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Research Papers

Kinematic Analysis of Spatial Geared Mechanisms

[+] Author and Article Information
Julie Penaud

ISAE,  Université de Toulouse, Avenue Edouard Belin, 1031055 Toulouse, Francejulie.penaud@isae.fr

Daniel Alazard

ISAE,  Université de Toulouse, Avenue Edouard Belin, 1031055 Toulouse, Francedaniel.alazard@isae.fr

Alexandre Amiez

ONERA Avenue Edouard Belin, 231055 Toulouse, Francealexandre.amiez@onera.fr

J. Mech. Des 134(2), 021009 (Feb 03, 2012) (6 pages) doi:10.1115/1.4005596 History: Received October 20, 2010; Revised November 28, 2011; Published February 03, 2012

In this paper, a general method for kinematic analysis of complex gear mechanisms, including bevel gear trains and noncollinear input and output axes, is presented. This new approach is based on the nullspace of the kinematic constraint matrix computed from the mechanism graph or its adjacency matrix. The novelty is that the elements of the adjacency matrix are weighted with complex coefficients allowing bevel gears to be taken into account and the angular velocity of each link to be directly expressed using polar coordinates. This approach is illustrated on a two-degree-of-freedom car differential and applied to a helicopter main gear box. A MATLAB open source software was developed to implement this method.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Picture of the car differential

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Figure 2

Car differential kinematic sketch

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Figure 3

Graph representation of the car differential (gear pair edges 4-5 and 3-6 are rounded for the legibility of the graph)

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Figure 4

Angle definition example for a pinion-crown bevel gear

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Figure 5

Angular velocity vectors of car differential links when left wheel is locked

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Figure 6

Kinematic sketch of the main gear box of Alouette III

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Figure 7

Graph representation of the MGB

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