Accuracy Comparison of Spherical Parallel Manipulators Based on Joint Clearance

In this paper, three types of Spherical Parallel Manipulators (SPM) are compared from accuracy point of view based on joint clearances. The 3-RRR SPM is an overconstraint parallel mechanism and one can presume that it may exhibits an accurate motion. But beside the foregoing advantage, this structure has some drawbacks such as requiring high manufacturing precision and the difficulty of assembling the mechanism. Two other types, 3-RRS and 3-RSR, are non-overconstrained and do not have the above disadvantages, therefore these two types with 3- RRR are put into contrast from accuracy point of view. First, a method to obtain a model of moving platform pose (position and orientation) error is introduced which leads to a standard convex optimization problem. Since error calculation depends on the end-effector configuration, more than 1000 configurations are taken into account in order to cover SPMs workspaces. Then maximum values of six components of the pose error in each configuration are computed for each type. Finally, the three SPMs are compared based on maximum position and orientation error for given joint clearances. 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.