A novel parallel robot, dubbed the SDelta, is the subject of this paper. SDelta is a simpler alternative to both the well-known Stewart–Gough platform (SGP) and current three-limb, full-mobility parallel robots, as it contains fewer components and all its motors are located on the base. This reduces the inertial load on the system, making it a good candidate for high-speed operations. SDelta features a symmetric structure; its forward-displacement analysis leads to a system of three quadratic equations in three unknowns, which admits up to eight solutions, or half the number of those admitted by the SGP. The kinematic analysis, undertaken with a geometrical method based on screw theory, leads to two Jacobian matrices, whose singularity conditions are investigated. Instead of using the determinant of a 6 × 6 matrix, we derive one simple expression that characterizes the singularity condition. This approach is also applicable to a large number of parallel robots whose six actuation wrench axes intersect pairwise, such as all three-limb parallel robots whose limbs include, each, a passive spherical joint. The workspace is analyzed via a geometric method, while the dexterity analysis is conducted via discretization. Both show that the given robot has the potential to offer both large workspace and good dexterity with a proper choice of design variables.

References

References
1.
Kong
,
X.
, and
Gosselin
,
C.
,
2007
,
Type Synthesis of Parallel Mechanisms
, Vol.
33
,
Springer
, Berlin.
2.
Merlet
,
J.-P.
,
2006
,
Parallel Robots
, Vol.
128
, Springer, Dordrecht, The Netherlands.
3.
Briot
,
S.
, and
Khalil
,
W.
,
2015
,
Dynamics of Parallel Robots
,
Springer
, Cham, Switzerland.
4.
Stewart
,
D.
,
1965
, “
A Platform With Six Degrees of Freedom
,”
Proc. Inst. Mech. Eng.
,
180
(
1
), pp.
371
386
.
5.
Fichter
,
F.
,
1986
, “
A Stewart Platform-Based Manipulator—General-Theory and Practical Construction
,”
Int. J. Rob. Res.
,
5
(
2
), pp.
157
182
.
6.
Podhorodeski
,
R. P.
, and
Pittens
,
K. H.
,
1994
, “
A Class of Parallel Manipulators Based on Kinematically Simple Branches
,”
ASME J. Mech. Des.
,
116
(
3
), pp.
908
914
.
7.
Yang
,
G.
,
Chen
,
I. M.
,
Chen
,
W.
, and
Lin
,
W.
,
2004
, “
Kinematic Design of a Six-DOF Parallel-Kinematics Machine With Decoupled-Motion Architecture
,”
IEEE Trans. Rob.
,
20
(
5
), pp.
876
884
.
8.
Behi
,
F.
,
1988
, “
Kinematic Analysis for a Six-Degree-of-Freedom 3-PRPS Parallel Mechanism
,”
IEEE J. Rob. Autom.
,
4
(
5
), pp.
561
565
.
9.
Kim
,
J.
,
Park
,
F. C.
,
Ryu
,
S. J.
,
Kim
,
J.
,
Hwang
,
J. C.
,
Park
,
C.
, and
Iurascu
,
C. C.
,
2001
, “
Design and Analysis of a Redundantly Actuated Parallel Mechanism for Rapid Machining
,”
IEEE Trans. Rob. Autom.
,
17
(
4
), pp.
423
434
.
10.
Sorli
,
M.
,
Ferraresi
,
C.
,
Kolarski
,
M.
,
Borovac
,
B.
, and
Vukobratovic
,
M.
,
1997
, “
Mechanics of Turin Parallel Robot
,”
Mech. Mach. Theory
,
32
(
1
), pp.
51
77
.
11.
Chen
,
C.
,
Gayral
,
T.
,
Caro
,
S.
,
Chablat
,
D.
,
Moroz
,
G.
, and
Abeywardena
,
S.
,
2012
, “
A Six Degree of Freedom Epicyclic-Parallel Manipulator
,”
ASME J. Mech. Rob.
,
4
(
4
), p.
041011
.
12.
Liu
,
X. J.
, and
Wang
,
J. S.
,
2003
, “
Some New Parallel Mechanisms Containing the Planar Four-Bar Parallelogram
,”
Int. J. Rob. Res.
,
22
(
9
), pp.
717
732
.
13.
Monsarrat
,
B.
, and
Gosselin
,
C. M.
,
2003
, “
Workspace Analysis and Optimal Design of a 3-Leg 6-DOF Parallel Platform Mechanism
,”
IEEE Trans. Rob. Autom.
,
19
(
6
), pp.
954
966
.
14.
Jin
,
Y.
,
Chen
,
I. M.
, and
Yang
,
G. L.
,
2009
, “
Kinematic Design of a Family of 6-DOF Partially Decoupled Parallel Manipulators
,”
Mech. Mach. Theory
,
44
(
5
), pp.
912
922
.
15.
Azulay
,
H.
,
Mahmoodi
,
M.
,
Zhao
,
R.
,
Mills
,
J. K.
, and
Benhabib
,
B.
,
2014
, “
Comparative Analysis of a New 3xPPRS Parallel Kinematic Mechanism
,”
Rob. Comput.-Integr. Manuf.
