Mechanical Couplings—A General Geometrical Theory, Part 2: Examples and Applications of the Theorems

Abstract

Having established “feather” as an invariant property of algebraic couplings with connectivity 1, and of some with 2, many examples of its use are now given, in both planar and spatial motion, to predict order of point-loci, class of plane-loci, and degree of line-loci. Apparent exceptions are explained and interpreted, thereby strengthening the general theory. Some theorems on line-loci attributable to Cayley are shown to be important keys to the determination of “feather” in a number of instances.