This paper introduces a new architecture of spherical parallel robot which significantly extends the workspace when compared to existing architectures. To this end, the singularity locus is studied and the design parameters are chosen so as to confine the singularities to areas already limited by other constraints such as mechanical interferences. First, the architecture of the spherical redundant robot is presented and the Jacobian matrices are derived. Afterwards, the analysis of the singularities is addressed from a geometric point of view, which yields a description of the singularity locus expressed as a function of the architectural parameters. Then, the results are applied to an example set of architectural parameters, which are chosen in order to illustrate the advantages of the redundant architecture over current designs in terms of workspace.

References

References
1.
Cox
,
D. J.
, and
Tesar
,
D.
,
1989
, “
The Dynamic Model of a Three Degree of Freedom Parallel Robotic Shoulder Module
,”
Advanced Robotics
,
Springer
,
Berlin
, pp.
475
487
.
2.
Sefrioui
,
J.
, and
Gosselin
,
C. M.
,
1994
, “
Étude et représentation des lieux de singularité des manipulateurs parallelles sphériques a trois degrés de liberté avec actionneurs prismatiques
,”
Mech. Mach. Theory
,
29
(
4
), pp.
559
579
.
3.
Kong
,
X.
,
Gosselin
,
C. M.
, and
Ritchie
,
J. M.
,
2011
, “
Forward Displacement Analysis of a Linearly Actuated Quadratic Spherical Parallel Manipulator
,”
ASME J. Mech. Rob.
,
3
(
12
), p.
011007
.
4.
Gosselin
,
C. M.
, and
Lavoie
,
E.
,
1993
, “
On the Kinematic Design of Spherical Three-Degree-of-Freedom Parallel Manipulators
,”
Int. J. Rob. Res.
,
12
(
4
), pp.
393
402
.
5.
Gosselin
,
C. M.
,
St-Pierre
,
E.
, and
Gagné
,
M.
,
1996
, “
On the Development of the Agile Eye: Mechanical Design, Control Issues and Experimentation
,”
IEEE Rob. Autom. Soc. Mag.
,
3
(
4
), pp.
29
37
.
6.
Gosselin
,
C. M.
,
Perreault
,
L.
, and
Vallancourt
,
C.
,
1995
, “
Simulation and Computer-Aided Kinematic Design of Three-Degree-of-Freedom Spherical Parallel Manipulators
,”
J. Rob. Syst.
,
12
(
12
), pp.
857
869
.
7.
Cammarata
,
A.
, and
Sinatra
,
R.
,
2008
, “
The Elastodynamics of the 3-CRU Spherical Robot
,”
Second International Workshop on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators
, Montpellier, France, Sept. 21–22, pp.
159
165
.
8.
Li
,
R.
, and
Guo
,
Y.
,
2014
, “
Research on Dynamics and Simulation of 3-RRP Spherical Parallel Mechanism
,”
Third International Workshop on Fundamental Issues and Future Directions for Parallel Mechanisms and Manipulators
, Tianjin, China, July 7–8, pp. 1–8.
9.
Huda
,
S.
,
Takeda
,
Y.
, and
Hanagasaki
,
S.
,
2008
, “
Kinematic Design of 3-URU Pure Rotational Parallel Mechanism to Perform Precise Motion Within a Large Workspace
,”
Second International Workshop on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators
, Montpellier, France, Sept. 21–22, pp.
49
56
.
10.
Hervé
,
J. M.
, and
Karouia
,
M.
,
2002
, “
The Novel 3-RUU Wrist With No Idle Pair
,”
First International Workshop on Fundamental Issues and Future Directions for Parallel Mechanisms and Manipulators
, Quebec City, QC, Canada, Oct. 3–4, pp.
284
286
.https://www.researchgate.net/publication/279197277_The_Novel_3-RUU_Wrist_with_No_Idle_Pair
11.
Yu
,
J.
,
Lu
,
D.
, and
Hao
,
G.
,
2014
, “
Design and Analysis of a 2-DOF Compliant Parallel Pan-Tilt Platform
,”
Third International Workshop on Fundamental Issues and Future Directions for Parallel Mechanisms and Manipulators
, Tianjin, China, July 7–8, pp. 1–8.https://www.researchgate.net/publication/264128915_Design_and_Analysis_of_a_2-DOF_Compliant_Parallel_Pan-Tilt_Platform
12.
Shen
,
H.
,
Yang
,
L.
,
Deng
,
J.
,
Li
,
J.
, and
Zhang
,
X.
,
2014
, “
A Parallel Shoulder Rehabilitation Training Mechanism and Its Kinematics Design
,”
Third International Workshop on Fundamental Issues and Future Directions for Parallel Mechanisms and Manipulators
, Tianjin, China, July 7–8, pp. 1–8.
