PPR-equivalent parallel manipulators (PMs) are a class of 3-DOF PMs with great application potential. They are indeed the parallel counterparts of the 3-DOF PPR serial robots, in which the moving platform can rotate arbitrarily about an axis undergoing a planar translation. This paper deals with the type synthesis of 3-DOF PPR-equivalent PMs. At first, virtual chains are introduced to represent the motion patterns of 3-DOF motions and relevant results from screw theory are recalled. A method is then proposed for the type synthesis of 3-DOF PPR-equivalent PMs. Using the proposed approach, the type synthesis of 3-DOF PPR-equivalent PMs is performed in three steps. In addition to all the 3-DOF PPR-equivalent parallel kinematic chains and 3-DOF PPR-equivalent PMs proposed in the literature, a number of new 3-DOF PPR-equivalent parallel kinematic chains and 3-DOF PPR-equivalent PMs are identified. It is also found that there are no PPR-equivalent PMs with identical type of legs. The type synthesis of PPR-equivalent PMs is well solved using the proposed approach. The characteristic of the proposed approach is that the type synthesis of PPR-equivalent parallel kinematic chains is reduced to the type synthesis of 3-DOF single-loop kinematic chains and thus easy to perform.

1.
Hunt
,
K. H.
, 1983, “
Structural Kinematics of In-Parallel-Actuated Robot-Arms
,”
ASME J. Mech., Transm., Autom. Des.
0738-0666,
105
(
4
), pp.
705
712
.
2.
Karouia
,
M.
, and
Hervé
,
J. M.
, 2002, “
A Family of Novel Orientational 3-DOF Parallel Robots
,”
Proceedings of RomanSy’2002
,
Udine
, Italy, pp.
359
368
.
3.
Kong
,
X.
, and
Gosselin
,
C. M.
, 2004, “
Type Synthesis of 3-DOF Spherical Parallel Manipulators Based on Screw Theory
,”
ASME J. Mech. Des.
1050-0472,
126
(
1
), pp.
101
108
.
4.
Hervé
,
J. M.
, and
Sparacino
,
F.
, 1991, “
Structural Synthesis of Parallel Robots Generating Spatial Translation
,” in
Proceedings of the Fifth International Conference on Advanced Robotics
,
Pisa
, Italy, Vol.
1
, pp.
808
813
.
5.
Frisoli
,
A.
,
Checcacci
,
D.
,
Salsedo
,
F.
, and
Bergamasco
,
M.
, 2000, “
Synthesis by Screw Algebra of Translating In-Parallel Actuated Mechanisms
,”
Advances in Robot Kinematics
,
J.
Lenarčič
and
M. M.
Stanišič
, eds.,
Kluwer Academic
, Dordrecht, pp.
433
440
.
6.
Kong
,
X.
, and
Gosselin
,
C. M.
, 2001, “
Generation of Parallel Manipulators With Three Translational Degrees of Freedom Based on Screw Theory
,” in
Proceedings of 2001 CCToMM Symposium on Mechanisms, Machines and Mechatronics
,
Saint-Hubert
, Montreal, Canada (available at http://www.cim.mcgill.ca/~alexvit/SM3/Papers/M3–01-012.pdfhttp://www.cim.mcgill.ca/~alexvit/SM3/Papers/M3–01-012.pdf)
7.
Huang
,
Z.
, and
Li
,
Q.-C.
, 2002, “
General Methodology for the Type Synthesis of Lower-Mobility Symmetrical Parallel Manipulators and Several Novel Manipulators
,”
Int. J. Robot. Res.
0278-3649,
21
(
2
), pp.
131
145
.
8.
Jin
,
Q.
, and
Yang
,
T.-L.
, 2004, “
Theory for Topology Synthesis of Parallel Manipulators and its Application to Three-Dimension-Translation Parallel Manipulators
,”
ASME J. Mech. Des.
1050-0472,
126
(
4
), pp.
625
639
.
9.
Yang
,
T.-L.
, 2004,
Topology Structure Design of Robot Mechanisms
(in Chinese),
China Machine Press
, Beijing.
10.
Carricato
,
M.
, and
Parenti-Castelli
,
V.
, 2003, “
A Family of 3-DOF Translational Parallel Manipulators
,”
ASME J. Mech. Des.
1050-0472,
125
(
2
), pp.
302
307
.
