On the advantages of instantaneous invariants and geometric kinematics

This paper points out the advantages of using geometric kinematics rather than time-based kinematics when dealing with the instantaneous geometric properties of rigid body motions. This paper is limited to planar motion, however the same principles apply to spherical and spatial motions. It is pointed out that the use of instantaneous invariants and canonical coordinate systems created a big advance in the elegance and rigor of studying instantaneous property. Examples are presented showing how to use invariants to design instantaneously equivalent mechanisms. In addition Erskine Crossley's contribution to facilitating the awareness of these advances is noted.