Isotropy analysis of spherical mechanisms using an instantaneous-pole based method

As the instant centers in planar mechanisms, the instantaneous poles can be used for instantaneous kinematic analysis of spherical mechanisms. In this paper, a novel geometrical method is presented for isotropy analysis of spherical mechanisms via the concept of instantaneous poles. First, a different form of the Jacobian matrix is formulated for multi-degree-of-freedom (multi-DOF) spherical mechanisms, based on the instantaneous poles. Then, using the obtained Jacobian matrix, isotropy analysis of spherical mechanisms is carried out, and general conditions to have isotropic configurations are determined. The proposed method is fast and applicable for all types of spherical mechanisms. At last, two illustrative examples are presented to show the efficiency of the method.