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Motion Simulation of Cycloidal Gears, Cams, and Other Mechanisms

Shih-Liang (Sid) Wang Department of Mechanical Engineering North Carolina A&T State University Greensboro, NC 27411 Tel (336)334-7620, Fax (336)334-7417, wang@ncat.edu

Introduction Cycloids are curves traced by a point on the circumference of a circle that rolls on a straight line or another circle. The latter category is often referred as trochoids. Mechanisms with cycloidal geometry include cams, gears, gear trains, rotary engines, and blowers.

Cycloidal gears, whose teeth have cycloidal profiles, are now almost obsolete, replaced by involute gears because of manufacturing costs. The Wankel engine, with its rotor and chamber based on cycloidal curves, has leakage problems and has not gained wide acceptance. Cams with cycloidal displacement are being replaced by those with polynomial function displacement. Consequently, most textbooks in kinematics do not cover these topics or cover them with limited scopes. Students and practicing engineers therefore do not have proper exposure of these subjects.

With new ways of gear manufacturing like injection molding, cycloidal gears are reemerged as an option. Additionally, cycloidal gears should also play an important role in the emerging field in Micro Electro-Mechanical Systems (MEMS) [1]. Moreover, there is a renewed interest [2] in the Wankel engine for hybrid vehicles with hydrogen fuel.

To help students understand and visualize the motion of these mechanisms, the author has developed courseware on cycloidal gears, cams, and other mechanisms, with simulation files generated from MATLAB, Working Model 2D, and visualNastran 4D.

Animations of different cycloidal curves can be found at Eric Weisstein’s World of Mathematics, a Wolfram Web Resource [3,4,5]. An interactive Java program Spirograph [6] is available on the web. However, computer simulation of cycloidal mechanisms cannot be found.

All curves shown in this paper are generated with MATLAB, and each MATLAB file can generates animated simulation. Working Model 2D files, based on the geometry generated from these MATLAB files, help students visualize the motion of these cycloidal mechanisms. The simulation files are hyperlinked with text files containing background information and cycloidal equations.

Cycloids, Trochoids, and Spirograph Cycloid is a curve traced by any point rigidly attached to a circle of radius a, at distance b from the center, when this circle rolls on a straight line. The equation is:

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Wang, S. S. (2002, June), Motion Simulation Of Cycloidal Gears, Cams, And Other Mechanisms Paper presented at 2002 Annual Conference, Montreal, Canada. 10.18260/1-2--10715