The Hoop Method

Orientation Order Analysis of Spherical Dyads (Tipparthi, Larochelle)

In this work we created a novel methodology for orientation order analysis of spherical 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.). The planar propeller methodology of Myszka, Murray, and Schmiedeler for assessing order in planar RR dyads is extended to yield a spherical hoop methodology. The hoop is a great circle on the design sphere that intersects the fixed axis of the spherical RR dyad. The hoop method involves rotating the hoop about the fixed axis and noting the order in which the relative rotation axes are encountered. 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.