,
30
(
4
), pp.
369
378
.
16.
Fu
,
J.
,
Gao
,
F.
,
Pan
,
Y.
, and
Du
,
H.
,
2015
, “
Forward Kinematics Solutions of a Special Six-Degree-of-Freedom Parallel Manipulator With Three Limbs
,”
Adv. Mech. Eng.
,
7
(
5
), pp.
1
11
.
17.
Wu
,
Y. N.
, and
Gosselin
,
C. M.
,
2004
, “
Synthesis of Reactionless Spatial 3-DOF and 6-DOF Mechanisms Without Separate Counter-Rotations
,”
Int. J. Rob. Res.
,
23
(
6
), pp.
625
642
.
18.
Wampler
,
C.
,
Morgan
,
A.
, and
Sommese
,
A.
,
1990
, “
Numerical Continuation Methods for Solving Polynomial Systems Arising in Kinematics
,”
ASME J. Mech. Des.
,
112
(
1
), pp.
59
68
.
19.
Faugère
,
J.-C.
, and
Lazard
,
D.
,
1995
, “
Combinatorial Classes of Parallel Manipulators
,”
Mech. Mach. Theory
,
30
(
6
), pp.
765
776
.
20.
Innocenti
,
C.
, and
Parenticastelli
,
V.
,
1990
, “
Direct Position Analysis of the Stewart Platform Mechanism
,”
Mech. Mach. Theory
,
25
(
6
), pp.
611
621
.
21.
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
(
Pt. 2
), pp.
239
254
.
22.
Merlet
,
J. P.
,
2004
, “
Solving the Forward Kinematics of a Gough-Type Parallel Manipulator With Interval Analysis
,”
Int. J. Rob. Res.
,
23
(
3
), pp.
221
235
.
23.
Gibson
,
C. G.
, and
Hunt
,
K. H.
,
1990
, “
Geometry of Screw Systems—1. Screws—Genesis and Geometry
,”
Mech. Mach. Theory
,
25
(
1
), pp.
1
10
.
24.
Merlet
,
J. P.
,
1989
, “
Singular Configurations of Parallel Manipulators and Grassmann Geometry
,”
Int. J. Rob. Res.
,
8
(
5
), pp.
45
56
.
25.
Park
,
F.
, and
Kim
,
J. W.
,
1999
, “
Singularity Analysis of Closed Kinematic Chains
,”
ASME J. Mech. Des.
,
121
(
1
), pp.
32
38
.
26.
Zlatanov
,
D.
,
Fenton
,
R. G.
, and
Benhabib
,
B.
,
1998
, “
Identification and Classification of the Singular Configurations of Mechanisms
,”
Mech. Mach. Theory
,
33
(
6
), pp.
743
760
.
27.
Bohigas
,
O.
,
Zlatanov
,
D.
,
Ros
,
L.
,
Manubens
,
M.
, and
Porta
,
J. M.
, and
IEEE
,
2012
, “
Numerical Computation of Manipulator Singularities
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), Saint Paul, MN, May 14–18, pp.
1351
1358
.
28.
Wen
,
J. T.
, and
O’Brien
,
J. F.
,
2003
, “
Singularities in Three-Legged Platform-Type Parallel Mechanisms
,”
IEEE Trans. Rob. Autom.
,
19
(
4
), pp.
720
726
.
29.
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. Rob.
,
22
(
4
), pp.
577
590
.
30.
Ben-Horin
,
P.
, and
Shoham
,
M.
,
2006
, “
Singularity Analysis of a Class of Parallel Robots Based on Grassmann–Cayley Algebra
,”
Mech. Mach. Theory
,
41
(
8
), pp.
958
970
.
31.
Kong
,
X. W.
, and
Gosselin
,
C. M.
,
2001
, “
Uncertainty Singularity Analysis of Parallel Manipulators Based on the Instability Analysis of Structures
,”
Int. J. Rob. Res.
,
20
(
11
), pp.
847
856
.
32.
Gosselin
,
C.
, and
Angeles
,
J.
,
1990
, “
Singularity Analysis of Closed-Loop Kinematic Chains
,”
IEEE Trans. Rob. Autom.
,
6
(
3
), pp.
281
290
.
33.
Bonev
,
I. A.
, and
Gosselin
,
C. M.
,
2000
, “
A Geometric Algorithm for the Computation of the Constant-Orientation Workspace of 6-RUS Parallel Manipulators
,”
ASME
Paper No. DETC2000/MECH-14106.http://etsmtl.ca/professeurs/ibonev/documents/pdf/MECH_14106.pdf
34.
Masory
,
O.
, and
Wang
,
J.
,
1994
, “
Workspace Evaluation of Stewart Platforms
,”
Adv. Rob.
,
9
(
4
), pp.
443
461
.
35.
Majid
,
M. Z. A.
,
Huang
,
Z.
, and
Yao
,
Y. L.
,
2000
, “
Workspace Analysis of a Six-Degrees of Freedom, Three-Prismatic-Prismatic-Spheric-Revolute Parallel Manipulator
,”
Int. J. Adv. Manuf. Technol.
