The unified formulation of dimensional synthesis of Stephenson linkages for motion generation is the subject of this paper. Burmester theory is applied to the six-bar linkage, which leads to a unified formulation applicable for all three types of Stephenson linkages. This is made possible by virtue of parameterized position vectors, which simplify the formulation of synthesis equations. A design example is included to demonstrate the application of the method developed.

References

References
1.
Shen
,
Q.
,
Lee
,
W.-T.
,
Russell
,
K.
, and
Sodhi
,
R. S.
,
2008
, “
On Motion Generation of Watt I Mechanisms for Mechanical Finger Design
,”
Trans. CSME
,
32
(
3–4
), pp.
411
421
.
2.
McLarnan
,
C. W.
,
1963
, “
Synthesis of Six-Link Plane Mechanisms by Numerical Analysis
,”
ASME J. Eng. Ind.
,
85
(
1
), pp.
5
10
.
3.
Kim
,
H. S.
,
Hamid
,
S.
, and
Soni
,
A. H.
,
1972
, “
Synthesis of Six-Link Mechanisms for Point Path Generation
,”
J. Mech.
,
6
(
4
), pp.
447
461
.
4.
Soh
,
G. S.
, and
McCarthy
,
J. M.
,
2008
, “
The Synthesis of Six-Bar Linkages as Constrained Planar 3R Chains
,”
Mech. Mach. Theory
,
43
(
2
), pp.
160
170
.
5.
Shiakolas
,
P. S.
,
Koladiya
,
D.
, and
Kebrle
,
J.
,
2005
, “
On the Optimum Synthesis of Six-Bar Linkages Using Differential Evolution and the Geometric Centroid of Precision Positions Technique
,”
Mech. Mach. Theory
,
40
(
3
), pp.
319
335
.
6.
Todorov
,
T. S.
,
1997
, “
Synthesis of Watt's Six-Link Mechanism for Manipulation Action in Relative Space
,”
Mech. Mach. Theory
,
32
(
5
), pp.
559
568
.
7.
Dong
,
H.
, and
Wang
,
D.
,
2007
, “
New Approach for Optimum Synthesis of Six-Bar Dwell Mechanisms by Adaptive Curve Fitting
,”
Twelfth World Congress in Mechanism and Machine Science
(
IFToMM 2007
), Besançon, France, June 17–21, pp.
17
21
.
8.
Liu
,
Y.
, and
McPhee
,
J.
,
2007
, “
Automated Kinematic Synthesis of Planar Mechanisms With Revolute Joints
,”
Mech. Based Des. Struct. Mach.
,
35
(
4
), pp.
405
445
.
9.
Bulatović
,
R. R.
, and
Dornević
,
S. R.
,
2012
, “
Optimal Synthesis of a Path Generator Six-Bar Linkage
,”
J. Mech. Sci. Technol.
,
26
(
12
), pp.
4027
4040
.
10.
Kinzel
,
E. C.
,
Schmiedeler
,
J. P.
, and
Pennock
,
G. R.
,
2007
, “
Function Generation With Finitely Separated Precision Points Using Geometric Constraint Programming
,”
ASME J. Mech. Des.
,
129
(
11
), pp.
1185
1190
.
11.
Hwang
,
W. M.
, and
Chen
,
Y. J.
,
2010
, “
Defect-Free Synthesis of Stephenson-II Function Generators
,”
ASME J. Mech. Rob.
,
2
(
4
), p.
041012
.
12.
Mirth
,
J. A.
, and
Chase
,
T. R.
,
1995
, “
Circuit Rectification for Four Precision Position Synthesis of Stephenson Six-Bar Linkages
,”
ASME J. Mech. Des.
,
117
(
4
), pp.
644
646
.
13.
Ting
,
K. L.
, and
Dou
,
X.
,
1996
, “
Classification and Branch Identification of Stephenson Six-Bar Chains
,”
Mech. Mach. Theory
,
31
(
3
), pp.
283
295
.
14.
Plecnik
,
M.
,
McCarthy
,
J. M.
, and
Wampler
,
C. W.
,
2014
, “
Kinematic Synthesis of a Watt I Six-Bar Linkage for Body Guidance
,”
Advances in Robot Kinematics
,
Springer
,
Cham, Switzerland
, pp.
317
325
.
15.
McCarthy
,
J. M.
, and
Soh
,
G. S.
,
2011
,
Geometric Design of Linkages
,
Springer
,
New York
.
16.
Hunt
,
K. H.
,
1978
,
Kinematic Geometry of Mechanisms
,
Oxford University Press
,
New York
.
17.
Chiang
,
C. H.
,
1988
,
Kinematics of Spherical Mechanism
,
Cambridge University Press
,
Cambridge, UK
.
18.
Bai
,
S.
, and
Angeles
,
J.
,
2012
, “
A Robust Solution of the Spatial Burmester Problem
,”
ASME J. Mech. Rob.
,
4
(
3
), p.
031003
.
19.
Bottema
,
O.
, and
Roth
,
B.
,
1979
,
Theoretical Kinematics
,
North-Holland
,
New York
.
20.
Riva
,
R.
,
1981
, “
Synthesis of Stephenson's Six-Bar Linkages by an Interactive Technique
,”
Meccanica
,
16
(
3
), pp.
157
166
.
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