This study concerns the degree-of-freedom, the arrangements of input and the type of mobility of multi-loop, multi-degree-of-freedom mechanisms. Firstly, “basic loops” are introduced, and a systematic scheme for identifying the actual degree-of-freedom of mechanisms is developed. The input, then, can be properly deployed, such that the mechanism has a totally constrained motion. Lastly, based on the input deployment, the mobility of mechanisms is classifed and identified into three types: total, partial and fractionated mobility. The procedure has been automated, and the atlas of all possible arrangements of input of up to eight-link planar mechanisms with only revolute joints is presented. The systematic method is helpful for the structural synthesis of multi-degree-of-freedom and multi-loop mechanisms, and for exploring their potential industrial applications.

1.
Davies
T. H.
,
1968
, “
An Extension of Manolescu’s Classification of Planar Kinematic Chains and Mechanisms of Mobility M ≥ 1, Using Graph Theory
,”
Mechanism and Machine Theory
, Vol.
3
, pp.
87
100
.
2.
Agrawal
V. P.
, and
Rao
J. S.
,
1987
, “
The Mobility Properties of Kinematic Chains
,”
Mechanism and Machine Theory
, Vol.
22
, No.
5
, pp.
497
504
.
3.
Agrawal
V. P.
, and
Rao
J. S.
,
1987
, “
Structural Classification of Kinematic Chains and Mechanisms
,”
Mechanism and Machine Theory
, Vol.
22
, No.
5
, pp.
489
496
.
4.
Agrawal
V. P.
, and
Rao
J. S.
,
1987
, “
Fractionated Freedom Kinematic Chains and Mechanisms
,”
Mechanism and Machine Theory
, Vol.
22
, No.
2
, pp.
125
130
.
5.
Freudenstein
F.
, and
Maki
E. R.
,
1979
, “
The Creation of Mechanisms according to Kinematic Structure and Function
,”
International Journal of Architecture and Design, Environment, and Planning B
, Vol.
6
, pp.
375
391
.
6.
Freudenstein
F.
, and
Maki
E. R.
,
1983
, “
Development of an Optimum Variable Stroke Internal Combustion Engine Mechanism From the Viewpoint of Kinematic Structure
,”
ASME JOURNAL OF MECHANISMS, TRANSMISSIONS, AND AUTOMATION IN DESIGN
, Vol.
105
, pp.
259
266
.
7.
Mayourian
M.
, and
Freudenstein
F.
,
1984
, “
The Development of an Atlas of Kinematic Structure of Mechanisms
,”
ASME JOURNAL OF MECHANISMS, TRANSMISSIONS, AND AUTOMATION IN DESIGN
, Vol.
106
, pp.
458
461
.
8.
Buchsbaum
F.
, and
Freudenstein
F.
,
1970
, “
Synthesis of Kinematic Structure of Geared Kinematic Chains and Other Mechanism
,”
Mechanism and Machine Theory
, Vol.
5
, pp.
357
392
.
9.
Harary, F., 1969, Graph Theory, Addison-Wesley Publishing.
10.
Deo, N., 1974, Graph Theory with Applications to Engineering and Computer Science, Prentice-Hall, Inc.
11.
Bagci
C.
,
1971
, “
Degree of Freedom of Motion in Mechanisms
,”
ASME Journal of Engineering for Industry
, Vol.
93
, pp.
140
148
.
12.
Liu, T., and Lee, T. W., 1984, “Kinematic Structural Analysis of Over-constrained Spatila Mechanisms, Part 1: Theory,” ASME 94-DET-215.
13.
Freudenstein, F., and Alizade, R., 1975, “On the Degree of Freedom of Mechanisms With Variable General Constraint,” Proceedings of Fourth World Congress on the Theory of Machines and Mechanisms, U.K., Vol. 10, pp. 51–56.
14.
Tang, C. S., and Liu, T., “The Degree Code—A New Mechanism Identifier,” ASME Journal of Mechanical Design, in press.
15.
Sohn
W. J.
, and
Freudenstein
F.
,
1986
, “
An Application of Dual Graphs to the Automatic Generation of the Kinematic Structures of Mechanisms
,”
ASME JOURNAL OF MECHANISMS, TRANSMISSIONS, AND AUTOMATION IN DESIGN
, Vol.
108
, pp.
392
398
.
This content is only available via PDF.
You do not currently have access to this content.