This paper presents a new family of maximally regular T2R1-type parallel manipulators with bifurcated spatial motion. In each branch, the moving platform has two independent translations (T2) and one rotation (R1) driven by three actuators mounted on the fixed base. The rotation axis is situated in the plane of translation and can bifurcate in two orthogonal directions. This bifurcation occurs in a constraint singularity in which the connectivity between the moving and fixed platforms increases instantaneously, incurring no change in limb connectivity. The Jacobian matrix of the maximally regular solutions presented in this paper is a 3×3 identity matrix in the entire workspace of each branch. This paper presents for the first time a family of maximally regular T2R1-type parallel manipulators with bifurcated spatial motion of the moving platform along with solutions using uncoupled motions.

1.
Gogu
,
G.
, 2008,
Structural Synthesis of Parallel Robots, Part 1: Methodology
,
Springer
,
Dordrecht
, pp.
266
299
.
2.
Hunt
,
K. H.
, 1982, “
Geometry of Robotic Devices
,”
Mechanical Engineering Transactions
,
7
(
4
), pp.
213
220
.
3.
Merlet
,
J. P.
, 2006,
Parallel Robots
,
Springer
,
Dordrecht
, pp.
27
28
.
4.
Kong
,
X.
, and
Gosselin
,
C. M.
, 2005, “
Type Synthesis of 3-DOF PPR-Equivalent Parallel Manipulators Based on Screw Theory and the Concept of Virtual Chain
,”
ASME J. Mech. Des.
0161-8458,
127
, pp.
1113
1121
.
5.
Kong
,
X.
, and
Gosselin
,
C.
, 2007,
Type Synthesis of Parallel Mechanisms
,
Springer-Verlag
,
Berlin
, pp.
125
139
.
6.
Zhang
,
L.
, and
Dai
,
J. S.
, 2009, “
Reconfiguration of Spatial Mechanisms
,”
ASME J. Mech. Rob.
1942-4302,
1
(
1
), p.
011012
.
7.
Sun
,
T.
,
Song
,
Y.
,
Li
,
Y.
, and
Zhang
,
J.
, 2010, “
Workspace Decomposition Based Dimensional Synthesis of a Novel Hybrid Reconfigurable Robot
,”
ASME J. Mech. Rob.
1942-4302,
2
(
3
), p.
031009
.
8.
Gan
,
D.
,
Dai
,
S. J.
, and
Liao
,
Q.
, 2009, “
Mobility Change in Two Types of Metamorphic Parallel Mechanisms
,”
ASME J. Mech. Rob.
1942-4302,
1
(
4
), p.
041007
.
9.
Li
,
Q.
, and
Hervé
,
J. M.
, 2009, “
Parallel Mechanisms With Bifurcation of Schoenflies Motion
,”
IEEE Trans. Rob. Autom.
1042-296X,
25
, pp.
158
164
.
10.
Hervé
,
J. M.
, 1995, “
Design of Parallel Manipulators via the Displacement Group
,”
Proceedings of the Ninth World Congress on the Theory of Machines and Mechanisms
, Milan, Italy, pp.
2079
2082
.
11.
Hervé
,
J. M.
, 1999, “
The Lie Group of Rigid Body Displacements, a Fundamental Tool for Mechanism Design
,”
Mech. Mach. Theory
0094-114X,
34
, pp.
719
730
.
12.
Huynh
,
P.
, and
Hervé
,
J. M.
, 2005, “
Equivalent Kinematic Chains of Three Degrees-of-Freedom Tripod Mechanisms With Planar-spherical Bonds
,”
ASME J. Mech. Des.
0161-8458,
127
, pp.
95
102
.
13.
Angeles
,
J.
, 2004, “
The Qualitative Synthesis of Parallel Manipulators
,”
ASME J. Mech. Des.
0161-8458,
126
, pp.
617
624
.
14.
Lee
,
C. C.
, and
Hervé
,
J. M.
, 2006, “
Pseudo-planar Motion Generators
,”
Advances in Robot Kinematics: Mechanisms and Motion
,
J.
Lenarčič
and
B.
Roth
, eds.,
Springer
,
Dordrecht
, pp.
435
444
.
15.
Rico
,
J. M.
,
Cervantes-Sancez
,
J. J.
,
Tadeo-Chavez
,
A.
,
Perez-Soto
,
G. I.
, and
Rocha-Chavaria
,
J.
, 2006, “
A Comprehensive Theory of Type Synthesis of Fully Parallel Platforms
,”
ASME
Paper No. DETC2006-99070.
16.
Tsai
,
L. -W.
, 1999,
Robot Analysis: The Mechanics of Serial and Parallel Manipulators
,
Wiley
,
New York
, pp.
91
108
.
17.
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.
Stanišić
, eds.,
Kluwer Academic
,
Dordrecht
, pp.
433
440
.
18.
Huang
,
Z.
