A Complete Notation for Dual Velocity

Abstract

A notation is developed which specifies a dual velocity without ambiguity. The point of interest, the moving body, the reference body, and the system of unit vectors in which a dual velocity is expressed are all clearly indicated. The equivalence between the equation of transformation and the coordinate-transformation matrix formulation is shown. Equations are developed to enable calculation of the dual velocity at a point in a body given the dual velocity at any other point, to change the system of unit vectors in which a dual velocity is expressed, and to calculate relative velocities. Use of these equations is demonstrated in an example using the spatial four-bar mechanism which is specialized to the Cardan joint and the wobble-plate mechanism, and the effect of some tolerance errors on output velocity is shown.