A Mathematical Model of a Universal Joint (UMAP)

In this module a universal joint is modeled to study its output pulsations. The angle of coupling that will alleviate these pulsations on a second shaft is determined. An attempt to determine the average angular velocity of the output through integration yields a strange result if tables are used. An introduction to spherical trigonometry is included. Students gain a basic understand of spherical geometry, an awareness of the possible pitfalls in using integral tables, and an appreciation of the usefulness of calculus as a tool in analyzing physical phenomena.

Table of Contents:

1. INTRODUCTION

2. CONSTRUCTING THE MATHEMATICAL MODEL

3. COMPENSATING WITH ANOTHER COUPLING

4. AVERAGE ANGULAR VELOCITY

5. SPHERICAL TRIGONOMETRY

6. EXERCISES

7. ANSWERS TO EXERCISES