A Brief Analysis of the Hooke's Joint

Abstract:

The purpose of this paper is to derive the mathematical equations which
govern the movements of a Hooke's joint, also known as a universal joint. A
Hooke's joint has an input shaft and an output shaft. If the input shaft rotates
through an angle IN, then the output shaft will simultaneously rotate through
an angle OUT. The functional relationship between input angle and output
angle is a function of the angular o¤sets between the two shafts and of the
original state of the Hooke's joint for zero angle IN. The derivation is obtained
by considering the individual three dimensional rotations that characterize an
arbitrary Hooke's joint state. These rotations are represented by 3x3 rotation
matrices. An electro-mechanical magnetic  flux-gate compass application is also
discussed.