On the Direct Kinematics of General Spherical Three-Degree-of-Freedom Parallel Manipulators

In this paper, the direct kinematics of general spherical parallel three-degree-of-freedom manipulators is investigated. A polynomial of degree 8 is obtained to describe this problem and it is shown that this polynomial is minimal since 8 real solutions corresponding to actual configurations have been found for a given set of actuator coordinates and a given architecture. This result completes the study on the direct kinematics of spherical three-degre-of-freedom parallel manipulators undertaken by the authors in a previous paper. An example of an architecture and a set of actuator coordinates which lead to 8 real solutions is presented to illustrate the results.