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RESEARCH PAPERS

# Kinematic and Geometric Analysis of a Pure-Rolling Epicyclic Train

[+] Author and Article Information
Chao Chen

Department of Mechanical Engineering & Centre for Intelligent Machines, McGill University, Montreal, Quebec, H3A 2A7, Canadacchen56@cim.mcgill.ca

Xiang Zhang

Department of Mechanical Engineering & Centre for Intelligent Machines, McGill University, Montreal, Quebec, H3A 2A7, Canadadzhang@velanvalve.com

Jorge Angeles

Department of Mechanical Engineering & Centre for Intelligent Machines, McGill University, Montreal, Quebec, H3A 2A7, Canadaangeles@cim.mcgill.ca

The sun cam displayed here has only one lob.

We use here the “floor function” $⌊∙⌋$, defined as the largest integer smaller than the real $(∙)$.

J. Mech. Des 129(8), 852-857 (Aug 12, 2006) (6 pages) doi:10.1115/1.2735343 History: Received January 25, 2006; Revised August 12, 2006

## Abstract

This paper reports an innovative design of epicyclic (planetary) cam trains based on pure-rolling contact, intended to overcome the drawbacks of gear trains, such as Coulomb friction and backlash. The kinematic relations of the mechanism with a given speed-reduction ratio are analyzed; accordingly, the profiles of the sun cam and ring cam, key elements of the mechanism, are obtained. Furthermore, the condition for undercutting avoidance of the ring cam is derived. For mechanical design, different layouts of the epicyclic cam trains are discussed for the structure and transmission optimization. Finally, an epicyclic cam-roller speed reducer is designed and prototyped.

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Topics: Design , Trains , Rollers , Gears

## Figures

Figure 1

Planar SoC train

Figure 2

(a) The sun cam and its roller follower with Ms=4 and N=5, (b) the pertinent notation

Figure 3

Sun cams with (a) two lobes, (b) three lobes, (c) five lobes, and (d) six lobes

Figure 4

The ring cam and its roller follower: (a) with Mr=10 and N=3, and (b) the pertinent notation

Figure 5

An ECT of the CDC type

Figure 6

An ECT of the DCD type

Figure 7

Assembly procedure of the sun cam and the planets

Figure 8

Assembly procedure of the ring cam and the planets

Figure 9

Virtual gear representation of a CDC train

Figure 10

Critical condition of a CDC train with a3=64.9900mm, a4=10.6667mm, N=7, Mr=17

Figure 11

Critical condition of a ring cam lobe with a3=64.9900mm, a4=10.6667mm, N=7, Mr=17

Figure 12

Undercutting of a ring cam lobe with a3=64.9900mm, a4=10.6667mm, N=7, Mr=18

Figure 13

An epicyclic cam transmission for a speed reduction of 12:1 with a plate diameter of 330mm, all parts machined by Alta Precision Inc.: (a) A view of the whole transmission and (b) a view with one plate removed to show the cams and rollers (input and output shafts are coaxial)

## Errata

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