This paper presents graphical techniques to locate the unknown instantaneous centers of zero velocity of planar, single-degree-of-freedom, linkages with kinematic indeterminacy. The approach is to convert a single-degree-of-freedom indeterminate linkage into a two-degree-of-freedom linkage. Two methods are presented to perform this conversion. The first method is to remove a binary link and the second method is to replace a single link with a pair of links connected by a revolute joint. First, the paper shows that a secondary instant center of a two-degree-of-freedom linkage must lie on a unique straight line. Then this property is used to locate a secondary instant center of the single-degree-of-freedom indeterminate linkage at the intersection of two lines. The two lines are obtained from a purely graphical procedure. The graphical techniques presented in this paper are illustrated by three examples of single-degree-of-freedom linkages with kinematic indeterminacy. The examples are a ten-bar linkage with only revolute joints, the single flier eight-bar linkage, and a ten-bar linkage with revolute and prismatic joints.

Keywords:
kinematics, mechanical engineering, Indeterminate Linkages, Instant Centers, Graphical Techniques, Ten-Bar Linkage With All Revolute Joints, Single Flier Eight-Bar Linkage, Ten-Bar Linkage With Revolute and Prismatic Joints
Topics:
Linkages
1.
Hartenberg, R. S., and Denavit, J., 1964, Kinematic Synthesis of Linkages, McGraw-Hill, New York.
2.
Waldron, K. J., and Kinzel, G. L., 1999, Kinematics, Dynamics, and Design of Machinery, Wiley and Sons, New York, pp. 114–133.
3.
Hain, K., 1967, Applied Kinematics, 2nd ed., McGraw-Hill, New York.
4.
Beyer, R., 1963, The Kinematic Synthesis of Mechanisms, McGraw-Hill, New York.
5.
Uicker, J. J., Jr., Pennock, G. R., and Shigley, J. E., 2003, Theory of Machines and Mechanisms, 3rd ed., Oxford University Press, New York.
6.
Erdman, A. G., Sandor, G. N., and Kota, S., 2001, Mechanism Design, 4th ed., Prentice-Hall, Upper Saddle River, NJ, Vol. 1.
7.
Hall, A. S., Jr., 1986, Kinematics and Linkage Design, Waveland, Prospect Heights, IL.
8.
Rosenauer, N., and Willis, A. H., 1953, Kinematics of Mechanisms, Associated General, Sydney, Australia.
9.
Yang
,
A. T.
,
Pennock
,
G. R.
, and
Hsia
,
L. M.
,
1994
, “
Instantaneous Invariants and Curvature Analysis of a Planar Four-Link Mechanism
,”
ASME J. Mech. Des.
,
116
(
4
), pp.
1173
–
1176
.
10.
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
), pp.
10
–
15
.
11.
Yan, H.-S., and Hsu, M.-H., 1992, “An Analytical Method for Locating Velocity Instantaneous Centers,” Proceedings of the 22nd Biennial ASME Mechanisms Conference, Scottsdale, AZ, 13–16 September, 1992, Vol. 47, pp. 353–359.
12.
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
), pp.
268
–
274
.
13.
Klein, A. W., 1917, Kinematics of Machinery, McGraw-Hill, New York.
14.
Pennock, G. R., and Sankaranarayanan, H., 2003, “Path Curvature of a Geared Seven-Bar Mechanism,” Mechanism and Machine Theory, The Scientific Journal of the International Federation for the Theory of Machines and Mechanisms, Pergamon, Oxford, Vol. 38, pp. 1345–1361.
15.
Pennock, G. R., and Raje, N. N., 2004, “Curvature Theory for the Double Flier Eight-Bar Linkage,” Mechanism and Machine Theory, The Scientific Journal of the International Federation for the Theory of Machines and Mechanisms, Pergamon, Oxford, Vol. 39, pp. 665–679.
16.
Foster
,
D. E.
, and
Cipra
,
R. J.
,
2002
, “
An Automatic Method for Finding the Assembly Configurations of Planar Non-Single-Input-Dyadic Mechanisms
,”
ASME J. Mech. Des.
,
124
(
1
), pp.
58
–
67
.
17.
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, IL, 2–6 September, 2003.
18.
Pennock
,
G. R.
, and
Kinzel
,
E. C.
,
2004
, “
Path Curvature of the Single Flier Eight-Bar Linkage
,”
ASME J. Mech. Des.
,
126
(
3
), pp.
268
–
274
.
19.
Crossley, F. R. E., 1965, “The Permutations of Kinematic Chains of Eight Members or Less From the Graph-Theoretic Viewpoint,” Developments in Theoretical and Applied Mechanics, W. A. Shaw, ed., Vol. 2. (Also appeared in the Proceedings of the Second Southeastern Conference on Theoretical and Applied Mechanics, Atlanta, GA, Mar. 5–6, 1964, pp. 467–486.)
20.
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, SYROM ’77, Bucharest, Romania, 16–21 June, 1977, Vol. 11, paper 17, pp. 185–212.
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