A variable-non-circular gear pair is introduced to achieve 2-dof (degree of freedom) function generation. Included is a mechanism where two independent input parameters (angular positions) uniquely determine the angular position of an output axis. Basic kinematic relationships necessary to parameterize the variable noncircular gear pair are presented. The mobility of the mechanism is considered by addressing the kinematic structure of the mechanism. An illustrative example is included where the functional requirements are specified and a graphical display of the corresponding variable-non-circular gears used to satisfy these requirements is presented.

1.
Benford, R. L., 1968, “Customized Motions,” Machine Design, Sept., pp. 151–154.
2.
Bottema, O., and Roth, B., 1979, Theoretical Kinematics, North-Holland Publishing Co., Amsterdam.
3.
Chen
N.
,
1998
, “
Curvatures and Sliding Ratios of Conjugate Surfaces
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
120
, March, pp.
126
132
.
4.
Chironis, N., 1991, Mechanisms and Mechanical Devices Sourcebook, McGraw-Hill, New York.
5.
Cunningham, F. W., 1957, “Non-circular Gears,” Transactions of the 5th Congress on Mechanisms, Purdue University, West Lafayette, Ind., pp. 96–103.
6.
Dimentberg, F., and Shor, J., 1940, “Bennet’s Mechanism,” USSR Academy of Sciences, Journal of Applied Mathematics and Mechanics, Vol. 4, No. 3, (in Russian).
7.
Dooner, D. B., and Seireg, A., 1995, The Kinematic Geometry of Gearing, John Wiley and Sons, Inc., Wiley Series on Design Engineering, New York.
8.
Erdman, A., Modern Kinematics, editor, John Wiley and Sons, Inc., Wiley Series on Design Engineering, New York.
9.
Freudenstein, F., and Alizade, R., 1975, “On the Degree of Freedom of Mechanisms with Variable General Constraints,” Proceedings of Fourth World Congress on the Theory of Machines and Mechanisms, pp. 51–56.
10.
Hirschhorn
J.
,
1989
, “
Path Curvatures in Three-Dimensional Constrained Motion of Rigid Body
,”
Mechanism and Machine Theory
, Vol.
24
, No.
2
, pp.
73
81
.
11.
Holditch, H. 1842, “On Rolling Curves,” Transactions of the Physics Society, London, No. 7, pp. 61–82.
12.
Horiuchi
Y.
,
1988
, “
On the Gear Theory Suggested by Leibnits
,”
Bulletin of the Japan Society of Precision Engineers
, Vol.
23
, No.
2
, June, pp.
146
152
.
13.
Hunt, K. H., 1978, The Kinematic Geometry of Mechanisms, Clarendon Press, Oxford.
14.
Kovar, E. P., 1995, “CNC Basics,” Gear Technology, Randall Publishing Inc., Jan/Feb, pp. 33–37.
15.
Litvin, F. L., 1960, Theory of Gearing (in Russian), Nauka, Moscow.
16.
Manolescu
N. I.
,
1968
, “
For a United Point of View in the Study of the Structural Analysis of Kinematic Chains and Mechanisms
,”
Journal of Mechanisms
, Vol.
3
, pp.
149
169
.
17.
Ollson, U., 1953, Non-circular Cylindrical Gears, Mechanical Engineering Series, No. 10, Acta Polytechnica, Stockholm.
18.
Ollson, U., 1959, Non-circular Bevel Gears, Mechanical Engineering Series, No. 10, Acta Polytechnica, Stockholm.
19.
Phillips, J., 1984, Freedom in Machinery, Vol. 1, Cambridge University Press, London.
20.
Phillips, J., 1990, Freedom in Machinery, Vol. 2, Cambridge University Press, London.
21.
Skriener
M.
,
1966
, “
A Study of the Geometry and the Kinematics of Instantaneous Spatial Motion
,”
Journal of Mechanisms
, Vol.
1
, pp.
115
143
.
22.
Varsimashvili, R., 1995, “Investigation of Noncircular Toothed Gear Transmission,” Proceedings of the International Congress-Gear Transmission’95, Sofia Bulgaria, (in Russian), pp. 134–138.
23.
Wu, D., and Luo, J., 1992, A Geometric Theory of Conjugate Tooth Surfaces, World Scientific, River Edge, N.J.
24.
Xiao
D. Z.
, and
Yang
A. T.
,
1989
, “
Kinematics of Three Dimensional Gearing
,”
Mechanism and Machine Theory
, Vol.
24
, No.
4
, pp.
245
255
.
25.
Yang, A. T., Kirson, Y., and Roth, B., 1975, “On the Kinematic Curvature Theory for Ruled Surfaces,” Proceeding of the 4th World Congress on the Theory of Machines and Mechanisms, pp. 737–142.
This content is only available via PDF.
You do not currently have access to this content.