A novel method to determine position and orientation errors in clearance-affected overconstrained mechanisms

Reaction forces and torques in overconstrained mechanisms are tied to the elasticity of the system. External wrenches applied to a mechanism generate joint reactions that can be determined only employing the stiffness analysis. This paper describes a novel method to find nodal displacements and rotations of overconstrained mechanisms due to clearance-affected joints. Unlike the previous formulations, the proposed method requires a single elastostatic analysis and employs the Virtual Work Principle to find the displacements at each node of the mechanism. Internal wrenches are first determined and then introduced in contact models of joints to obtain relative displacements/rotations of the kinematic pairs. The case of the journal-bearing is recalled introducing two contact scenarios, without limiting the use of other contact models. The method is applied to the 3-RRR spherical parallel manipulator under different clearance and pose parameters. Finally, feasible applications are supplied: multiple nodal loads, influence of preload and flexible joints, tradeoff between flexibility and clearance errors, introduction of manufacturing error in joints' axes. The method has been validated using an equivalent Adams© model. The results revealed in good accordance making the method suitable to evaluate the influence of clearance in overconstrained mechanisms.