Application of Matroid Method in Kinematic Analysis of Parallel Axes Epicyclic Gear Trains

[+] Author and Article Information
Ilie Talpasanu

Department of Electronics and Mechanical, Wentworth Institute of Technology, 550 Huntington Ave, Boston, MA 02115-5998talpasanui@wit.edu

T. C. Yih

Vice Provost for Research, Oakland University, 2200 N. Squirrel Road, Rochester, MI 48309–4401vih@oakland.edu

P. A. Simionescu

Department of Mechanical Engineering, The University of Tulsa, 600 South College Ave, Tulsa, OK 74104-3989psimionescu@utulsa.edu

J. Mech. Des 128(6), 1307-1314 (Jan 23, 2006) (8 pages) doi:10.1115/1.2337310 History: Received May 24, 2005; Revised January 23, 2006

A novel method for kinematic analysis of parallel-axes epicyclic gear trains is presented, called the incidence and transfer method, which uses the incidence matrices associated with the edge-oriented graph associated to the mechanism and the transfer joints (teeth contact joints). Relative to such joints, a set of independent equations can be generated for calculating the angular positions, velocities, and accelerations. Complete kinematic equations are obtained in matrix form using a base of circuits from a cycle matroid. The analysis uses the relationships between the number of mobile links, number of joints, and number of circuits in the base of circuits, together with the Latin matrix (whose entries are function of the absolute values of the partial gear ratios of the transmission). Calculating the rank of the Latin matrix can identify singularities, like groups of gears that rotate as a whole. Relationships between the output and input angular velocities and accelerations are then determined in a matrix-based approach without using any derivative operations. The proposed method has general applicability and can be employed for systems with any number of gears and degrees of freedom, as illustrated by the numerical examples presented.

Copyright © 2006 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

(a) EGT mechanism and (b) graph and circuits

Grahic Jump Location
Figure 2

Spanning trees for the graph

Grahic Jump Location
Figure 3

Ravigneaux epicyclic transmission: (a) mechanism and (b) graph and circuits

Grahic Jump Location
Figure 4

Ferguson paradox: (a) mechanism and (b) graph and circuits




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