To discover single-degree-of-freedom (DOF) single-loop overconstrained mechanisms is still an open problem. This paper deals with the type synthesis of single DOF single-loop overconstrained 6RMCTs (6R spatial mechanisms for circular translation). These mechanisms provide alternatives to planar parallelograms and are also associated with self-motion of several translational parallel mechanisms. 6RMCTs are to be obtained using a construction approach in combination with the approaches to the type synthesis of parallel mechanisms. By imposing certain conditions on the hybrid overconstrained 6R (plano-spherical, plano-Bennett, double-spherical, and spherico-Bennett) mechanisms, Bricard plane symmetric mechanism, and Bricard line symmetric mechanism, six special cases of 6RMCTs are obtained. By combining planar parallelograms with these special mechanisms, the general cases of 6RMCTs are then constructed. Finally, 4R2H, 2R4H, and 6H mechanisms for circular translation are obtained from the above 6RMCTs by replacing one or more pairs of R (revolute) joints with parallel axes each with a pair of H (helical) joints with parallel axes and the same pitch. This work contributes to the research on overconstrained six-bar mechanisms and further reveals that the research areas of parallel mechanisms and single-loop overconstrained mechanisms are closely related.

References

References
1.
Waldron
,
K. J.
,
1968
, “
Hybrid Overconstrained Linkages
,”
J. Mech.
,
3
(2), pp.
73
78
.10.1016/0022-2569(68)90016-5
2.
Baker
,
J. E.
,
1979
, “
The Bennett, Goldberg and Myard Linkages—In Perspective
,”
Mech. Mach. Theory
,
14
(4), pp.
239
253
.10.1016/0094-114X(79)90011-9
3.
Mavroidis
,
C.
, and
Roth
,
B.
,
1995
, “
Analysis of Overconstrained Mechanisms
,”
ASME J. Mech. Des.
,
117
(
1
), pp.
69
74
.10.1115/1.2826119
4.
Dietmaier
,
P.
,
1995
, “
A New 6R Space Mechanism
,”
9th World Congress on the Theory of Machines and Mechanisms
, Milano, Italy, August 29–September 5, Vol.
1
, pp.
52
56
.
5.
Wohlhart
,
K.
,
1991
, “
Merging Two General Goldberg 5R Linkages to Obtain a New 6R Space Mechanism
,”
Mech. Mach. Theory
,
26
(
2
), pp.
659
668
.10.1016/0094-114X(91)90028-3
6.
Six
,
K.
, and
Kecskeméthy
,
A.
,
1999
, “
Steering Properties of a Combined Wheeled and Legged Striding Excavator
,”
10th World Congress on the Theory of Machines and Mechanisms
, Oulu, Finland, June 20–24, Vol.
1
, pp.
135
140
.
7.
Zsombor-Murray
,
P. J.
, and
Gfrerrer
,
A.
,
2002
, “
‘Robotrac’ Mobile 6R Closed Chain
,”
CSME Forum 2002
, Kingston, Canada, May 21–24, Paper No. 02-05
8.
Baker
,
J. E.
,
2003
, “
Overconstrained Six-Bars With Parallel Adjacent Joint-Axes
,”
Mech. Mach. Theory
,
38
(
2
), pp.
103
117
.10.1016/S0094-114X(02)00097-6
9.
Chen
,
Y.
, and
You
,
Z.
,
2008
, “
An Extended Myard Linkage and Its Derived 6R Linkage
,”
ASME J. Mech. Des.
,
130
(
5
), p.
052301
.10.1115/1.2885506
10.
Baker
,
J. E.
,
2010
, “
Using the Single Reciprocal Screw to Confirm Mobility of a Six-Revolute Linkage
,”
Proc. Inst. Mech. Eng.
,
224
(
10
), pp.
2247
2255
.10.1243/09544062JMES2062
11.
Pfurner
,
M.
,
2012
, “
A New Family of Overconstrained 6R-Mechanisms
,”
Proceedings of EUCOMES 08
,
M.
Ceccarelli
, ed.,
Springer
,
Dordrecht, Netherlands
, pp.
117
124
.10.1007/978-1-4020-8915-2_15
12.
Hervé
,
J. M.
,
2011
, “
A New Four-Bar Linkage Completing Delassus' Findings
,” Trans. Can. Soc. Mech. Eng.,
35
(
1
), pp.
57
62
. Available at http://www.tcsme.org/Papers/Vol35/Vol35No1Paper4.pdf
13.
Cui
,
L.
, and
Dai
,
J. S.
,
2011
, “
Axis Constraint Analysis and Its Resultant 6R Double-Centered Overconstrained Mechanisms
,”
ASME J. Mech. Rob.
,
3
(
3
), p.
031004
.10.1115/1.4004225
14.
Hegedüs
,
G.
,
Schicho
,
J.
, and
Schröcker
,
H.-P.
,
2012
, “
Construction of Overconstrained Linkages by Factorization of Rational Motions
,”
Latest Advances in Robot Kinematics
,
J.
Lenarčič
, and
M.
Husty
, eds.,
Springer
,
Dordrecth, Netherlands
, pp.
213
220
.10.1007/978-94-007-4620-6_27
15.
Chen
,
Y.
, and
You
,
Z.
,
2012
, “
Spatial Overconstrained Linkage—The Lost Jade
,”
Explorations in the History of Machines & Mechanisms
,
T.
Koetsier
, and
M.
Ceccarelli
, eds.,
Springer
,
Dordrecht, Netherlands
, pp.
535
550
.10.1007/978-94-007-4132-4_37
16.
Kong
,
X.
, and
Gosselin
,
C.
,
2007
,
Type Synthesis of Parallel Mechanisms
,
Springer
,
Berlin
.10.1007/978-3-540-71990-8
17.
Kong
,
X.
, and
Gosselin
,
C.
,
2004
, “
Type Synthesis of Three-Degree-of- Freedom Spherical Parallel Manipulators
,”
Int. J. Rob. Res.
,
23
(
3
), pp.
237
245
.10.1177/0278364904041562
18.
Kong
,
X.
, and
Yang
,
T.-L.
,
1996
, “
Dimensional Type Synthesis and Special Configuration of Analytical 6-SPS Parallel Manipulators
,” High-Tech Letters (in Chinese),
6
, pp.
17
20
. Available at http://www.cqvip.com/QK/97187X/199606/2297788.html
19.
Li
,
Z.
, and
Schicho
,
J.
,
2013
, “
Classification of Angle-Symmetric 6R Linkages
,”
Mech. Mach. Theory
,
70
, pp.
372
379
.10.1016/j.mechmachtheory.2013.08.002
20.
Li
,
Z.
, and
Schicho
,
J.
,
2014
, “
Three Types of Parallel 6R Linkages
,”
Computational Kinematics
,
F.
Thomas
, and
A.
Perez Gracia
, eds.,
Springer
,
Dordrecht, Netherlands
, pp.
111
119
.10.1007/978-94-007-7214-4_13
21.
Kong
,
X.
, and
Huang
,
C.
,
2009
, “
Type Synthesis of Single-DOF Single-Loop Mechanisms With Two Operation Modes
,” ASME/IFToMM International Conference on Reconfigurable Mechanisms and Robots (ReMAR 2009), London, June 22–24, pp.
136
141
.
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