Abstract

This paper derives the kinematically identical manipulators (KIMs) of the 2-RPU + UPR parallel manipulators (PMs) and performs a comparison study among them. Based on the principle for deriving KIMs, ten non-overconstrained and 12 overconstrained KIMs of the 2-RPU + UPR PMs are derived. The 2-RPU + UPR PM and its KIMs has identical kinematics but different constraints. On the basis of motion/force transmission indices, the optimal design of the 2-RPU + UPR PM and its KIMs is carried out and the optimal parameters are obtained. With the optimal parameters and the definition of constraint performance, their constraint performances are compared. The comparison study with the 2-RPU + UPR PM and its KIMs is helpful for obtaining the optimal architectures among them.

References

1.
Neumann
,
K. E.
,
1988
,
Robot
,
U.S. Patent No. 4732525
.
2.
Wahl
,
J.
,
2000
,
Articulated Tool Head
,
WIPO Patent No. WO/2000/025976
.
3.
Li
,
Y.
, and
Xu
,
Q.
,
2007
, “
Kinematic Analysis of a 3-PRS Parallel Manipulator
,”
Rob. Comput.-Integr. Manuf.
,
23
(
4
), pp.
395
408
. 10.1016/j.rcim.2006.04.007
4.
Neumann
,
K. E.
,
2008
, “
Adaptive In-Jig High Load Exechon Machining Technology Assembly, 2008 Aerospace Manufacturing and Automated Fastening Conference and Exhibition
,”
Society of Automotive Engineers Technical Paper Series
,
North Charleston, SC
,
SAE International
, SAE Paper No. 08AMT-0044, pp.
124
135
.
5.
Bi
,
Z. M.
, and
Jin
,
Y.
,
2011
, “
Kinematic Modeling of Exechon Parallel Kinematic Machine
,”
Rob. Comput.-Integr. Manuf.
,
27
(
1
), pp.
186
193
. 10.1016/j.rcim.2010.07.006
6.
Bi
,
Z. M.
, and
Wang
,
L.
,
2012
, “
Energy Modeling of Machine Tools for Optimization of Machine Setups
,”
IEEE Trans. Autom. Sci. Eng.
,
9
(
3
), pp.
607
612
. 10.1109/TASE.2012.2195173
7.
Hu
,
B.
,
Lu
,
Y.
,
Xu
,
J. Y.
, and
Yu
,
J. J.
,
2011
, “
Solving Kinematics for a Novel Over-Constrained 2UPR + UPU Parallel Manipulator, Jixie Gongcheng Xuebao
,”
J. Mech. Eng.
,
47
(
11
), pp.
36
43
. 10.3901/JME.2011.11.036
8.
Hu
,
B.
and
Li
,
B.
,
2016
, “
An Overconstrained PM With Two Rotations and One Translation
,” CN Patent No. ZL 201410215044.6.
9.
Hu
,
B.
, and
Huang
,
Z.
,
2016
, “
Kinetostatic Model of Over-Constrained Lower Mobility Parallel Manipulators
,”
Nonlinear Dyn.
,
86
(
1
), pp.
309
322
. 10.1007/s11071-016-2890-2
10.
Li
,
Q.
, and
Herve
,
J. M.
,
2014
, “
Type Synthesis of 3-DOF RPR-Equivalent Parallel Mechanisms
,”
IEEE Trans. Rob.
,
30
(
6
), pp.
1333
1343
. 10.1109/TRO.2014.2344450
11.
Tang
,
T.
, and
Zhang
,
J.
,
2017
, “
Conceptual Design and Comparative Stiffness Analysis of an Exechon-Like Parallel Kinematic Machine With Lockable Spherical Joints
,”
Int. J. Adv. Rob. Syst.
,
14
(
4
), pp.
1
13
. 10.1177/1729881417724134
12.
Hu
,
B.
,
2016
, “
Kinematically Identical Manipulators for the Exechon Parallel Manipulator and Their Comparison Study
,”
Mech. Mach. Theory
,
103
, pp.
117
137
. 10.1016/j.mechmachtheory.2016.05.001
13.
Ball
,
R. S.
,
1900
,
A Treatise on the Theory of Screws
,
Cambridge University Press
,
Cambridge, UK
.
14.
Yuan
,
M. S. C.
,
Freudenstein
,
F.
, and
Woo
,
L. S.
,
1971
, “
Kinematic Analysis of Spatial Mechanism by Means of Screw Coordinates. Part 2-Analysis of Spatial Mechanisms
,”
J. Manuf. Sci. Eng.
,
93
(
1
), pp.
67
73
. 10.1115/1.3427919
15.
Tsai
,
M. J.
, and
Lee
,
H. W.
,
1994
, “
Generalized Evaluation for the Transmission Performance of Mechanisms
,”
Mech. Mach. Theory
,
29
(
4
), pp.
607
618
. 10.1016/0094-114X(94)90098-1
16.
Chen
,
C.
, and
Angeles
,
J.
,
2007
, “
Generalized Transmission Index and Transmission Quality for Spatial Linkages
,”
Mech. Mach. Theory
,
42
(
9
), pp.
1225
1237
. 10.1016/j.mechmachtheory.2006.08.001
