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TECHNICAL PAPERS

# Algorithms for Involute and Octoidal Bevel-Gear Generation

[+] Author and Article Information
Giorgio Figliolini

DiMSAT University of Cassino, G. Di Biasio 43, 03043 Cassino (Fr), Italyfigliolini@unicas.it

Jorge Angeles

Dept. of Mechanical Engineering & CIM, McGill University, 817 Sherbrooke St. Montreal, Quebec H3A 2K6, Canada

J. Mech. Des 127(4), 664-672 (Oct 15, 2004) (9 pages) doi:10.1115/1.1900147 History: Received May 25, 2004; Revised October 15, 2004

## Abstract

A suitable formulation and the implementing algorithms for involute and octoidal bevel-gear generation are proposed in this paper. In particular, the exact spherical involute tooth profile of bevel gears and their crown rack is obtained through the pure-rolling motion of a great circle of the fundamental sphere on the base cone. Moreover, the tooth flank surface of octoidal bevel gears is obtained as the envelope of the tooth flat flank of the octoidal crown rack during the pure-rolling motion of its flat pitch (surface) on the pitch cone. The proposed algorithms have been implemented in MATLAB ; several examples are included to illustrate their applicability.

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Topics: Algorithms , Gears

## Figures

Figure 1

Generation of the exact spherical involute

Figure 2

XZ view of the exact spherical involute tooth profile of the bevel gear for r=100mm, β=45deg, ϕ=40deg and βb=32.80deg

Figure 3

YZ view of the exact spherical involute tooth profile of the crown rack for r=100mm, β=90deg, ϕ=40deg and βb=50deg

Figure 4

Axonometric view of the exact spherical involute tooth profile of Fig. 2

Figure 5

Axonometric view of the exact spherical involute tooth profile of Fig. 3

Figure 6

Exact spherical involute tooth profile for r=100mm, β=60deg, ϕ=40deg and βb=41.56deg

Figure 7

Exact spherical involute tooth profile of the crown rack for r=200mm, β=90deg, ϕ=40deg, βb=50deg

Figure 8

Exact spherical involute tooth profile for r=100mm, β=30deg, ϕ=20deg and βb=28.02deg

Figure 9

Exact spherical involute tooth profile of crown rack for r=100mm, β=90deg, ϕ=20deg and βb=70deg

Figure 10

Sketch for the octoidal tooth flank generation

Figure 11

Sketch of the tooth flat flank for octoidal crown rack

Figure 12

Enveloped spherical profile for r=100mm, β=30deg, α=20deg

Figure 13

Enveloped spherical profile for r=100mm, β=30deg, α=50deg

Figure 14

Enveloped spherical profile for r=100mm, β=30deg, α=0deg

Figure 15

Enveloped spherical profile for r=100mm, β=90deg, α=20deg

Figure 16

Enveloped spherical profile for r=100mm, β=50deg, α=20deg

Figure 17

Enveloped spherical profile for r=100mm, β=50deg, α=30deg

Figure 18

Enveloped spherical profile for r=100mm, β=50deg, α=0deg

Figure 19

Enveloped spherical profile for r=100mm, β=90deg, α=30deg

Figure 20

Spherical profile and the octoidal curve of the contact points for r=100mm, β=90deg, α=45deg

Figure 21

XZ view of the enveloped spherical profile and the octoid curve of the contact points for r=100mm, β=90deg, α=45deg

Figure 22

Enveloped spherical profile and the octoid curve of the contact points for r=100mm, β=30deg, α=20deg

Figure 23

XZ view of the enveloped spherical profile and the octoid curve of the contact points for r=100mm, β=30deg, α=20deg

## Errata

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