This paper presents a graphical technique to locate the center of curvature of the path traced by an arbitrary coupler point of the single flier eight-bar linkage. The first step is to locate the pole for the instantaneous motion of the coupler link; i.e., the point in the fixed plane coincident with the absolute instant center of the coupler link. Since the single flier is an indeterminate linkage, comprised of one four-bar and two five-bar chains, then the Aronhold-Kennedy theorem cannot locate this instant center. The paper presents a novel graphical technique which can locate this instant center in a direct manner. Then the paper focuses on a graphical method to locate the center of curvature of the path traced by the coupler point. The method locates six equivalent four-bar linkages for the two five-bar chains, investigates six kinematic inversions and obtains a four-bar linkage from each inversion. This systematic procedure produces a four-bar linkage with a coupler link whose motion is equivalent up to, and including, the second-order properties of motion of the single flier coupler link. The radius of curvature and the center of curvature of the path traced by the coupler point can then be obtained in a straightforward manner from the Euler-Savary equation.

1.
Hall, A. S., Jr., 1986, Kinematics and Linkage Design, Waveland Press, Inc., Prospect Heights, Illinois. (Originally published by Prentice-Hall, Inc., Engelwood Cliffs, N.J., 1961.)
2.
Hain, K., 1967, Applied Kinematics, Second Edition, McGraw-Hill Book Co., Inc., New York.
3.
Klein, A. W., 1917, Kinematics of Machinery, McGraw-Hill Book Company, Inc., New York.
4.
Bagci
,
C.
,
1983
, “
Turned Velocity Image and Turned Velocity Superposition Techniques for the Velocity Analysis of Multi-Input Mechanisms Having Kinematic Indeterminacies
,”
Mechanical Engineering News
,
20
(
1
), February, pp.
10
15
.
5.
Dijksman, E. A., 1977, “Why Joint-Joining is Applied on Complex Linkages,” Proceedings of the Second IFToMM International Symposium on Linkages and Computer Aided Design Methods, Vol. I1, paper 17, pp. 185–212, SYROM’77, Bucharest, Romania, June 16–21.
6.
Foster
,
D. E.
, and
Pennock
,
G. R.
,
2003
, “
A Graphical Method to Find the Secondary Instantaneous Centers of Zero Velocity for the Double Butterfly Linkage
,”
ASME J. Mech. Des.
,
125
(
2
), June, pp.
268
274
.
7.
Pennock
,
G. R.
, and
Sankaranarayanan
,
H.
,
2003
, “
Path Curvature of a Geared Seven-Bar Mechanism
,”
Mech. Mach. Theory
,
38
(
12
), October, pp.
1345
1361
, Pergamon Press, Ltd., Great Britain.
8.
Rosenauer, N., and Willis, A. H., 1953, Kinematics of Mechanisms, Associated General Publications Pty. Ltd., Sydney, Australia.
9.
Dijksman
,
E. A.
,
1984
, “
Geometric Determination of Coordinated Centers of Curvature in Network Mechanisms Through Linkage Reduction
,”
Mech. Mach. Theory
,
19
(
3
), pp.
289
295
, Pergamon Press, Ltd., Great Britain.
10.
Hartenberg, R. S., and Denavit, J., 1964, Kinematic Synthesis of Linkages, McGraw-Hill Book Co., Inc., New York.
11.
Uicker, J. J., Jr., Pennock, G. R., and Shigley, J. E., 2003, Theory of Machines and Mechanisms, Third Edition, Oxford University Press, Inc., New York.
12.
Pennock, G. R., and Kinzel, E. C., 2003, “The Radius of Curvature of a Coupler Curve of the Single Flier Eight-Bar Linkage,” Proceedings of the 2003 ASME International Design Engineering Technical Conferences and the Computers and Information in Engineering Conference, CD ROM Format, Chicago, Illinois, September 2–6.
13.
Hasan, A., 1999, “A Kinematic Analysis of an Indeterminate Single-Degree-of-Freedom Eight-Bar Linkage,” M.S.M.E. Thesis, School of Mechanical Engineering, Purdue University, West Lafayette, Indiana, December.
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