The instant centers of velocity (ICs) of most planar mechanisms can be determined as the intersection of the lines of centers, also known as Aronhold–Kennedy lines, along which the ICs of three distinct links in relative motion are located. It is shown how these intersections can be kept track of in matrix form, very suitable to algorithmic implementation on a computer. Solving for the coordinates of the actual instant centers can be also cast in matrix form. Moreover, the singularity and force transmissivity of the mechanism are reflected in the condition numbers of these matrices and the degree of dispersion of the secondary instant centers i.e., the instant centers that cannot be found by inspection.

1.
Hartenberg
,
R. S.
, and
Denavit
,
J.
, 1964,
Kinematic Synthesis of Linkages
,
McGraw-Hill
,
New York
.
2.
Paul
,
B.
, 1979,
Kinematics and Dynamics of Planar Machinery
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
3.
Zypman
,
F. R.
, 2007, “
Instantaneous Center of Rotation and Centrodes: Background and New Examples
,”
Int. J. Mech. Eng. Educ.
0306-4190,
35
, pp.
79
90
.
4.
Hain
,
K.
, 1967,
Applied Kinematics
,
McGraw-Hill
,
New York
.
5.
Tao
,
D. C.
, 1967,
Fundamentals of Applied Kinematics
,
Addison-Wesley
,
Reading, MA
.
6.
Gillespie
,
T. D.
, 1992,
Fundamentals of Vehicle Dynamics
,
SAE International
,
Warrendale, PA
.
7.
Luck
,
K. L.
, and
Modler
,
C. H.
, 1990,
Getriebetechnik. Analyse Synthese Optimirung
,
Springer
,
New York
.
8.
Frankel
,
V. H.
,
Burstein
,
A. H.
, and
Brooks
,
D. B.
, 1971, “
Biomechanics of Internal Derangement of the Knee. Patomechanics as Determined by Analysis of the Instant Center of Motion
,”
The Journal of Bone and Joint Surgery
,
53-A
, pp.
945
977
.
9.
Gilmore
,
B. J.
, and
Cipra
,
R. J.
, 1983, “
An Analytical Method for Computing the Instant Centers, Centrodes, Inflection Circles, and Centers of Curvature of the Centrodes by Successively Grounding Each Link
,”
ASME J. Mech., Transm., Autom. Des.
0738-0666,
105
, pp.
407
414
.
10.
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
, Jun. 16–21, Paper No. 17, Vol.
11
, pp.
185
212
.
11.
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
.
12.
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
, Sept. 13–16, Vol.
47
, pp.
353
359
.
13.
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.
1050-0472,
125
(
2
), pp.
268
274
.
14.
Foster
,
D. E.
, and
Pennock
,
G. R.
, 2005, “
A Graphical Method to Find the Secondary Instantaneous Centers of Zero Velocity for the Double Butterfly Linkage
,”
ASME J. Mech. Des.
1050-0472,
127
(
2
), pp.
249
256
.
15.
Di Gregorio
,
R.
, 2008, “
An Algorithm for Analytically Calculating the Positions of the Secondary Instant Centers of Indeterminate Linkages
,”
ASME J. Mech. Des.
1050-0472,
130
(
4
), p.
042303
.
16.
Chang
,
Y-P.
, and
Her
,
I.
, 2008, “
A Virtual Cam Method for Locating Instant Centers of Kinematically Indeterminate Linkages
,”
ASME J. Mech. Des.
1050-0472,
130
(
6
), p.
062304
.
17.
Cleghorn
,
W. L.
, 2005,
Mechanics of Machines
,
Oxford University Press
,
New York
.
18.
Erdman
,
A. G.
,
Sandor
,
G. N.
, and
Kota
,
S.
, 2001,
Mechanism Design: Analysis and Synthesis
,
4th ed.
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
19.
Norton
,
R. L.
, 2007,
Design of Machinery
,
4th ed.
,
McGraw-Hill
,
New York
.
20.
Uicker
,
J. J.
,
Pennock
,
G. R.
, and
Shigley
,
J. E.
, 2003,
Theory of Machines and Mechanisms
,
3rd ed.
,
Oxford University Press
,
New York
.
21.
Waldron
,
K. J.
, and
Kinzel
,
G. L.
, 2003,
Kinematics, Dynamics, and Design of Machinery
,
2nd ed.
,
Wiley
,
New York
.
22.
Simionescu
,
P. A.
, and
Beale
,
D. G.
, 2002, “
Synthesis and Analysis of the Five-Link Rear Suspension System Used in Automobiles
,”
Mech. Mach. Theory
0094-114X,
37
, pp.
815
832
.
23.
Tsai
,
L-W.
, 2001,
Mechnism Design. Enumeration of Kinematic Structures According to Function
,
CRC
,
Boca Raton, FL
.
24.
Oderfeld
,
J.
, and
Pogorzelski
,
A.
, 1978, “
A Computer Algorithm for Instantaneous Center of Rotation
,”
Mech. Mach. Theory
0094-114X,
13
, pp.
85
93
.
25.
Di Gregorio
,
R.
, 2007, “
A Novel Geometric and Analytic Technique for the Singularity Analysis of One-dof Planar Mechanisms
,”
Mech. Mach. Theory
0094-114X,
42
(
11
), pp.
1462
1483
.
27.
Gosselin
,
C. M.
, and
Angeles
,
J.
, 1990, “
Singularity Analysis of Closed-Loop Kinematic Chains
,”
IEEE Trans. Rob. Autom.
1042-296X,
6
(
3
), pp.
281
290
.
28.
Lin
,
C. C.
, and
Chang
,
W. T.
, 2002, “
The Force Transmissivity Index of Planar Linkage Mechanisms
,”
Mech. Mach. Theory
0094-114X,
37
, pp.
1465
1485
.
29.
Myszka
,
D. H.
,
Murray
,
A. P.
, and
Schmiedeler
,
J. P.
, 2008, “
Singularity Analysis of an Extensible Kinematic Architecture: Assur Class N., Order N-1
,”
ASME J. Mech. Rob.
1942-4302,
1
(
1
), p.
011009
.
30.
Yan
,
H.-S.
, and
Wu
,
L.-I.
, 1989, “
On the Dead-Center Positions of Planar Linkage Mechanisms
,”
ASME J. Mech., Transm., Autom. Des.
0738-0666,
111
, pp.
40
46
.
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