Kinematic Analysis of Epicyclic Bevel Gear Trains With Matroid Method

Abstract

The paper presents a novel technique for the kinematic analysis of bevel gear trains using the incidence matrices of an edge-oriented graph of the mechanism. The kinematic equations are then obtained in matrix form using a cycle basis from a cycle matroid. These equations can be systematically generated, and allow for an efficient computation of the angular velocities of the gears and planet carriers of the mechanism without employing time derivative operations. As illustrated in the paper, the method is applicable to bevel gear trains of any number of gears or degrees of freedom.

Kinematic analysis of geared robotic mechanism using Matroid and T–T graph methods

“…Now, according to Kutzbach criterion [33] in Eq. (21), we can calculate the degrees of freedom by determining the number of inputs and then output relative velocities in terms of input relative velocities:…”

“…In [33], two orthogonality conditions, one for relative velocities and another for relative moments, are defined so that Eq. (14) holds true.…”

“…each edge). Twist matrix is defined as a product between screw and twist intensity [33]: The relative motions of rotation between links are:…”

“…In order to overcome the weaknesses of the methods developed by Tsai and Tokad, both methods were combined and the so called T-T Graph method was introduced [29]. Most recently, Talpasanu [30] and Talpasanu et al [31][32][33] developed the Matroid method for the kinematic analysis of geared mechanisms based on directed graph as well.…”

“…In recent years, a number of methods concerning the general approach to kinematic analysis [1][2][3][4][5][6][7][8][9][10], the structure of geared mechanisms [11][12][13][14] and the kinematic and dynamic analyses of geared systems [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] have been developed.…”