Abstract

The kinematics and dynamics of n(3RRlS) reconfigurable series–parallel manipulators (RSPMs) are the theoretical foundations for capturing noncooperative targets in space. In this study, a unified kinematic and dynamic modeling method of n(3RRlS) RSPMs is proposed based on geometric constraints, the vector method, recursive and inductive methods, and the principle of recursive virtual power, and the kinematic and dynamic modeling progress has clear concepts, unified format, and fast calculation. Then, the theoretical and simulated results of the 3RRlS reconfigurable series–parallel manipulator (RPM) and 3(3RRlS) RSPM are compared verifying the correctness of the derived kinematic and dynamic models. Finally, the reconfiguration, position accuracy, and deformation measurement experiments of the two-driven-unit 3RRlS RPM and 3(3RRlS) RSPM are carried out, and the results show that the 3(3RRlS) RSPM has the advantages of high folding ratio, motion uncoupling, and stiffness improvement.

References

1.
Deng
,
Z.
,
Huang
,
H.
,
Li
,
B.
, and
Liu
,
R.
,
2011
, “
Synthesis of Deployable/Foldable Single Loop Mechanisms With Revolute Joints
,”
ASME J. Mech. Rob.
,
3
(
3
), p.
031006
.
2.
Zhang
,
X.
,
Nie
,
R.
,
Chen
,
Y.
, and
He
,
B.
,
2021
, “
Deployable Structures: Structural Design and Static/Dynamic Analysis
,”
J. Elasticity
,
146
(
2
), pp.
199
235
.
3.
Liu
,
H.
,
Huang
,
T.
,
Chetwynd
,
D. G.
, and
Kecskeméthy
,
A.
,
2017
, “
Stiffness Modeling of Parallel Mechanisms at Limb and Joint/Link Levels
,”
IEEE Trans. Rob.
,
33
(
3
), pp.
734
741
.
4.
Jin
,
X.
,
Fang
,
Y.
, and
Zhang
,
D.
,
2019
, “
Design of a Class of Generalized Parallel Mechanisms With Large Rotational Angles and Integrated End-Effectors
,”
Mech. Mach. Theory
,
134
, pp.
117
134
.
5.
Wang
,
R.
,
Song
,
Y.
, and
Dai
,
J. S.
,
2021
, “
Reconfigurability of the Origami-Inspired Integrated 8R Kinematotropic Metamorphic Mechanism and Its Evolved 6R and 4R Mechanisms
,”
Mech. Mach. Theory
,
161
, p.
104245
.
6.
Nurahmi
,
L.
, and
Gan
,
D.
,
2020
, “
Reconfiguration of a 3-(rR) PS Metamorphic Parallel Mechanism Based on Complete Workspace and Operation Mode Analysis
,”
ASME J. Mech. Rob.
,
12
(
1
), p.
011002
.
7.
Ye
,
W.
,
Chai
,
X.
, and
Zhang
,
K.
,
2020
, “
Kinematic Modeling and Optimization of a New Reconfigurable Parallel Mechanism
,”
Mech. Mach. Theory
,
149
, p.
103850
.
8.
Joshi
,
S. A.
, and
Tsai
,
L. W.
,
2002
, “
Jacobian Analysis of Limited-DOF Parallel Manipulators
,”
ASME J. Mech. Des.
,
124
(
2
), pp.
254
258
.
9.
Rico
,
J. M.
,
Gallardo
,
J.
, and
Duffy
,
J.
,
1999
, “
Screw Theory and Higher Order Kinematic Analysis of Open Serial and Closed Chains
,”
Mech. Mach. Theory
,
34
(
4
), pp.
559
586
.
10.
Rico
,
J. M.
,
Gallardo
,
J.
, and
Ravani
,
B.
,
2003
, “
Lie Algebra and the Mobility of Kinematic Chains
,”
J. Rob. Syst.
,
20
(
8
), pp.
477
499
.
11.
Gallardo
,
J.
,
Rico
,
J. M.
,
Frisoli
,
A.
,
Checcacci
,
D.
, and
Bergamasco
,
M.
,
2003
, “
Dynamics of Parallel Manipulators by Means of Screw Theory
,”
Mech. Mach. Theory
,
38
(
11
), pp.
1113
1131
.
12.
Gan
,
D.
,
Dai
,
J. S.
,
Dias
,
J.
, and
Seneviratne
,
L.
,
2013
, “
Unified Kinematics and Singularity Analysis of a Metamorphic Parallel Mechanism With Bifurcated Motion
,”
ASME J. Mech. Rob.
,
5
(
3
), p.
031004
.
13.
Gan
,
D.
,
Dai
,
J. S.
,
Dias
,
J.
, and
Seneviratne
,
L.
,
2013
, “
Reconfigurability and Unified Kinematics Modeling of a 3rTPS Metamorphic Parallel Mechanism With Perpendicular Constraint Screws
,”
Rob. Comput.-Integr. Manuf.
,
29
(
4
), pp.
121
128
.
14.
Gan
,
D.
,
Dias
,
J.
, and
Seneviratne
,
L.
