Abstract

In this paper, a novel 3-UPU (P and U stand for prismatic and universal joints, respectively) parallel mechanism (PM) and its variant PM are proposed. Both of them have two rotational and one translational (2R1T) degrees of freedom (DOFs) without involving any parasitic motion. Mobility analysis shows that the three constraint forces provided by three limbs of the mechanism are located on the same plane and the mobile platform can translate perpendicular to this plane and rotate around any axis on it. Analysis of the mechanism’s motion characteristics demonstrates that the mobile platform outputs either pure rotation or pure translation. Moreover, the rotational axis can be fixed during the rotation process, which means no parasitic motion is involved. The causes of the motion characteristics are analyzed by the combination of an overall Jacobian matrix, a statistical method, and a geometric method. The PMs only need to translate or rotate once to move from the initial configuration to the final configuration, which allows for easy control of speeds. The relationship between mechanism parameters and singularity is analyzed. A speed control method for the PMs is proposed and a prototype is designed and made. Experiments are conducted to verify the determined motion characteristics, the speed control method, and the singularity analysis.

References

References
1.
Terrier
,
M.
,
Dugas
,
A.
, and
Hascoët
,
J. Y.
,
2004
, “
Qualification of Parallel Kinematics Machines in High-Speed Milling on Free Form Surfaces
,”
Int. J. Mach. Tools Manuf.
,
44
(
7–8
), pp.
865
877
. 10.1016/j.ijmachtools.2003.11.003
2.
Weck
,
M.
, and
Staimer
,
D.
,
2002
, “
Parallel Kinematic Machine Tools—Current State and Future Potentials
,”
CIRP Ann. – Manuf. Technol.
,
51
(
2
), pp.
671
683
. 10.1016/S0007-8506(07)61706-5
3.
Cao
,
W.-A.
,
Ding
,
H.
, and
Yang
,
D.
,
2017
, “
A Method for Compliance Modeling of Five Degree-of-Freedom Overconstrained Parallel Robotic Mechanisms With 3T2R Output Motion
,”
ASME J. Mech. Robot.
,
9
(
1
), p.
011011
. 10.1115/1.4035270
4.
Xie
,
F.
, and
Liu
,
X.-J.
,
2015
, “
Design and Development of a High-Speed and High-Rotation Robot With Four Identical Arms and a Single Platform
,”
ASME J. Mech. Robot.
,
7
(
4
), p.
041015
. 10.1115/1.4029440
5.
Siciliano
,
B.
,
1999
, “
Tricept Robot: Inverse Kinematics, Manipulability Analysis and Closed-Loop Direct Kinematics Algorithm
,”
Robotica
,
17
(
4
), pp.
437
445
. 10.1017/S0263574799001678
6.
Liu
,
H. T.
,
Huang
,
T.
,
Zhao
,
X. M.
,
Mei
,
J. P.
, and
Chetwynd
,
D. G.
,
2007
, “
Optimal Design of the TriVariant Robot to Achieve a Nearly Axial Symmetry of Kinematic Performance
,”
Mech. Mach. Theory
,
42
(
12
), pp.
1643
1652
. 10.1016/j.mechmachtheory.2006.12.001
7.
Bi
,
Z. M.
, and
Jin
,
Y.
,
2011
, “
Kinematic Modeling of Exechon Parallel Kinematic Machine
,”
Robot. Comput. Integr. Manuf.
,
27
(
1
), pp.
186
193
. 10.1016/j.rcim.2010.07.006
8.
Wahl
,
J.
,
2000
, “
Articulated Tool Head
,”
DS Technologie Werkzeugmaschinenbau GmbHUS
,
Monschau, Germany
, U.S. Patent No. 2,349,579.
9.
Huang
,
T.
, and
Liu
,
H.
,
2010
, “
Parallel Mechanism Having Two Rotational and One Translational Degrees of Freedom
,”
Tianjin University
,
Tianjin, China
, U.S. Patent No. 7,793,564.
10.
Carretero
,
J. A.
,
Podhorodeski
,
R. P.
,
Nahon
,
M. A.
, and
Gosselin
,
C. M.
,
2000
, “
Kinematic Analysis and Optimization of a New Three Degree-of-Freedom Spatial Parallel Manipulator
,”
ASME J. Mech. Des.
,
122
(
1
), pp.
17
24
. 10.1115/1.533542
11.
Li
,
Q.
,
Chen
,
Z.
,
Chen
,
Q.
,
Wu
,
C.
, and
Hu
,
X.
,
2011
, “
Parasitic Motion Comparison of 3-PRS Parallel Mechanism With Different Limb Arrangements
,”
Rob. Comput. Integr. Manuf.
,
27
(
2
), pp.
389
396
. 10.1016/j.rcim.2010.08.007
12.
Liu
,
X.
,
Wu
,
C.