17.
Wang
,
J. S.
,
Wu
,
C.
, and
Liu
,
X. J.
,
2010
, “
Performance Evaluation of Parallel Manipulators: Motion/Force Transmissibility and Its Index
,”
Mech. Mach. Theory
,
45
(
10
), pp.
1462
1476
. 10.1016/j.mechmachtheory.2010.05.001
18.
Liu
,
X. J.
,
Wu
,
C.
, and
Wang
,
J. S.
,
2012
, “
A New Approach for Singularity Analysis and Closeness Measurement to Singularities of Parallel Manipulators
,”
ASME J. Mech. Rob.
,
4
(
4
), p.
041001
. 10.1115/1.4007004
19.
Wang
,
F. B.
,
Chen
,
Q. H.
, and
Li
,
Q. C.
,
2015
, “
Optimal Design of a 2-UPR-RPU Parallel Manipulator
,”
ASME J. Mech. Des.
,
137
(
5
), p.
054501
. 10.1115/1.4029587
20.
Russo
,
M.
,
Ceccarelli
,
M.
, and
Takeda
,
Y.
,
2018
, “
Force Transmission and Constraint Analysis of a 3-SPR Parallel Manipulator. Proceedings of the Institution of Mechanical Engineers
,”
Part C: J. Mech. Eng. Sci.
,
232
(
23
), pp.
4399
4409
. 10.1177/0954406217750190
21.
Wang
,
L. P.
,
Xu
,
H. Y.
, and
Guan
,
L. W.
,
2017
, “
Optimal Design of a 3-PUU Parallel Mechanism With 2R1 T DOFs
,”
Mech. Mach. Theory
,
114
, pp.
190
203
. 10.1016/j.mechmachtheory.2017.03.008
22.
Liang
,
X.
, and
Takeda
,
Y.
,
2019
, “
Transmission Index of a Class of Parallel Manipulators With 3-RS(SR) Primary Structures Based on Pressure Angle and Equivalent Mechanism With 2-SS Chains Replacing RS Chain
,”
Mech. Mach. Theory
,
139
, pp.
359
378
. 10.1016/j.mechmachtheory.2019.04.018
23.
Xie
,
F. G.
,
Liu
,
X. J.
, and
Li
,
T. M.
,
2013
, “
A Comparison Study on the Orientation Capability and Parasitic Motions of Two Novel Articulated Tool Heads With Parallel Kinematics
,”
Adv. Mech. Eng.
, p.
249103
. 10.1155/2013/249103
24.
Chen
,
X.
,
Liu
,
X. J.
, and
Xie
,
F. G.
,
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. Rob. Syst.
,
11
(
1
), pp.
1
10
. 10.5772/57458
25.
Liu
,
X. J.
,
Chen
,
X.
, and
Nahon
,
M.
,
2014
, “
Motion/Force Constrainability Analysis of Lower-Mobility Parallel Manipulators
,”
ASME J. Mech. Rob.
,
6
(
3
), p.
031006
. 10.1115/1.4026632
26.
Gan
,
D. M.
,
Dai
,
J. S.
, and
Dias
,
J.
,
2016
, “
Variable Motion/Force Transmissibility of a Metamorphic Parallel Mechanism With Reconfigurable 3 T and 3R Motion
,”
J. Mech. Rob.
,
8
(
5
), p.
051001
. 10.1115/1.4032409
27.
Hu
,
B.
,
2010
, “
Theoretical Study of Limited-dof Parallel Manipulators and Serial-Parallel Manipulators Based on Constrained Force/Torque
,”
Ph.D. thesis
,
Yanshan University
,
Qinhuangdao, China
.
28.
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
29.
Pullman
,
N. P.
,
1976
,
Matrix Theory and Its Application
,
Academic Press
,
New York
.
30.
Liang
,
D.
,
Song
,
Y.
,
Sun
,
T.
, and
Dong
,
G.
,
2016
, “
Optimum Design of a Novel Redundantly Actuated Parallel Manipulator With Multiple Actuation Modes for High Kinematic and Dynamic Performance
,”
Nonlinear Dyn.
,
83
(
1–2
), pp.
631
658
. 10.1007/s11071-015-2353-1
31.
Sun
,
T.
,
Song
,
Y.
,
Li
,
Y.
, and
Liu
,
L.
,
2010
, “
Dimensional Synthesis of a 3-DOF Parallel Manipulator Based on Dimensionally Homogeneous Jacobian Matrix
,”
Sci. China-Technol. Sci.
,
53
(
1
), pp.
168
174
. 10.1007/s11431-009-0375-y
32.
Bonev
,
I. A.
,
2002
, “
Geometric Analysis of Parallel Mechanisms
,”
Ph.D. thesis
,
Laval University
,
Quebec
.
33.
Liu
,
X. J.
, and
Wang
,
J. S.
,
2007
, “
A New Methodology for Optimal Kinematic Design of Parallel Mechanisms
,”
Mech. Mach. Theory
,
42
(
9
), pp.
1210
1224
. 10.1016/j.mechmachtheory.2006.08.002
34.
Xie
,
F. G.
,
Liu
,
X. J.
, and
Wang
,
J. S.
,
2011
, “
Performance Evaluation of Redundant Parallel Manipulators Assimilating Motion/Force Transmissibility
,”
Int. J. Adv. Rob. Syst.
,
85
(
5
), pp.
113
124
. 10.5772/50904
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