,
2016
, “
Unified Kinematics and Optimal Design of a 3rRPS Metamorphic Parallel Mechanism With a Reconfigurable Revolute Joint
,”
Mech. Mach. Theory
,
96
, pp.
239
254
.
15.
Meng
,
Q.
,
Xie
,
F.
,
Liu
,
X. J.
, and
Takeda
,
Y.
,
2020
, “
Screw Theory-Based Motion/Force Transmissibility Analysis of High-Speed Parallel Robots With Articulated Platforms
,”
ASME J. Mech. Rob.
,
12
(
4
), p.
041011
.
16.
Huang
,
Z.
, and
Fang
,
Y. F.
,
1996
, “
Kinematic Characteristics Analysis of 3 DOF In-Parallel Actuated Pyramid Mechanism
,”
Mech. Mach. Theory
,
31
(
8
), pp.
1009
1018
.
17.
Wang
,
H. B.
, and
Huang
,
Z.
,
1990
, “
Kinematic Influence Coefficient Method of Kinematic and Dynamic Analysis
,”
Mech. Mach. Theory
,
25
(
2
), pp.
167
173
.
18.
Di Gregorio
,
R.
,
2001
, “
A New Parallel Wrist Using Only Revolute Pairs: The 3-RUU Wrist
,”
Robotica
,
19
(
3
), pp.
305
309
.
19.
Di Gregorio
,
R.
,
2004
, “
Kinematics of the Translational 3-URC Mechanism
,”
ASME J. Mech. Des.
,
126
(
6
), pp.
1113
1117
.
20.
Kim
,
S. G.
, and
Ryu
,
J.
,
2003
, “
New Dimensionally Homogeneous Jacobian Matrix Formulation by Three End-Effector Points for Optimal Design of Parallel Manipulators
,”
IEEE Trans. Rob. Autom.
,
19
(
4
), pp.
731
736
.
21.
Lu
,
Y.
,
Hu
,
B.
, and
Yu
,
J. P.
,
2009
, “
Analysis of Kinematics/Statics and Workspace of a 2(SP+ SPR+ SPU) Serial–Parallel Manipulator
,”
Multibody Syst. Dyn.
,
21
(
4
), pp.
361
374
.
22.
Lu
,
Y.
,
Hu
,
B.
, and
Sun
,
T.
,
2009
, “
Analyses of Velocity, Acceleration, Statics, and Workspace of a 2(3-SPR) Serial-Parallel Manipulator
,”
Robotica
,
27
(
4
), pp.
529
538
.
23.
Hu
,
B.
,
Shi
,
Y.
,
Xu
,
L.
, and
Bai
,
P.
,
2020
, “
Reconsideration of Terminal Constraint/Mobility and Kinematics of 5-DOF Hybrid Manipulators Formed by One 2R1T PM and one RR SM
,”
Mech. Mach. Theory
,
149
, p.
103837
.
24.
Hu
,
B.
,
2019
, “
Terminal Position and Orientation Coupling in Lower Mobility Robots
,”
ASME J. Mech. Rob.
,
11
(
3
), p.
031008
.
25.
Sánchez-Alonso
,
R. E.
,
González-Barbosa
,
J. J.
,
Castillo-Castaneda
,
E.
, and
Gallardo-Alvarado
,
J.
,
2016
, “
Kinematic Analysis of a Novel 2(3-RUS) Parallel Manipulator
,”
Robotica
,
34
(
10
), pp.
2241
2256
.
26.
Rahmani
,
A.
, and
Ghanbari
,
A.
,
2016
, “
Application of Neural Network Training in Forward Kinematics Simulation for a Novel Modular Hybrid Manipulator With Experimental Validation
,”
Intell. Serv. Rob.
,
9
(
1
), pp.
79
91
.
27.
Nayak
,
A.
,
Caro
,
S.
, and
Wenger
,
P.
,
2019
, “
Kinematic Analysis of the 3-RPS-3-SPR Series–Parallel Manipulator
,”
Robotica
,
37
(
7
), pp.
1240
1266
.
28.
Nurahmi
,
L.
, and
Gan
,
D.
,
2019
, “
Dynamic Analysis of the 3-RRPS Metamorphic Parallel Mechanism Based on Instantaneous Screw Axis
,”
Proceedings of the ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
Anaheim, CA
,
Aug. 18–21
, 59230, p. V05AT07A064.
29.
Lu
,
Y.
, and
Dai
,
Z.
,
2016
, “
Dynamics Model of Redundant Hybrid Manipulators Connected in Series by Three or More Different Parallel Manipulators With Linear Active Legs
,”
Mech. Mach. Theory
,
103
, pp.
222
235
.
30.
Lu
,
Y.
,
Wang
,
P.
, and
Ye
,
N.
,
2018
, “
Kinematics/Dynamics Analysis of Novel 3UPUR SP-Type Hybrid Hand With Three Flexible Fingers
,”
Nonlinear Dyn.
,
91
(
2
), pp.
1127
1144
.
31.
Gallardo
,
J.
,
Aguilar
,
C. R.
,
Casique
,
L.
,
Pérez
,
L.