,
16
(
6
), pp.
441
449
.
36.
Dash
,
A. K.
,
Chen
,
I. M.
,
Yeo
,
S. H.
, and
Yang
,
G. L.
,
2005
, “
Workspace Generation and Planning Singularity-Free Path for Parallel Manipulators
,”
Mech. Mach. Theory
,
40
(
7
), pp.
776
805
.
37.
Jo
,
D. Y.
, and
Haug
,
E. J.
,
1989
, “
Workspace Analysis of Closed Loop Mechanisms With Unilaterial Constraints
,” ASME Design Automation Conferences, Montreal, QC, Canada, Sept. 17–21, pp.
53
60
.
38.
Adkins
,
F. A.
, and
Haug
,
E. J.
,
1997
, “
Operational Envelope of a Spatial Stewart Platform
,”
ASME J. Mech. Des.
,
119
(
2
), pp.
330
332
.
39.
Haug
,
E.
,
Luh
,
C.-M.
,
Adkins
,
F.
, and
Wang
,
J.-Y.
,
1996
, “
Numerical Algorithms for Mapping Boundaries of Manipulator Workspaces
,”
ASME J. Mech. Des.
,
118
(
2
), pp.
228
234
.
40.
Merlet
,
J. P.
,
1999
, “
Determination of 6D Workspaces of Gough-Type Parallel Manipulator and Comparison Between Different Geometries
,”
Int. J. Rob. Res.
,
18
(
9
), pp.
902
916
.
41.
Patel
,
S.
, and
Sobh
,
T.
,
2014
, “
Manipulator Performance Measures—A Comprehensive Literature Survey
,”
J. Intell. Rob. Syst.
,
77
(
3–4
), pp.
547
570
.
42.
Moreno
,
H. A.
,
Saltaren
,
R.
,
Carrera
,
I.
,
Puglisi
,
L.
, and
Aracil
,
R.
,
2012
, “
Performance Indices for Robotic Manipulators: A Review of the State of the Art
,”
Rev. Iberoam. Autom. Inf. Ind.
,
9
(
2
), pp.
111
122
.
43.
Harada
,
T.
,
Friedlaender
,
T.
, and
Angeles
,
J.
,
2014
, “
The Development of an Innovative Two-DOF Cylindrical Drive: Design, Analysis and Preliminary Tests
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), Hong Kong, China, May 31–June 7, pp.
6338
6344
.
44.
Nanua
,
P.
,
Waldron
,
K. J.
, and
Murthy
,
V.
,
1990
, “
Direct Kinematic Solution of a Stewart Platform
,”
IEEE Trans. Rob. Autom.
,
6
(
4
), pp.
438
444
.
45.
Hunt
,
K. H.
,
1986
, “
Special Configurations of Robot-Arms Via Screw Theory
,”
Robotica
,
4
(
3
), pp.
171
179
.
46.
Angeles
,
J.
,
2014
,
Fundamentals of Robotic Mechanical Systems. Theory, Methods, Algorithms
,
4th ed.
,
Springer
,
New York
.
47.
Burdick
,
J. W.
,
1995
, “
A Classification of 3R Regional Manipulator Singularities and Geometries
,”
Mech. Mach. Theory
,
30
(
1
), pp.
71
89
.
48.
Notash
,
L.
,
1998
, “
Uncertainty Configurations of Parallel Manipulators
,”
Mech. Mach. Theory
,
33
(
1–2
), pp.
123
138
.
49.
Yang
,
G.
,
Chen
,
I.-M.
,
Lin
,
W.
, and
Angeles
,
J.
,
2001
, “
Singularity Analysis of Three-Legged Parallel Robots Based on Passive-Joint Velocities
,”
IEEE Trans. Rob. Autom.
,
17
(
4
), pp.
413
422
.
50.
Downing
,
D. M.
,
Samuel
,
A. E.
, and
Hunt
,
K. H.
,
2002
, “
Identification of the Special Configurations of the Octahedral Manipulator Using the Pure Condition
,”
Int. J. Rob. Res.
,
21
(
2
), pp.
147
159
.
51.
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
,
216
(
1
), pp.
81
93
.
52.
FarzanehKaloorazi
,
M.
,
Masouleh
,
M. T.
, and
Caro
,
S.
,
2016
, “
Collision-Free Workspace of Parallel Mechanisms Based on an Interval Analysis Approach
,”
Robotica
,
1
(
1
), pp.
1
14
.
53.
Angeles
,
J.
, and
López-Cajún
,
C. S.
,
1992
, “
Kinematic Isotropy and the Conditioning Index of Serial Robotic Manipulators
,”
Int. J. Rob. Res.
,
11
(
6
), pp.
560
571
.
54.
Zanganeh
,
K. E.
, and
Angeles
,
J.
,
1997
, “
Kinematic Isotropy and the Optimum Design of Parallel Manipulators
,”
Int. J. Rob. Res.
,
16
(
2
), pp.
185
197
.
You do not currently have access to this content.