A Hoop Method for Orientation Order Analysis of Spherical Mechanisms

In this paper we present a novel methodology for orientation order analysis of spherical RR dyads. The methodology is a spherical generalization of the recent works of Myszka, Murray, and Schmiedeler for assessing position order of planar RR dyads. The objective of the methodology is to determine if a prescribed fixed axis location for a spherical RR dyad will result in the dyad guiding a moving rigid-body through a set of finitely separated spherical orientations in the desired order (e.g. 1, 2, 3, 4, etc.). First, the prior works on the order analysis of planar RR dyads via the propeller method are briefly reviewed. Next, the planar propeller methodology of Myszka, Murray, and Schmiedeler is extended to yield a spherical hoop methodology. The result is a useful tool to determine if a given spherical RR dyad will guide a moving body through a set of prescribed orientations in the desired order. Finally, we demonstrate the utility of the hoop method for order analysis of spherical RR dyads in three case studies.