,
Wang
,
J.
, and
Bonev
,
I.
,
2008
, “
Attitude Description Method of [PP]S Type Parallel Robotic Mechanisms
,”
Chin. J. Mech. Eng.
,
44
(
10
), pp.
19
23
. 10.3901/JME.2008.10.019
13.
Huang
,
Z.
,
Wang
,
J.
, and
Fang
,
Y. F.
,
2002
, “
Analysis of Instantaneous Motions of Deficient-Rank 3-RPS Parallel Manipulators
,”
Mech. Mach. Theory
,
37
(
2
), pp.
229
240
. 10.1016/S0094-114X(01)00075-1
14.
Li
,
Q.
,
Chai
,
X.
,
Chen
,
Q.
, and
Huang
,
Z.
,
2013
, “
Analysis of Rotational Axes of 2-UPR-SPR Parallel Mechanism
,”
J. Mech. Eng.
,
49
(
21
), pp.
62
69
. 10.3901/JME.2013.21.062
15.
Lin
,
R.
,
Guo
,
W.
, and
Gao
,
F.
,
2016
, “
On Parasitic Motion of Parallel Mechanisms
,”
40th Mech. Robot. Conf.
,
Charlotte, NC
,
Aug. 21–24
, Vol.
5B
, p.
V05BT07A077
.
16.
Sun
,
T.
, and
Huo
,
X.
,
2018
, “
Type Synthesis of 1T2R Parallel Mechanisms With Parasitic Motions
,”
Mech. Mach. Theory
,
128
, pp.
412
428
. 10.1016/j.mechmachtheory.2018.05.014
17.
Wang
,
L.
,
Xu
,
H.
,
Guan
,
L.
, and
Zhi
,
Y.
,
2016
, “
A Novel 3-PUU Parallel Mechanism and Its Kinematic Issues
,”
Robot. Comput. Integr. Manuf.
,
42
, pp.
86
102
. 10.1016/j.rcim.2016.05.003
18.
Li
,
Q.
, and
Hervé
,
J. M.
,
2010
, “
1T2R Parallel Mechanisms Without Parasitic Motion
,”
IEEE Trans. Robot.
,
26
(
3
), pp.
401
410
. 10.1109/TRO.2010.2047528
19.
Xie
,
F.
,
Liu
,
X. J.
, and
Li
,
T.
,
2013
, “
A Comparison Study on the Orientation Capability and Parasitic Motions of Two Novel Articulated Tool Heads With Parallel Kinematics
,”
Adv. Mech. Eng.
,
2013
, p.
249103
. 10.1155/2013/249103
20.
Xie
,
F.
,
Liu
,
X. J.
, and
Wang
,
J.
,
2012
, “
A 3-DOF Parallel Manufacturing Module and Its Kinematic Optimization
,”
Robot. Comput. Integr. Manuf.
,
28
(
3
), pp.
334
343
. 10.1016/j.rcim.2011.10.003
21.
Chen
,
Z.
,
Zhang
,
Y.
,
Huang
,
K.
, and
Huang
,
Z.
,
2016
, “
Symmetrical 2R1T Parallel Mechanism Without Parasitic Motion
,”
J. Mech. Eng.
,
52
(
3
), pp.
9
17
. 10.3901/JME.2016.03.009
22.
Chen
,
Z.
,
Cheng
,
D.
,
Zhang
,
Y.
,
Yang
,
Z.
, and
Zhou
,
J.
,
2017
, “
Influence Coefficients and Singularity Analysis of a Novel 3-UPU Parallel Mechanism
,”
ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
Cleveland, OH
,
Aug. 6–9
, p.
V05AT08A054
. 10.1115/DETC2017-68372
23.
Gosselin
,
C.
, and
Angeles
,
J.
,
1990
, “
Singularity Analysis of Closed-Loop Kinematic Chains
,”
IEEE Trans. Robot. Autom.
,
6
(
3
), pp.
281
290
. 10.1109/70.56660
24.
Sefrioui
,
J.
, and
Gosselin
,
C. M.
,
1995
, “
On the Quadratic Nature of the Singularity Curves of Planar Three-Degree-of-Freedom Parallel Manipulators
,”
Mech. Mach. Theory
,
30
(
4
), pp.
533
551
. 10.1016/0094-114X(94)00052-M
25.
Zlatanov
,
D.
,
Fenton
,
R. G.
, and
Benhabib
,
B.
,
1994
, “
Singularity Analysis of Mechanisms and Robots Via a Motion-Space Model of the Instantaneous Kinematics
,”
Proc. 1994 IEEE Int. Conf. Robot. Autom.
,
San Diego, CA
,
May 8–13
, pp.
980
985
.
26.
Zhang
,
Y.
,
Liu
,
H.
, and
Wu
,
X.
