This paper focuses on the problem of synthesis of spatial four-bar linkages of the RCCC type for rigid-body guidance with four given poses, R denoting a revolute, C a cylindrical kinematic pair. While synthesis equations for CC and RC dyads are available in the literature, the synthesis of spatial RCCC four-bar linkages requires special attention, due to its asymmetric topology. We revisit the problem to cope robustly with the asymmetry, namely, the approximate nature of the RC dyad and the infinity of exact solutions of the CC dyad for the number of given poses. Our approach includes a robust formulation of the synthesis of CC dyads, for the determination of axis-congruences. Moreover, we formulate a uniform synthesis equation, which enables us to treat both RC and CC dyads, with properly selected constraints for both cases. Two design examples are included.

References

References
1.
Pérez
,
A.
, and
McCarthy
,
J. M.
,
2003
, “
Dimensional Synthesis of Bennett Linkages
,”
ASME J. Mech. Des.
,
125
(
1
), pp.
98
104
.10.1115/1.1539507
2.
Brunnthaler
,
K.
,
Schrocker
,
H.
, and
Husty
,
M.
,
2005
, “
A New Method for the Synthesis of Bennett Mechanisms
,”
CK2005 International Workshop on Computational Kinematics
, Cassino, Italy, May 4–6.
3.
Tsai
,
L. W.
, and
Roth
,
B.
,
1972
, “
Design of Dyads With Helical, Cylindrical, Spherical, Revolute and Prismatic Joints
,”
Mech. Mach. Theory
,
7
(
1
), pp.
85
102
.10.1016/0094-114X(72)90019-5
4.
Jamalov
,
R. I.
,
Litvin
,
F. L.
, and
Roth
,
B.
,
1984
, “
Analysis and Design of RCCC Linkages
,”
Mech. Mach. Theory
,
19
(
4–5
), pp.
397
407
.10.1016/0094-114X(84)90098-3
5.
Innocenti
,
C
.,
1995
, “
Polynomial Solution of the Spatial Burmester Problem
,”
ASME J. Mech. Des.
,
117
(
1
), pp.
64
68
.10.1115/1.2826118
6.
Larochelle
,
P. M.
,
1995
, “
On the Design of Spatial 4C Mechanisms for Rigid-Body Guidance Through 4 Positions
,”
ASME Design Engineering Technical Conferences
, Boston, MA, Sept. 17–20, pp.
825
832
.
7.
Wampler
,
C. W.
,
Morgan
,
A. P.
, and
Sommese
,
A. J.
,
1990
, “
Numerical Continuation Methods for Solving Polynomial Systems Arising in Kinematics
,”
ASME J. Mech. Des.
,
112
(
1
), pp.
59
68
.10.1115/1.2912579
8.
Murray
,
A.
, and
McCarthy
,
J. M.
,
1994
, “
Five Position Synthesis of Spatial CC Dyads
,” ASME Mechanisms Conference, Minneapolis, MN, Sept. 11–14, pp.
143
152
.
9.
Huang
,
C.
,
Kuo
,
W.
, and
Ravani
,
B.
,
2010
, “
On the Regulus Associated With the General Displacement of a Line and Its Application in Determining Displacement Screws
,”
ASME J. Mech. Rob.
,
2
(
4
), p.
041013
.10.1115/1.4001729
10.
Bai
,
S.
, and
Angeles
,
J.
,
2012
, “
A Robust Solution of the Spatial Burmester Problem
,”
ASME J. Mech. Rob.
,
4
(
3
), p.
031003
.10.1115/1.4006658
11.
McCarthy
,
J. M.
, and
Soh
,
G. S.
,
2011
,
Geometric Design of Linkages
,
Springer
,
New York
.
12.
Martínez
,
J. R.
, and
Duffy
,
J.
,
1993
, “
The Principle of Transference: History, Statement and Proof
,”
Mech. Mach. Theory
,
28
(
1
), pp.
165
177
.10.1016/0094-114X(93)90055-Z
13.
Pottmann
,
H.
, and
Wallner
,
J.
,
2001
,
Computational Line Geometry
,
Springer Verlag
,
Berlin
.
14.
Tsai
,
L. W.
, and
Roth
,
B.
,
1973
, “
Incompletely Specified Displacements: Geometry and Spatial Linkage Synthesis
,”
ASME J. Manuf. Sci. Eng.
,
95
(
2
), pp.
603
611
.10.1115/1.3438197
15.
Angeles
,
J.
,
2002
,
Fundamentals of Robotic Mechanical Systems
,
Springer-Verlag
,
New York
.
16.
Chen
,
C.
,
Bai
,
S.
, and
Angeles
,
J.
,
2008
, “
The Synthesis of Dyads With One Prismatic Joint
,”
ASME J. Mech. Des.
,
130
(
3
), p.
034501
.10.1115/1.2829979
17.
Angeles
,
J.
,
2012
, “
MECH541 Kinematic Synthesis Lecture Notes
,”
Department of Mechanical Engineering, McGill University
,
Montreal, QC
.
18.
Chiang
,
C. H.
,
1988
,
Kinematics of Spherical Mechanism
,
Cambridge University Press
,
Cambridge
, UK.
19.
Nash
,
S.
, and
Sofer
,
A.
,
1996
,
Linear and Nonlinear Programming
,
The McGraw-Hill Companies, Inc.
,
New York
.
20.
Al-Widyan
,
K.
, and
Angeles
,
J.
,
2012
, “
The Kinematic Synthesis of a Robust RCCC Mechanism for Pick-and-Place Operations
,”
ASME
DETC2012-70878.10.1115/DETC2012-70878
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