A general algorithm for analytically determining all the instantaneous pole axis locations in single-DOF spherical mechanisms

In spherical mechanisms (SMs), instantaneous pole axes (IPAs) play the same role as instant centres in planar mechanisms. Their use in kinematic analyses requires general techniques to determine them. In the literature, such techniques have not been proposed yet. That is why they are not used for studying the kinematics of SMs in all the problems whose planar counterparts are efficiently solved by exploiting instant centres’ properties. This article aims to fill this lack of techniques. For SMs with one degree of freedom (DOF), a general method to analytically locate all the IPAs as a function of the mechanism configuration is presented. The presented method is directly deduced from an algorithm already proposed by the author for the determination of the instant centres in single-DOF planar mechanisms.