Two kinds of mechanical redundancies, namely kinematic redundancy and actuation redundancy, have been extensively studied due to their advantageous features in autonomous industry. Screw theory has been successfully applied to develop an analytical Jacobian of nonredundant parallel manipulators (PMs). However, to the best of our knowledge, screw theory has not been attempted for modeling of PMs with kinematic redundancies. Thus, first, through the mobility analysis of a simple nonredundant planar PM and its variations, this paper reviews kinematic and actuation redundancy systematically. Then, we demonstrated how to derive analytical Jacobian and also static force relationship for a PM with both kinematic and actuation redundancies by using the screw theory. Finally, simulations were performed to demonstrate the advantageous features of kinematic and actuation redundancies.

References

References
1.
Maciejewski
,
A. A.
, and
Klein
,
C. A.
,
1985
, “
Obstacle Avoidance for Kinematically Redundant Manipulators in Dynamically Varying Environments
,”
Int. J. Rob. Res.
,
4
(
3
), pp.
109
117
.
2.
Wang
,
J.
, and
Gosselin
,
C. M.
,
2004
, “
Kinematic Analysis and Design of Kinematically Redundant Parallel Mechanisms
,”
ASME J. Mech. Des.
,
126
(
1
), pp.
109
118
.
3.
Ebrahimi
,
I.
,
Carretero
,
J. A.
, and
Boudreau
,
R.
,
2007
, “
3-PRRR Redundant Planar Parallel Manipulator: Inverse Displacement, Workspace and Singularity Analyses
,”
Mech. Mach. Theory
,
42
(
8
), pp.
1007
1016
.
4.
Gosselin
,
C. M.
,
Laliberté
,
T.
, and
Veillette
,
A.
,
2015
, “
Singularity-Free Kinematically Redundant Planar Parallel Mechanisms With Unlimited Rotational Capability
,”
IEEE Trans. Rob.
,
31
(
2
), pp.
457
467
.
5.
Shimizu
,
M.
,
Yoon
,
W. K.
, and
Kitagaki
,
K.
, “
A Practical Redundancy Resolution for 7 DOF Redundant Manipulators With Joint Limits
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), Rome, Italy, Apr. 10–14, pp.
4510
4516
.
6.
Flacco
,
F.
,
Luca
,
A. D.
, and
Khatib
,
O.
, “
Motion Control of Redundant Robots Under Joint Constraints: Saturation in the Null Space
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), Saint Paul, MN, May 14–18, pp.
285
292
.
7.
Hollerbach
,
J.
, and
Ki
,
S.
,
1987
, “
Redundancy Resolution of Manipulators Through Torque Optimization
,”
IEEE J. Rob. Autom.
,
3
(
4
), pp.
308
316
.
8.
Chiaverini
,
S.
,
1997
, “
Singularity-Robust Task-Priority Redundancy Resolution for Real-Time Kinematic Control of Robot Manipulators
,”
IEEE Trans. Rob. Autom.
,
13
(
3
), pp.
398
410
.
9.
Klein
,
C. A.
, and
Blaho
,
B. E.
,
1987
, “
Dexterity Measures for the Design and Control of Kinematically Redundant Manipulators
,”
Int. J. Rob. Res.
,
6
(
2
), pp.
72
83
.
10.
Nakamura
,
Y.
,
1991
,
Advanced Robotics: Redundancy and Optimization
,
Addison-Wesley
,
Boston, MA
.
11.
Yi
,
B.-J.
,
Na
,
H. Y.
,
Lee
,
J. H.
,
Hong
,
Y.-S.
,
Oh
,
S.-R.
,
Suh
,
I. H.
, and
Kim
,
W. K.
,
2002
, “
Design of a Parallel-Type Gripper Mechanism
,”
Int. J. Rob. Res.
,
21
(
7
), pp.
661
676
.
12.
Mohamed
,
M. G.
, and
Gosselin
,
C. M.
,
2005
, “
Design and Analysis of Kinematically Redundant Parallel Manipulators With Configurable Platforms
,”
IEEE Trans. Rob.
,
21
(
3
), pp.
277
287
.
13.
Isaksson
,
M.
,
Gosselin
,
C.
, and
Marlow
,
K.
,
2016
, “
An Introduction to Utilising the Redundancy of a Kinematically Redundant Parallel Manipulator to Operate a Gripper
,”
Mech. Mach. Theory
,
101
, pp.
50
59
.
14.
Saglia
,
J. A.
,
Dai
,
J. S.
, and
Caldwell
,
D. G.
,
2008
, “
Geometry and Kinematic Analysis of a Redundantly Actuated Parallel Mechanism That Eliminates Singularities and Improves Dexterity
,”
ASME J. Mech. Des.
