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Consortium for Mathematics and its Applications

Product ID: 99566
Supplementary Print
Undergraduate
High School

A Mathematical Model of a Universal Joint (UMAP)

Author: Thomas O'Neil


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

©1983 by COMAP, Inc.
UMAP Module
21 pages

Mathematics Topics:

Precalculus & Trigonometry , Calculus

Application Areas:

Engineering & Construction

Prerequisites:

Trigonometry; calculus, differentiation and integration of trigonometric functions and improper integration

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