13.
Congzhe
,
W.
,
Yuefa
,
F.
,
Sheng
,
G.
, and
Zhihong
,
C.
,
2014
, “
Design and Kinematics of a Reconfigurable Robot for Ankle and Knee Rehabilitation
,”
Third International Workshop on Fundamental Issues and Future Directions for Parallel Mechanisms and Manipulators
, Tianjin, China, July 7–8, pp. 1–10.
14.
Hayes
,
M. J. D.
,
Weiss
,
A.
, and
Langlois
,
R. G.
,
2008
, “
Atlas Motion Platform Generalized Kinematic Model
,”
Second International Workshop on Fundamental Issues and Future Directions for Parallel Mechanisms and Manipulators
, Montpellier, France, Sept. 21–22, pp.
227
234
.https://www.researchgate.net/publication/225466236_Atlas_motion_platform_generalized_kinematic_model_Atlas_motion_platform
15.
Wu
,
G.
,
Caro
,
S.
, and
Wang
,
J.
,
2015
, “
Design and Transmission Analysis of an Asymmetrical Spherical Parallel Manipulator
,”
Mech. Mach. Theory
,
94
, pp.
119
131
.
16.
Stanisic
,
M. M.
, and
Duta
,
O.
,
1990
, “
Symmetrically Actuated Double Pointing Systems: The Basis of Singularity-Free Robot Wrists
,”
IEEE Trans. Rob. Autom.
,
6
(
5
), pp.
562
569
.
17.
Leguay-Durand
,
S.
, and
Reboulet
,
C.
,
1997
, “
Optimal Design of a Redundant Spherical Parallel Manipulator
,”
Robotica
,
15
(
4
), pp.
399
405
.
18.
Di Gregorio
,
R.
,
2002
, “
A New Family of Spherical Parallel Manipulators
,”
Robotica
,
20
(
4
), pp.
353
358
.
19.
Bai
,
S.
,
2010
, “
Optimum Design of Spherical Parallel Manipulators for a Prescribed Workspace
,”
Mech. Mach. Theory
,
45
(
2
), pp.
200
211
.
20.
Liu
,
X.-J.
,
Jin
,
Z.-L.
, and
Gao
,
F.
,
2000
, “
Optimum Design of 3-DOF Spherical Parallel Manipulators With Respect to the Conditioning and Stiffness Indices
,”
Mech. Mach. Theory
,
35
(
9
), pp.
1257
1267
.
21.
Lum
,
M. J.
,
Rosen
,
J.
,
Sinanan
,
M. N.
, and
Hannaford
,
B.
,
2006
, “
Optimization of a Spherical Mechanism for a Minimally Invasive Surgical Robot: Theoretical and Experimental Approaches
,”
IEEE Trans. Biomed. Eng.
,
53
(
7
), pp.
1440
1445
.
22.
Kurtz
,
R.
, and
Hayward
,
V.
,
1992
, “
Multiple-Goal Kinematic Optimization of a Parallel Spherical Mechanism With Actuator Redundancy
,”
IEEE Trans. Rob. Autom.
,
8
(
5
), pp.
644
651
.
23.
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
.
24.
Bonev
,
I. A.
,
Zlatanov
,
D.
, and
Gosselin
,
C. M.
,
2002
, “
Advantages of the Modified Euler Angles in the Design and Control of PKMs
,”
Third Chemnitz Parallel Kinematics Seminar/2002 Parallel Kinematic Machines International Conference
, Chemnitz, Germany, Apr. 23–25, pp.
171
188
.
25.
Gosselin
,
C. M.
, and
Angeles
,
J.
,
1990
, “
Singularity Analysis of Closed-Loop Kinematic Chains
,”
IEEE Trans. Rob. Autom.
,
6
(
3
), pp.
281
290
.
26.
Wang
,
J.
, and
Gosselin
,
C. M.
,
2004
, “
Singularity Loci of a Special Class of Spherical 3-DOF Parallel Mechanisms With Prismatic Actuators
,”
ASME J. Mech. Des.
,
126
(2), pp.
319
326
.
27.
Bonev
,
I. A.
, and
Gosselin
,
C. M.
,
2005
, “
Singularity Loci of Spherical Parallel Mechanisms
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), Barcelona, Spain, Apr. 18–22, pp.
2968
2973
.
28.
Bonev
,
I. A.
, and
Gosselin
,
C. M.
,
2006
, “
Analytical Determination of the Workspace of Symmetrical Spherical Parallel Mechanisms
,”
IEEE Trans. Rob.
,
22
(
5
), pp.
2968
2973
.
You do not currently have access to this content.