11.
Kim
,
D.
, and
Chung
,
W. K.
, 2003, “
Kinematic Condition Analysis of Three-DOF Pure Translational Parallel Manipulators
,”
ASME J. Mech. Des.
1050-0472,
125
(
2
), pp.
323
331
.
12.
Kong
,
X.
, and
Gosselin
,
C. M.
, 2004, “
Type Synthesis of 3-DOF Translational Parallel Manipulators Based on Screw Theory
,”
ASME J. Mech. Des.
1050-0472,
126
(
1
), pp.
83
92
.
13.
Fang
,
Y.
, and
Tsai
,
L.-W.
, 2004, “
Analytical Identification of Limb Structures for Translational Parallel Manipulators
,”
J. Rob. Syst.
0741-2223,
21
(
5
), pp.
209
218
.
14.
Hunt
,
K. H.
, 1973, “
Constant-Velocity Shaft Couplings: A General Theory
,”
ASME J. Eng. Ind.
0022-0817,
95B
, pp.
455
464
.
15.
Liu
,
X. J.
,
Wang
,
J.
,
Gao
,
F.
, and
Wang
,
L.-P.
, 2001, “
On the Analysis of a New Spatial Three-Degrees-of-Freedom Parallel Manipulator
,”
IEEE Trans. Rob. Autom.
1042-296X,
17
(
6
), pp.
959
968
.
16.
Huang
,
Z.
, and
Fang
,
Y. F.
, 1996, “
Kinematic Characteristics Analysis of 3-DOF In-Parallel Actuated Pyramid Mechanisms
,”
Mech. Mach. Theory
0094-114X,
31
(
8
), pp.
1009
1018
.
17.
Kong
,
X.
, 1999, “
Detection of Input Interference in Spatial Linkages
,”
Journal of Mechanical Transmission (in Chinese)
,
23
(
4
), pp.
23
25
.
18.
Agrawal
,
S. K.
, 1990, “
Rate Kinematics of In-Parallel Manipulators Systems
,” in
Proceedings of the 1990 IEEE International Conference on Robotics and Automation
,
Cincinnati
, USA, Vol.
1
, pp.
104
109
.
19.
Huang
,
Z.
, and
Zhao
,
T. S.
, 2000, “
Theory and Application of Selecting Components of Spatial Mechanisms
,”
Chin. J. Mech. Eng.
0577-6686,
36
(
10
), pp.
81
85
.
20.
Hunt
,
K. H.
, 1978,
Kinematic Geometry of Mechanisms
,
Cambridge University Press
, Cambridge.
21.
Tsai
,
L.-W.
, 1999,
Robot Analysis: The Mechanics of Serial and Parallel Manipulators
,
Wiley
, New York.
22.
Kumar
,
V.
,
Waldron
,
K. J.
,
Chrikjian
,
G.
, and
Lipkin
,
H.
, 2000,
Applications of screw system system theory and Lie theory to spatial kinematics: A Tutorial
, 2000 ASME Design Engineering Technical Conferences, Baltimore, USA.
23.
Davidson
,
J. K.
, and
Hunt
,
K. H.
, 2004,
Robots and Screw Theory: Applications of Kinematics and Statics to Robotics
,
Oxford University Press
, Oxford.
24.
Zlatanov
,
D.
,
Bonev
,
I.
, and
Gosselin
,
C. M.
, 2002, “
Constraint Singularities of Parallel Mechanisms
,” in
Proceedings of the 2002 IEEE International Conference on Robotics and Automation
, Washington, D.C., pp.
496
502
.
25.
Gao
,
F.
,
Li
,
W.
,
Zhao
,
X.
,
Jin
,
Z.
, and
Zhao
,
H.
, 2002, “
New Kinematic Structures for 2-, 3-, 4-, and 5-DOF Parallel Manipulator Designs
,”
Mech. Mach. Theory
0094-114X,
37
(
11
), pp.
1395
1411
.
26.
Kong
,
X.
, and
Gosselin
,
C. M.
, 2004, “
Type Synthesis of 3-DOF Translational Parallel Manipulators Based on Screw Theory and a Virtual Joint
,” in
Proceedings of the 15th CISM-IFToMM Symposium on Robot Design, Dynamics and Control
, Saint-Hubert, Montreal, Canada. No. Rom-04–06.
You do not currently have access to this content.