of the pose error are computed in more than 1000 different configurations within their workspace. It is shown that this displacement is configuration dependent. The obtained results revealed that the 3-RRR SPM has better position accuracy while in the case of orientation, the 3-RRS SPM has lowest maximum error between SPMs under study in the prescribed workspace. It can be concluded that non-overconstrained structures can be used instead of the overconstrained structure. Finally, a comparison was made between the performance indices and the method presented in this paper and results showed that the kinematic sensitivity index is most consistent with the accuracy of the robot.