, and
Li
,
Q. C.
, 2002, “
General Methodology for Type Synthesis of Symmetrical Lower-Mobility Parallel Manipulators and Several Novel Manipulators
,”
Int. J. Robot. Res.
0278-3649,
21
, pp.
131
145
.
19.
Di Gregorio
,
R.
, and
Parenti-Castelli
,
V.
, 1998, “
A Translational 3-dof Parallel Manipulator
,”
Advances in Robot Kinematics: Analysis and Control
,
J.
Lenarčič
and
M.
Husty
, eds.,
Kluwer Academic
,
Dordrecht
, pp.
49
58
.
20.
Gogu
,
G.
, 2004, “
Structural Synthesis of Fully-Isotropic Translational Parallel Robots via Theory of Linear Transformations
,”
Eur. J. Mech. A/Solids
0997-7538,
23
, pp.
1021
1039
.
21.
Gogu
,
G.
, 2004, “
Fully-Isotropic T3R1–Type Parallel Manipulators
,”
On Advances in Robot Kinematics
,
J.
Lenarčič
and
C.
Galletti
, eds.,
Kluwer Academic
,
Dordrecht
, pp.
265
272
.
22.
Gogu
,
G.
, 2006, “
Fully-Isotropic Hexapods
,”
Advances in Robot Kinematics: Mechanisms and Motion
,
J.
Lenarčič
and
B.
Roth
, eds.,
Springer
,
Dordrecht
, pp.
323
330
.
23.
Gogu
,
G.
, 2007, “
Structural Synthesis of Fully-Isotropic Parallel Robots With Schönflies Motions via Theory of Linear Transformations and Evolutionary Morphology
,”
Eur. J. Mech. A/Solids
0997-7538,
26
, pp.
242
269
.
24.
Gogu
,
G.
, 2009, “
Structural Synthesis of Maximally-Regular T3R2-Type Parallel Robots via Theory of Linear Transformations and Evolutionary Morphology
,”
Robotica
0263-5747,
27
, pp.
79
101
.
25.
Gogu
,
G.
, 2009,
Structural Synthesis of Parallel Robots, Part 2: Translational Topologies with Two and Three Degrees of Freedom
,
Springer
,
Dordrecht
, pp.
7
15
.
26.
Gogu
,
G.
, 2005, “
Mobility and Spatiality of Parallel Robots Revisited via Theory of Linear Transformations
,”
Eur. J. Mech. A/Solids
0997-7538,
24
, pp.
690
711
.
27.
Gogu
,
G.
, 2005, “
Mobility of Mechanisms: A Critical Review
,”
Mech. Mach. Theory
0094-114X,
40
, pp.
1068
1097
.
28.
Ionescu
,
T. G.
, 2003, “
Terminology for Mechanisms and Machine Science
,”
Mech. Mach. Theory
0094-114X,
38
, pp.
597
901
.
29.
Gogu
,
G.
, 2005, “
Chebychev–Grubler–Kutzbach’s Criterion for Mobility Calculation of Multi-Loop Mechanisms Revisited via Theory of Linear Transformations
,”
Eur. J. Mech. A/Solids
0997-7538,
24
, pp.
427
441
.
30.
Zlatanov
,
D.
,
Bonev
,
I. A.
, and
Gosselin
,
C. M.
, 2002, “
Constraint Singularities of Parallel Mechanisms
,”
Proceedings of the IEEE International Conference on Robotics and Automation
, Washington, DC, pp.
496
502
.
31.
Gogu
,
G.
, 2008, “
Constraint Singularities and the Structural Parameters of Parallel Robots
,”
Advances in Robot Kinematics
,
J.
Lenarčič
and
P.
Wenger
, eds.,
Springer
,
Dordrecht
, pp.
21
28
.
32.
Wohlhart
,
K.
, 1996, “
Kinematotropic Linkages
,”
Advances in Robot Kinematics
,
J.
Lenarčič
and
V.
Parenti-Castelli
, eds.,
Kluwer Academic
,
Dordrecht
, pp.
359
368
.
33.
Fanghella
,
P.
,
Galletti
.
C.
, and
Giannotti
,
E.
, 2006, “
Parallel Robots That Change Their Group of Motion
,”
J.
Lenarčič
and
B.
Roth
, eds.,
Advances in Robot Kinematics: Mechanisms and Motion
,
Springer
,
Dordrecht
, pp.
49
56
.
34.
Galletti
,
C.
, and
Fanghella
,
P.
, 2001, “
Single-Loop Kinematotropic Mechanisms
,”
Mech. Mach. Theory
0094-114X,
37
, pp.
787
798
.
35.
Gogu
,
G.
, 2009, “
Branching Singularities in Kinematotropic Parallel Mechanisms
,”
Computational Kinematics: Proceedings of the Fifth International Workshop on Computational Kinematics
,
A.
Kecskeméthy
and
A.
Müller
, eds.,
Springer
,
New York
, pp.
341
348
.
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