Forward displacement analysis of a 2-DOF RR-R̲R̲R-RRR spherical parallel manipulator

Spherical parallel manipulators can be used as wrists or hip joints of humanoid robots. This paper deals with the forward displacement analysis (FDA) of a 2-DOF RR-RR-RRR-RRR spherical parallel manipulator. The kinematic equations of the 2-DOF SPM are formulated at first. The singularity analysis of the 2-DOF SPM is then dealt with. After a closed-form solution to the FDA has been presented, a formula that produces a unique current solution to the FDA is revealed for the 2-DOF spherical parallel manipulator. A regular square in the input space, which is singularity free, is also proposed for the 2-DOF SPM. This work will facilitate the control of the 2-DOF SPM.