An efficient methodology for the topological synthesis of articulated gear mechanisms (AGMs) is presented. A hierarchical model is developed to represent the structural topology of an AGM in which sub-systems in the bottom level are used as design primitives. By a proposed partition algorithm, design specifications are decomposed along the model to determine the attributes of the sub-systems in each level. The decomposition results in a composition polynomial that symbolically reveals all structural compositions of desired mechanisms. With the polynomial and the database of design primitives, the number of admissible mechanisms for a given design specification can be derived and all possible graph representations can be efficiently enumerated. Two 3-dof examples are presented for illustration.

Issue Section:
Research Papers
Topics:
Gears, Design, Polynomials, Algorithms, Databases, Topology
1.
Andrews, G. E., 1976, The Theory of Partitions, Addison-Wesley Pub. Co.
2.
Belfoire, N. P., and Tsai, L. W., 1991, “A New Methodology for Structural Synthesis of Geared Robotic Wrists,” Proc. of the Second National Conference on Applied Mechanisms and Robotics, Paper No. VIB.5.
3.
Chang
S. L.
, and
Tsai
L. W.
,
1990
, “
Topological Synthesis of Articulated Gear Mechanisms
,”
IEEE Journal of Robotics and Automation
, Vol.
6
, No.
1
, pp.
97
–
103
.
4.
Chen
D. Z.
,
1995
, “
Gear Train Configuration Arrangement for Articulated Gear Mechanisms Based on the Generalized Principle of Inertia Match
,”
J. of Chinese Society of Mechanical Engineers
, Vol.
16
, No.
1
, pp.
29
–
38
.
5.
Chen, D. Z., and Shiue, S. C., 1996, “Topological Synthesis of Geared Robotic Mechanism,” Proc. of ASME Design Engineering Technical Conf., Paper No. 96-DETC/MECH-1024.
6.
Freudenstein
F.
,
1971
, “
An Application of Boolean Algebra to The Motion of Epicyclic Drives
,”
ASME JOURNAL OF ENGINEERING FOR INDUSTRY
, Vol.
93
, Series B, pp.
176
–
182
.
7.
Hsu, C. H., 1992, “An Application of Generalized Kinematic Chains to The Structural Synthesis of Non-fractionated Epicyclic Gear Trains,” Proc. of the 22nd Biennial ASME Mechanisms Conference, DE-Vol. 46, pp. 451–458.
8.
Kim
J. T.
, and
Kwak
B. M.
,
1990
, “
Application of Edge Permutation Group to Structural Synthesis of Epicyclic Gear Trains
,”
Mechanism and Machine Theory
, Vol.
25
, No.
5
, pp.
563
–
574
.
9.
Lin
C. C.
, and
Tsai
L. W.
,
1989
, “
The Creation of Non-fractionated Two-Degree-of-Freedom Epicyclic Gear Trains
,”
ASME JOURNAL OF MECHANISMS, TRANSMISSIONS, AND AUTOMATION IN DESIGN
, Vol.
111
, pp.
524
–
529
.
10.
Lin, C. C., and Tsai, L. W., 1989, “The Development of An Atlas of Bevel-Gear-Type Spherical Wrist Mechanisms,” Proc. of the First National Conf. on Applied Mechanisms and Robotics, Paper No. 89-AMR-2A-3.
11.
Liu
T.
, and
Yu
C. H.
,
1995
, “
identification and Classification of Multi-Degree-of-Freedom and Multi-loop Mechanisms
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
117
, pp.
104
–
111
.
12.
Ravisankar
R.
, and
Mruthyunjaya
T. S.
,
1985
, “
Computerized Synthesis of The Structure of Geared Kinematic Chains
,”
Mechanism and Machine Theory
, Vol.
20
, No.
5
, pp.
367
–
387
.
13.
Tsai
L. W.
,
1987
, “
An Application of the Linkage Characteristic Polynomial to The Topological Synthesis of Epicyclic Gear Trains
,”
ASME JOURNAL OF MECHANISMS, TRANSMISSIONS, AND AUTOMATION IN DESIGN
, Vol.
109
, No.
3
, pp.
329
–
336
.
14.
Tsai
L. W.
,
1988
, “
The Kinematics of Spatial Robotic Bevel-Gear Train
,”
IEEE Journal of Robotics and Automation
, Vol.
4
, No.
2
, pp.
150
–
156
.
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