, and
Rico
,
J. M.
,
2008
, “
Solving the Kinematics and Dynamics of a Modular Spatial Hyper-Redundant Manipulator by Means of Screw Theory
,”
Multibody Syst. Dyn.
,
20
(
4
), pp.
307
325
.
32.
Gallardo
,
J.
,
Aguilar
,
C. R.
,
Casique
,
L.
, and
Islam
,
M. N.
,
2008
, “
Kinematics and Dynamics of 2(3-RPS) Manipulators by Means of Screw Theory and the Principle of Virtual Work
,”
Mech. Mach. Theory
,
43
(
10
), pp.
1281
1294
.
33.
Gallardo
,
J.
,
Lesso
,
R.
,
Rico
,
J. M.
, and
Alici
,
G.
,
2011
, “
The Kinematics of Modular Spatial Hyper-redundant Manipulators Formed From RPS-Type Limbs
,”
Rob. Auton. Syst.
,
59
(
1
), pp.
12
21
.
34.
Ibrahim
,
O.
, and
Khalil
,
W.
,
2010
, “
Inverse and Direct Dynamic Models of Hybrid Robots
,”
Mech. Mach. Theory
,
45
(
4
), pp.
627
640
.
35.
Hu
,
B.
,
Yu
,
J.
, and
Lu
,
Y.
,
2016
, “
Inverse Dynamics Modeling of a (3-UPU)+(3-UPS + S) Serial-Parallel Manipulator
,”
Robotica
,
34
(
3
), pp.
687
702
.
36.
Hu
,
B.
,
Zhao
,
J.
, and
Cui
,
H.
,
2019
, “
Terminal Constraint and Mobility Analysis of Serial-Parallel Manipulators Formed by 3-RPS and 3-SPR PMs
,”
Mech. Mach. Theory
,
134
, pp.
685
703
.
37.
Hu
,
B.
, and
Yu
,
J.
,
2015
, “
Unified Solving Inverse Dynamics of 6-DOF Serial–Parallel Manipulators
,”
Appl. Math. Modell.
,
39
(
16
), pp.
4715
4732
.
38.
Taherifar
,
A.
,
Salarieh
,
H.
,
Alasty
,
A.
, and
Honarvar
,
M.
,
2016
, “
Inverse and Forward Dynamics of N-3RPS Manipulator With Lockable Joints
,”
Robotica
,
34
(
6
), pp.
1383
1402
.
39.
Shan
,
M.
,
Guo
,
J.
, and
Gill
,
E.
,
2016
, “
Review and Comparison of Active Space Debris Capturing and Removal Methods
,”
Prog. Aerosp. Sci.
,
80
, pp.
18
32
.
40.
Davis
,
J. P.
,
Mayberry
,
J. P.
, and
Penn
,
J. P.
,
2019
,
On-Orbit Servicing: Inspection Repair Refuel Upgrade and Assembly of Satellites in Space
. The Aerospace Corporation Report.
41.
Zhang
,
X.
,
Liu
,
J.
,
Feng
,
J.
,
Liu
,
Y.
, and
Ju
,
Z.
,
2019
, “
Effective Capture of Non-graspable Objects for Space Robots Using Geometric Cage Pairs
,”
IEEE/ASME Trans. Mechatron.
,
25
(
1
), pp.
95
107
.
42.
Li
,
C.
,
Angeles
,
J.
,
Guo
,
H.
,
Tang
,
D.
,
Liu
,
R.
,
Qin
,
Z.
, and
Xiao
,
H.
, 2021, “
On the Actuation Modes of a Multiloop Mechanism for Space Applications
,”
IEEE/ASME Trans. Mechatron.
43.
Jia
,
G.
,
Huang
,
H.
,
Wang
,
S.
, and
Li
,
B.
,
2021
, “
Type Synthesis of Plane-Symmetric Deployable Grasping Parallel Mechanisms Using Constraint Force Parallelogram law
,”
Mech. Mach. Theory
,
161
, p.
104330
.
44.
Zhao
,
C.
,
Guo
,
H.
,
Liu
,
R.
,
Deng
,
Z.
, and
Li
,
B.
,
2018
, “
Design and Kinematic Analysis of a 3RRlS Metamorphic Parallel Mechanism for Large-Scale Reconfigurable Space Multifingered Hand
,”
ASME J. Mech. Rob.
,
10
(
4
), p.
041012
.
45.
Zhao
,
C.
,
Guo
,
H.
,
Liu
,
R.
,
Deng
,
Z.
,
Li
,
B.
, and
Tian
,
J.
,
2019
, “
Actuation Distribution and Workspace Analysis of a Novel 3 (3RRlS) Metamorphic Serial-Parallel Manipulator for Grasping Space Non-cooperative Targets
,”
Mech. Mach. Theory
,
139
, pp.
424
442
.
46.
Zhao
,
C.
,
Guo
,
H.
,
Zhang
,
D.
,
Liu
,
R.
,
Li
,
B.
, and
Deng
,
Z.
,
2020
, “
Stiffness Modeling of n (3RRlS) Reconfigurable Series-Parallel Manipulators by Combining Virtual Joint Method and Matrix Structural Analysis
,”
Mech. Mach. Theory
,
152
, p.
103960
.
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