On the positioning error of a 2-DOF spherical parallel wrist with flexible links and joints - an FEM approach

This paper deals with an elasto-static analysis of a 2-DOF (degrees of freedom) spherical parallel wrist where the links and the joints are considered flexible. Theoretically, the mobile platform of the wrist rotates around a fixed point which is the intersection of all the joint axes. However, if the flexibility of the limbs is taken into account, while the base platform (BP) and the mobile platform (MP) are assumed rigid, two centers can be identified: one for the BP and the other for the MP. In general such points are not coincident; as a result, the positioning of the MP is affected by inaccuracies, which can be evaluated in terms of displacement and orientation errors. A finite-element method (FEM) approach is used to analyze the problem in a series of configurations of the wrist; the results are elaborated in order to obtain continuous maps of the errors over the workspace of the machine.