,
130
(
12
), p.
124501
.
15.
Shayya
,
S.
,
Krut
,
S.
,
Company
,
O.
,
Baradat
,
C.
, and
Pierrot
,
F.
,
2013
, “
A Novel (3T-1R) Redundant Parallel Mechanism With Large Operational Workspace and Rotational Capability
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
(
IROS
), Tokyo, Japan, Nov. 3–7, pp.
436
443
.
16.
Shin
,
H.
,
Lee
,
S.
,
Jeong
,
J. I.
, and
Kim
,
J.
,
2013
, “
Antagonistic Stiffness Optimization of Redundantly Actuated Parallel Manipulators in a Predefined Workspace
,”
IEEE/ASME Trans. Mechatronics
,
18
(
3
), pp.
1161
1169
.
17.
Wang
,
C.
,
Fang
,
Y.
,
Guo
,
S.
, and
Chen
,
Y.
,
2013
, “
Design and Kinematical Performance Analysis of a 3-RUS/RRR Redundantly Actuated Parallel Mechanism for Ankle Rehabilitation
,”
ASME J. Mech. Rob.
,
5
(
4
), p.
041003
.
18.
Corbel
,
D.
,
Gouttefarde
,
M.
,
Company
,
O.
, and
Pierrot
,
F.
,
2010
, “
Actuation Redundancy as a Way to Improve the Acceleration Capabilities of 3T and 3T1R Pick-and-Place Parallel Manipulators
,”
ASME J. Mech. Rob.
,
2
(
4
), p.
041002
.
19.
Li
,
Q.
,
Zhang
,
N.
, and
Wang
,
F.
,
2016
, “
New Indices for Optimal Design of Redundantly Actuated Parallel Manipulators
,”
ASME J. Mech. Rob.
,
9
(
1
), p.
011007
.
20.
Kang
,
L.
,
Kim
,
W.
, and
Yi
,
B. J.
, 2016, “
Kinematic Modeling, Analysis, and Load Distribution Algorithm for a Redundantly Actuated 4-DOF Parallel Mechanism
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
(
IROS
), Daejeon, South Korea, Oct. 9–14, pp.
356
361
.
21.
Yung
,
T.
,
Tosunoglu
,
S.
, and
Freeman
,
R.
,
1993
, “
Actuator Saturation Avoidance for Fault-Tolerant Robots
,”
32nd IEEE Conference on Decision and Control
(
CDC
), San Antonio, TX, Dec. 15–17, pp.
2125
2130
.
22.
Gouttefarde
,
M.
,
Daney
,
D.
, and
Merlet
,
J. P.
,
2011
, “
Interval-Analysis-Based Determination of the Wrench-Feasible Workspace of Parallel Cable-Driven Robots
,”
IEEE Trans. Rob.
,
27
(
1
), pp.
1
13
.
23.
Gosselin
,
C.
, and
Grenier
,
M.
,
2011
, “
On the Determination of the Force Distribution in Overconstrained Cable-Driven Parallel Mechanisms
,”
Meccanica
,
46
(
1
), pp.
3
15
.
24.
Bouchard
,
S.
,
Gosselin
,
C.
, and
Moore
,
B.
,
2009
, “
On the Ability of a Cable-Driven Robot to Generate a Prescribed Set of Wrenches
,”
ASME J. Mech. Rob.
,
2
(
1
), p.
011010
.
25.
Hassan
,
M.
, and
Khajepour
,
A.
,
2008
, “
Optimization of Actuator Forces in Cable-Based Parallel Manipulators Using Convex Analysis
,”
IEEE Trans. Rob.
,
24
(
3
), pp.
736
740
.
26.
Yuan
,
H.
,
Courteille
,
E.
, and
Deblaise
,
D.
,
2016
, “
Force Distribution With Pose-Dependent Force Boundaries for Redundantly Actuated Cable-Driven Parallel Robots
,”
ASME J. Mech. Rob.
,
8
(
4
), p.
041004
.
27.
Davies
,
T. H.
,
1981
, “
Kirchhoff's Circulation Law Applied to Multi-Loop Kinematic Chains
,”
Mech. Mach. Theory
,
16
(
3
), pp.
171
183
.
28.
Mohamed
,
M. G.
, and
Duffy
,
J.
,
1985
, “
A Direct Determination of the Instantaneous Kinematics of Fully Parallel Robot Manipulators
,”
ASME. J. Mech., Transm., Autom. Des.
,
107
(
2
), pp.
226
229
.
29.
Joshi
,
S. A.
, and
Tsai
,
L.-W.
,
2002
, “
Jacobian Analysis of Limited-DOF Parallel Manipulators
,”
ASME J. Mech. Des.
