Abstract

The paper presents a novel and simple technique for the kinematic analysis of bevel gear trains (BGT). The approach is based on edge-oriented graphs for efficient computation of BGT’s absolute and relative velocities of links using incidence matrices. The kinematic equations are generated in matrix form using a cycle basis from a cycle matroid. The set of independent equations is automatically obtained from matrix orthogonalities and not by taking derivatives. Equation coefficients are expressed as function of speed ratios and have minimal variables. Then the relationships between the output and input angular velocities can be determined. In addition, a simple procedure is demonstrated to check for mechanism singularities. The method presented here has general applicability and can be employed for spatial geared mechanisms with any number of gears and degrees of freedom (DOF) as illustrated by numerical examples of robotic wrist mechanisms.

Issue Section:
Research Papers
Keywords:
mechanical hands, robotics, digraph, velocity matroidal, computational kinematics, spatial mechanisms
Topics:
Cycles, Gears, Robotics, Kinematic analysis, Wheels

References

1.
Willis
,
R.
,
1870
,
Principles of Mechanisms
, 2nd ed.,
Longmans, Green
,
London
.
2.
Norton
,
R. L.
,
2004
,
Design of Machinery
,
McGraw-Hill
,
New York
, pp.
497
–
499
.
3.
Gibson
,
D.
, and
Kramer
,
S.
,
1984
, “
Symbolic Notation and Kinematic Equations of Motion of the Twenty-Two Basic Spur Planetary Gear Trains
,”
ASME J. Mech. Des.
,
106
(
3
), pp.
333
–
340
.10.1115/1.3267416
4.
Voinea
,
R.
,
Atanasiu
,
M.
,
Iordache
,
M.
, and
Talpasanu
,
I.
,
1983
, “
Determination of the Kinematic Parameters for a Planar Linkage Mechanism by the Independent Loop Method
,”
5th International Conference on Control Systems and Computer Science
,
Bucharest
, June 8–11, Vol.
1
, pp.
20
–
23
.
5.
Freudenstein
,
F.
,
1971
, “
An Application of Boolean Algebra to the Motion of Epicyclic Drives
,”
ASME J. Eng. Ind.
,
93
(
1
), pp.
176
–
182
.10.1115/1.3427871
6.
Tsai
,
L. W.
,
1988
, “
The Kinematics of Spatial Robotic Bevel-Gear Trains
,”
IEEE J. Rob. Autom.
,
4
(
2
), pp.
150
–
155
.10.1109/56.2078
7.
Hsieh
,
H. I.
, and
Tsai
,
L. W.
,
1995
, “
Kinematic Analysis of Epicyclic-Type Transmissions Mechanisms Using the Concept of Fundamental Gear Entities
,”
ASME
Design Engineering Technical Conferences (DETC'95), Boston, Sept. 17–20, Vol.
82
, pp.
545
–
552
.
8.
Hsu
,
C. H.
, and
Lam
,
K. T.
,
1992
, “
A New Graph Representation for the Automatic Kinematic Analysis of Planetary Spur-Gear Trains
,”
ASME J. Mech. Des.
,
114
(
1
), pp.
196
–
200
.10.1115/1.2916916
9.
Nelson
,
C. A.
, and
Cipra
,
R. J.
,
2005
, “
Simplified Kinematic Analysis of Bevel Epicyclic Gear Trains With Application to Power-Flow and Efficiency Analyses
,”
ASME J. Mech. Des.
,
127
(
2
), pp.
278
–
286
.10.1115/1.1814392
10.
Shai
,
O.
, and
Preiss
,
K.
,
1999
, “
Graph Theory Representation of Engineering Systems and Their Embedded Knowledge
,”
Artif. Intell. Eng.
,
13
(
3
), pp.
273
–
284
.10.1016/S0954-1810(99)00002-3
11.
Talpasanu
,
I.
,
2004
, “
Kinematics and Dynamics of Mechanical Systems Based on Graph-Matroid Theory
,” Ph.D. dissertation,
University of Texas at Arlington
,
Arlington, TX
.
12.
Talpasanu
,
I.
,
Yih
,
T. C.
, and
Simionescu
,
P. A.
,
2006
, “
Application of Matroid Method in Kinematic Analysis of Parallel Axes Epicyclic Gear Trains
,”
ASME J. Mech. Des.
,
128
(
6
), pp.
1307
–
1314
.10.1115/1.2337310
13.
Talpasanu
,
I.
,
Yih
,
T. C.
, and
Simionescu
,
P. A.
,
2012
, “
Kinematic Analysis of Epicyclic Bevel Gear Trains With Matroid Method
,”
ASME J. Mech. Des.
,
134
(
11
), p.
114501
.10.1115/1.4007144
14.
Amirinezhad
,
S. V.
, and
Uyguroğlu
,
M. K.
,
2015
, “
Kinematic Analysis of Geared Robotic Mechanism Using Matroid and T–T Graph Methods
,”
Mech. Mach. Theory
,
88
, pp.
16
–
30
.10.1016/j.mechmachtheory.2015.02.002
15.
Whitney
,
H.
,
1935
, “
On the Abstract Properties of Linear Dependence
,”
Am. J. Math.
,
57
(3), pp.
509
–
533
.10.2307/2371182
16.
Kaveh
,
A.
,
1997
,
Optimal Structural Analysis
,
Research Studies Press (Wiley)
,
Exeter, UK
.
17.
Recski
,
A.
,
1989
,
Matroid Theory and Its Applications in Electric Network Theory and in Statics
,
Springer-Verlag
,
Berlin
.
18.
Ball
,
R. S.
,
1998
,
A Treatise on the Theory of Screws
,
Cambridge University Press
,
London
.
19.
Selgado
,
D. R.
, and
Del Castillo
,
J. M.
,
2005
, “
A Method for Detecting Degenerate Structures in Planetary Gear Trains
,”
Mech. Mach. Theory
,
40
(8), pp.
948
–
962
.10.1016/j.mechmachtheory.2004.12.019
Copyright © 2015 by ASME
You do not currently have access to this content.