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RESEARCH PAPERS

# Geometric Design Using Hypotrochoid and Nonundercutting Conditions for an Internal Cycloidal Gear

[+] Author and Article Information
Yii-Wen Hwang1

Department of Mechanical Engineering, National Chung-Cheng University, 168 San-Hsing, Ming-Hsiung, Chia-Yi 621, Taiwan, R.O.C.imeywh@ccu.edu.tw

Chiu-Fan Hsieh

Department of Mechanical Engineering, National Chung-Cheng University, 168 San-Hsing, Ming-Hsiung, Chia-Yi 621, Taiwan, R.O.C.d9143002@ccu.edu.tw

1

Corresponding author.

J. Mech. Des 129(4), 413-420 (Apr 22, 2006) (8 pages) doi:10.1115/1.2437806 History: Received November 24, 2005; Revised April 22, 2006

## Abstract

This paper uses the theory of gearing to derive the mathematical model of an internal cycloidal gear with tooth difference. Whereas the outer rotor profile is based on a curve equidistant to a hypotrochoidal (or extended hypocycloid) curve, the inner rotor design generally depends upon type of use—e.g., when used as a speed reducer, it is a pin wheel. Therefore, this analysis proposes designs for both a gerotor and a speed reducer. Specifically, for an inner rotor used as a gerotor pump, it outlines a mathematical model to improve pump efficiency and derives a dimensionless equation of nonundercutting. For the speed reducer, it develops and demonstrates with numerical examples, a feasible design region without undercutting on the tooth profile or interference between the adjacent pins.

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Topics: Design , Rotors , Equations , Gears

## Figures

Figure 7

Design result of Case 1 for gerotor

Figure 8

Design result of Case 2 for gerotor

Figure 9

Undercutting example of Case 2 for gerotor

Figure 10

Feasible design region of gerotor

Figure 6

The tooth top and tooth bottom radii of the outer rotor for m=2

Figure 5

The tooth top and tooth bottom radii of the outer rotor for m=1

Figure 4

Coordinate system for generating inner rotor

Figure 3

Applied coordinate system

Figure 2

Generation of the extended hypocycloidal curve

Figure 1

Figure 11

Feasible design region for m=1 and N=10

Figure 12

Feasible design region for m=2 and N=10

Figure 13

Feasible design region for m=3 and N=10

Figure 14

Design result of Case 1 of speed reducer

Figure 15

Design result of Case 2 of speed reducer

Figure 16

Design result of Case 3 of speed reducer

Figure 17

Undercutting and interference example of Case 1 for speed reducer

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