,
124
(
2
), pp.
254
258
.
30.
Cox
,
D. J.
,
1981
, “
The Dynamic Modeling and Command Signal Formulation for Parallel Multi-Parameter Robotic Devices
,” Master's thesis, University of Florida, Gainesville, FL.
31.
Cox
,
D. J.
, and
Tesar
,
D.
,
1989
, “
The Dynamic Model of a Three Degree of Freedom Parallel Robotic Shoulder Module
,”
Advanced Robotics: Proceedings of the 4th International Conference on Advanced Robotics
,
K. J.
Waldron
, ed.,
Springer
,
Berlin
, pp.
475
487
.
32.
Yi
,
B.-J.
,
Kim
,
S. M.
,
Kwak
,
H. K.
, and
Kim
,
W.
,
2013
, “
Multi-Task Oriented Design of an Asymmetric 3T1R Type 4-DOF Parallel Mechanism
,”
Proc. Inst Mech Eng. Part C
,
227
(
10
), pp.
2236
2255
.
33.
Kang
,
L.
, and
Yi
,
B. J.
,
2016
, “
Design of Two Foldable Mechanisms Without Parasitic Motion
,”
IEEE Robot. Autom. Lett.
,
1
(
2
), pp.
930
937
.
34.
Isaksson
,
M.
,
Gosselin
,
C.
, and
Marlow
,
K.
,
2017
, “
Singularity Analysis of a Class of Kinematically Redundant Parallel Schönflies Motion Generators
,”
Mech. Mach. Theory
,
112
, pp.
172
191
.
35.
Isaksson
,
M.
,
2017
, “
Kinematically Redundant Planar Parallel Mechanisms for Optimal Singularity Avoidance
,”
ASME J. Mech. Des.
,
139
(
4
), p.
042302
.
36.
Gogu
,
G.
,
2005
, “
Mobility of Mechanisms: A Critical Review
,”
Mech. Mach. Theory
,
40
(
9
), pp.
1068
1097
.
37.
Li
,
Q. C.
, and
Huang
,
Z.
,
2004
, “
Mobility Analysis of a Novel 3-5R Parallel Mechanism Family
,”
ASME J. Mech. Des.
,
126
(
1
), pp.
79
82
.
38.
Dai
,
J. S.
,
Huang
,
Z.
, and
Lipkin
,
H.
,
2004
, “
Mobility of Overconstrained Parallel Mechanisms
,”
ASME J. Mech. Des.
,
128
(
1
), pp.
220
229
.
39.
Zanchettin
,
A. M.
,
Rocco
,
P.
,
Robertsson
,
A.
, and
Johansson
,
R.
, 2011, “
Exploiting Task Redundancy in Industrial Manipulators During Drilling Operations
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), Shanghai, China, May 9–13, pp.
128
133
.
40.
Nokleby
,
S. B.
,
Fisher
,
R.
,
Podhorodeski
,
R. P.
, and
Firmani
,
F.
,
2005
, “
Force Capabilities of Redundantly-Actuated Parallel Manipulators
,”
Mech. Mach. Theory
,
40
(
5
), pp.
578
599
.
41.
Gosselin
,
C.
, and
Angeles
,
J.
,
1988
, “
The Optimum Kinematic Design of a Planar Three-Degree-of-Freedom Parallel Manipulator
,”
ASME. J. Mech., Transm., Autom. Des.
,
110
(
1
), pp.
35
41
.
42.
Bonev
,
I. A.
,
Zlatanov
,
D.
, and
Gosselin
,
C. M. M.
,
2003
, “
Singularity Analysis of 3-DOF Planar Parallel Mechanisms Via Screw Theory
,”
ASME J. Mech. Des.
,
125
(
3
), pp.
573
581
.
43.
Huang
,
T.
,
Liu
,
H. T.
, and
Chetwynd
,
D. G.
,
2011
, “
Generalized Jacobian Analysis of Lower Mobility Manipulators
,”
Mech. Mach. Theory
,
46
(
6
), pp.
831
844
.
44.
Cha
,
S. H.
,
Lasky
,
T. A.
, and
Velinsky
,
S. A.
, 2007, “
Singularity Avoidance for the 3-RRR Mechanism Using Kinematic Redundancy
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), Rome, Italy, Apr. 10–14, pp.
1195
1200
.
45.
Chen
,
X.
,
Chen
,
C.
, and
Liu
,
X.-J.
,
2015
, “
Evaluation of Force/Torque Transmission Quality for Parallel Manipulators
,”
ASME J. Mech. Rob.
,
7
(
4
), p.
041013
.
You do not currently have access to this content.