,
2009
, “
Kinematics Analysis of a Novel Parallel Manipulator
,”
Mech. Mach. Theory
,
44
(
9
), pp.
1648
1657
. 10.1016/j.mechmachtheory.2009.01.006
27.
Merlet
,
J.-P.
,
1989
, “
Singular Configurations of Parallel Manipulators and Grassmann Geometry
,”
Int. J. Robot. Res.
,
8
(
5
), pp.
45
56
. 10.1177/027836498900800504
28.
Monsarrat
,
B.
, and
Gosselin
,
C. M.
,
2001
, “
Singularity Analysis of a Three-Leg Six-Degree-of-Freedom Parallel Platform Mechanism Based on Grassmann Line Geometry
,”
Int. J. Robot. Res.
,
20
(
4
), pp.
312
326
. 10.1177/02783640122067426
29.
Amine
,
S.
,
Tale Masouleh
,
M.
,
Caro
,
S. P.
,
Wenger
,
P.
, and
Gosselin
,
C. M.
,
2011
, “
Singularity Analysis of the 4-RUU Parallel Manipulator Using Grassmann-Cayley Algebra and Grassmann Geometry
,”
Proc. ASME Des. Eng. Tec. Conf.
,
Washington, DC
,
Aug. 28–31
, pp.
1017
1026
.
30.
Ben-Horin
,
P.
, and
Shoham
,
M.
,
2006
, “
Singularity Condition of Six-Degree-of-Freedom Three-Legged Parallel Robots Based on Grassmann—Cayley Algebra
,”
IEEE Trans. Robot.
,
22
(
4
), pp.
577
590
. 10.1109/TRO.2006.878958
31.
Kanaan
,
D.
,
Wenger
,
P.
, and
Chablat
,
D.
,
2008
, “
Singularity Analysis of Limited-DoF Parallel Manipulators Using Grassmann-Cayley Algebra
,”
11th International Symposium on Advances in Robot Kinematics
,
Batz-sur-Mer, France
,
June 22–26
,
Springer Verlag
, pp.
59
68
.
32.
Ebert-Uphoff
,
I.
,
Lee
,
J. K.
, and
Lipkin
,
H.
,
2002
, “
Characteristic Tetrahedron of Wrench Singularities for Parallel Manipulators With Three Legs
,”
Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci.
,
216
(
1
), pp.
81
94
. 10.1243/0954406021524936
33.
Li
,
Q.
,
Xiang
,
J. N.
,
Chai
,
X.
, and
Wu
,
C.
,
2015
, “
Singularity Analysis of a 3-RPS Parallel Manipulator Using Geometric Algebra
,”
Chin. J. Mech. Eng.
,
28
(
6
), pp.
1204
1212
. 10.3901/CJME.2015.0728.103
34.
Chen
,
X.
,
Liu
,
X. J.
,
Xie
,
F. G.
, and
Sun
,
T.
,
2014
, “
A Comparison Study on Motion/Force Transmissibility of Two Typical 3-DOF Parallel Manipulators: The Sprint Z3 and A3 Tool Heads
,”
Int. J. Adv. Robot. Syst.
,
11
(
1
), pp.
1
10
. 10.5772/56810
35.
Liu
,
X.-J.
,
Wu
,
C.
, and
Wang
,
J.
,
2012
, “
A New Approach for Singularity Analysis and Closeness Measurement to Singularities of Parallel Manipulators
,”
ASME J. Mech. Robot.
,
4
(
4
), p.
041001
. 10.1115/1.4007004
36.
Fang
,
Y.
, and
Tsai
,
L. W.
,
2002
, “
Structure Synthesis of a Class of 4-DoF and 5-DoF Parallel Manipulators With Identical Limb Structures
,”
Int. J. Robot. Res.
,
21
(
9
), pp.
799
810
. 10.1177/0278364902021009314
37.
Chen
,
Z.
,
Cao
,
W.-A.
,
Ding
,
H.
, and
Huang
,
Z.
,
2015
, “
Continuous Motion of a Novel 3-CRC Symmetrical Parallel Mechanism
,”
Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci.
,
230
(
3
), pp.
392
405
.
38.
Joshi
,
S. A.
, and
Tsai
,
L.-W.
,
2002
, “
Jacobian Analysis of Limited-DOF Parallel Manipulators
,”
ASME J. Mech. Des.
,
124
(
2
), pp.
254
258
. 10.1115/1.1469549
39.
Hunt
,
K. H.
,
1973
, “
Constant-Velocity Shaft Couplings: A General Theory
,”
ASME J. Eng. Ind. Trans.
,
95 Ser B
(
2
), pp.
455
464
. 10.1115/1.3438177
40.
Barus
,
C.
,
1900
, “
A Treatise on the Theory of Screws
,”
Science
,
12
(
313
), pp.
1001
1003
. 10.1126/science.12.313.1001
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