On the location of the secondary instantaneous poles in two-degree-of-freedom spherical mechanisms

As the instant centers in planar mechanisms, the instantaneous poles (or instant poles, in brief) can be used for kinematic analysis in spherical mechanisms. One of the mandatory steps in this analysis is the determination of the location of these poles. This paper presents a theorem showing analytically that the locus of an unknown secondary instant pole in two-degree-of-freedom (2-DOF) spherical mechanisms is a great circle (GC). The exact location of the pole on its GC is obtained based on the configuration of the mechanism and velocity ratio of the two inputs. Moreover, using the results of the theorem, a geometrical technique is presented to determine the GC of the pole.