Spherical 4R mechanisms are studied for which the crank is relatively smaller than the remaining links. The theory of small-crank mechanisms is applied to obtain approximate descriptions for the follower angular displacement in terms of the input crank angle. The follower angle is presumed to comprise a mean and a perturbational motion. This results in an approximate expression in which the follower displacement is given as a linear combination of simple harmonic functions of the first and second harmonics of the crank angle. The approximate equations are utilized for synthesis of spherical 4R mechanisms for function generation. In contrast to the conventional design procedures, the use of the approximate equations allows the synthesis of spherical mechanisms in which a prescribed function is satisfied for the entire motion of the mechanism. In addition to design examples, sample error charts are provided to assist the designer in ascertaining feasible ranges for design and corresponding orders of error.

1.
Bagci, C., 1971, “Static Force and Torque Analysis Using 3 × 3 Screw Matrix, and Transmission Criteria for Space Mechanism,” ASME Journal of Engineering for Industry, pp. 90–101.
2.
Basu
P. S.
, and
Farhang
K.
,
1994
, “
Kinematic Analysis and Design of Two-Input, Five-Bar Mechanisms Driven by Relatively Small Cranks
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
116
, pp.
1108
1114
.
3.
Bodduluri, R. M. C, 1986, “Interactive Design of Spherical Four-Bar Linkages Using High Speed Graphics,” Master’s Thesis, Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania.
4.
Chiang, C. H., 1988, Kinematics of Spherical Mechanism, Cambridge University Press, Cambridge, England.
5.
Dooley, J. R., and McCarthy, J. M., 1992a, “Dynamic Analysis of a Spherical Four-Bar Mechanism,” Proceedings of the 22nd Biennial Mechanisms Conference, DE-Vol. 47, pp. 161–166.
6.
Dooley, J. R., and McCarthy, J. M., 1992b, “Dynamics of Open and Closed Chain Spherical Mechanisms Using Quaternion Coordinated,” Proceedings of the 22nd Biennial Mechanisms Conference, DE-Vol. 47, pp. 167–172.
7.
Dooley, J. R., 1995, “Dynamic Force and Torque Analysis of a Spherical Four-Bar Mechanism,” Proceedings of the Design Engineering Technical Conferences, DE-Vol. 82, pp. 593–599.
8.
Edrman, A. G., (editor), 1993, Modern Kinematics, The Last Forty Years, Design Engineering Series, Wiley Interscience.
9.
Farhang
K.
,
Midha
A.
, and
Bajaj
A. K.
,
1987
, “
A Higher-Order Analysis of Basic Linkages for Harmonic Motion Generation
,”
ASME Journal of Mechanisms, Transmissions, and Automation in Design
, Vol.
109
, No.
3
, pp.
301
307
.
10.
Farhang
K.
,
Midha
A.
, and
Bajaj
A. K.
,
1988
a, “
Synthesis of Harmonic Motion Generating Linkages—Part I; Function Generation
,”
ASME Journal of Mechanisms, Transmissions, and Automation in Design
, Vol.
110
, No.
1
, pp.
16
21
.
11.
Farhang
K.
,
Midha
A.
, and
Hall
A. S.
,
1988
b, “
Synthesis of Harmonic Motion Generating Linkages, Part II: Path and Motion Generation
,”
ASME Journal of Mechanisms, Transmissions, and Automation in Design
, Vol.
101
, No.
1
, pp.
22
27
.
12.
Farhang
K.
, and
Basu
P. S.
,
1994
a, “
Kinematic Analysis and Synthesis of Three-Input, Eight-Bar Mechanisms Driven by Relatively Small Cranks
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
116
, pp.
930
936
.
13.
Farhang
K.
, and
Basu
P. S.
,
1994
b, “
Approximate Kinematic Equations for Multiple-Input Small-Crank Mechanisms: Four-Bar Based Mechanisms
,”
Mechanism Synthesis and Analysis
, DE-Vol.
70
, ASME, pp.
75
84
.
14.
Gill, G. S., and Freudenstein, F., 1983a, “Minimization of Inertia-Induced Forces in Spherical Four-Bar Mechanisms: Part 1: The General Spherical Four-Bar Linkage,” ASME Journal of Mechanisms, Transmission, and Automation in Design, pp. 471–477.
15.
Gill, G. S., and Freudenstein, F., 1983b, “Minimization of Inertia-Induced Forces in Spherical Four-Bar Mechanisms: Part 2: Wobble-Plate Engines,” ASME Journal of Mechanisms, Transmission, and Automation in Design, pp. 478–483.
16.
Ham, K., Erdman, A., and Hong, B., 1996, “Spherical Four-Bar Linkage Mechanism for Continuous Passive Movement Rehabilitation Treatment of the Ankle,” Proceedings of the 1996 ASME Design Engineering Technical Conferences and Computers in Engineering Conference, 96-DETC/MECH-1223.
17.
Hong, B., Erdman, A., and Ham, K., 1996, “Design of Adjustable Spherical Four-Bar Linkages as Continuous Passive Motion Devices for Anatomic Joints Rehabilitation,” Proceedings of the 1996 ASME Design Engineering Technical Conferences and Computers in Engineering Conference, 96-DETC/MECH-1220.
18.
Larochelle, P., Dooley, J. R., Murray, A., and McCarthy, J. M., 1993, “Software for Synthesizing Spherical 4R Mechanisms,” Proceedings of NSF Conference.
19.
Larochelle, P., and McCarthy, J. M., 1992, “Static Analysis of nr Kinematic Chains with Joint Friction,” Proceedings of the 22nd Biennial Mechanisms Conference, DE-Vol. 47, pp. 173–178.
20.
Midha
A.
,
Cipra
R. J.
, and
Farhang
K.
,
1985
, “
Analysis and Design of Basic Linkages for Harmonic Motion Generation
,”
ASME Journal of Mechanisms, Transmissions, and Automation in Design
, Vol.
107
, No.
4
, pp.
499
507
.
21.
Murray, A. P., and McCarthy, J. M., 1995, “A Linkage Type Map for Spherical 4 Position Synthesis,” Proceedings of the 1995 ASME Design Engineering Conferences, Vol. 1, DE-Vol. 82, pp. 833–838.
22.
Suh, C. H., and Radcliffe, C. W., 1978, Kinematics and Mechanism Design, John Wiley and Sons, New York.
23.
Yang, A. T., 1965, “Static Force and Torque Analysis of Spherical Four-Bar Mechanisms,” ASME JOURNAL OF ENGINEERING FOR INDUSTRY, pp. 221–227.
24.
Yang, A. T., and Zhishang, S., 1985, “Dynamic Force and Torque Analysis of Spherical Four Link Mechanism,” ASME Journal of Mechanisms, Transmission and Automation in Design, pp. 1985.
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