This paper presents a uniform method of evaluating both transmission quality and singularity applicable for a class of parallel Schönflies-motion generators (SMGs) with four RRΠRR limbs. It turns out that the determinant of the forward Jacobian matrices for this class of parallel robots can be expressed as the scalar product of two vectors, the first vector being the cross product of the four unit vectors along the parallelograms, and the second one being related to the rotation of the mobile platform (MP). The pressure angles, derived from the determinants of forward and inverse Jacobians, respectively, are used for the evaluation of the transmission quality and the detection of robot singularities. Four robots are compared based on the proposed indices as illustrative examples.

References

References
1.
Krut
,
S.
,
Nabat
,
V.
,
Company
,
O.
, and
Pierrot
,
F.
,
2004
, “
A High-Speed Parallel Robot for SCARA Motions
,”
IEEE International Conference on Robotics and Automation
(
ICRA '04
), New Orleans, LA, Apr. 26–May 1, pp.
4109
4115
.
2.
Pierrot
,
F.
,
Nabat
,
V.
,
Company
,
O.
,
Krut
,
S.
, and
Poignet
,
P.
,
2009
, “
Optimal Design of a 4-DOF Parallel Manipulator: From Academia to Industry
,”
IEEE Trans. Robot
,
25
(
2
), pp.
213
224
.
3.
Kim
,
S. M.
,
Kim
,
W.
, and
Yi
,
B. J.
,
2009
, “
Kinematic Analysis and Optimal Design of a 3T1R Type Parallel Mechanism
,”
IEEE International Conference on Robotics and Automation
(
ICRA '09
), Kobe, Japan, May 12–17, pp.
2199
2204
.
4.
Altuzarra
,
O.
,
Şandru
,
B.
,
Pinto
,
C.
, and
Petuya
,
V.
,
2011
, “
A Symmetric Parallel Schönflies-Motion Manipulator for Pick-and-Place Operations
,”
Robotica
,
29
(
06
), pp.
853
862
.
5.
Liu
,
S. T.
,
Huang
,
T.
,
Mei
,
J. P.
,
Zhao
,
X. M.
,
Wang
,
P. F.
, and
Chetwynd
,
D. G.
,
2012
, “
Optimal Design of a 4-DOF SCARA Type Parallel Robot Using Dynamic Performance Indices and Angular Constraints
,”
ASME J. Mech. Rob
,
4
(
3
), p.
0310053
.
6.
Wu
,
G.
,
Bai
,
S.
, and
Hjønet
,
P.
,
2016
, “
On the Stiffness of Three/Four Degree-of-Freedom Parallel Pick-and-Place Robots With Four Identical Limbs
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), Stockholm, Sweden, May 16–21, pp.
861
866
.
7.
Pierrot
,
F.
, and
Company
,
O.
,
1999
, “
H4: A New Family of 4-DOF Parallel Robots
,”
IEEE/ASME
International Conference on Advanced Intelligent Mechatronics
, Atlanta, GA, Sept. 19–23, pp.
508
513
.
8.
Company
,
O.
,
Krut
,
S.
, and
Pierrot
,
F.
,
2006
, “
Internal Singularity Analysis of a Class of Lower Mobility Parallel Manipulators With Articulated Traveling Plate
,”
IEEE Trans. Rob.
,
22
(
1
), pp.
1
11
.
9.
Krut
,
S.
,
Company
,
O.
,
Benoit
,
M.
,
Ota
,
H.
, and
Pierrot
,
F.
,
2003
, “
I4: A New Parallel Mechanism for SCARA Motions
,”
IEEE International Conference on Robotics and Automation
(
ICRA '03
), Taipei, Taiwan, Sept. 14–19, pp.
1875
1880
.
10.
Nabat
,
V.
,
de la O Rodriguez
,
M.
,
Company
,
O.
,
Krut
,
S.
, and
Pierrot
,
F.
,
2005
, “
Par4: Very High Speed Parallel Robot for Pick-and-Place
,”
IEEE/RSJ International Conference on Intelligent Robotic System
(
IROS
), Edmonton, AB, Canada, Aug. 2–6, pp.
553
558
.
11.
Adpet Technology, Inc.
, 2008, “
Adept Quattro Parallel Robots
,” Adpet Technology, Livermore, CA, accessed June 1, 2018, http://www1.adept.com/main/ke/data/Archived/Quattro/sQuattro_UG.pdf
12.
Penta Robotics
, 2014, “
Veloce. Robot
,” Penta Robotics, Delft, The Netherlands, accessed June 1, 2018, http://pentarobotics.com/products/#brochure
13.
Salgado
,
O.
,
Altuzarra
,
O.
,
Petuya
,
V.
, and
Hernández
,
A.
,
2008
, “
Synthesis and Design of a Novel 3T1R Fully-Parallel Manipulator
,”
ASME J. Mech. Des.
,
130
(
4
), p.
042305
.
14.
Xie
,
F.
, and
Liu
,
X.
,
2015
, “
Design and Development of a High-Speed and High-Rotation Robot With Four Identical Arms and a Single Platform
,”
ASME J. Mech. Rob.
,
7
(
4
), p.
041015
.
15.
Wu
,
G.
,
Bai
,
S.
, and
Hjønet
,
P.
,
2016
, “
Architecture Optimization of a Parallel Schönfliesmotion Robot for Pick-and-Place Applications in a Predefined Workspace
,”
Mech. Mach. Theory
,
106
, pp.
148
165
.
16.
Kong
,
X.
, and
Gosselin
,
C. M.
,
2004
, “
Type Synthesis of 3T1R 4-DOF Parallel Manipulators Based on Screw Theory
,”
IEEE Trans. Rob. Autom
,
20
(
2
), pp.
181
190
.
17.
Gogu
,
G.
, “
Structural Synthesis of Fully-Isotropic Parallel Robots With Schönflies Motions Via Theory of Linear Transformations and Evolutionary Morphology
,”
Eur. J. Mech. A/Solids
,
26
(
2
), pp.
242
269
.
18.
Richard
,
P.-L.
,
Gosselin
,
C. M.
, and
Kong
,
X.
,
2007
, “
Kinematic Analysis and Prototyping of a Partially Decoupled 4-DOF 3T1R Parallel Manipulator
,”
ASME J. Mech. Des.
,
129
(
6
), pp.
611
616
.
19.
Li
,
Q.
, and
Hervé
,
J. M.
,
2009
, “
Parallel Mechanisms With Bifurcation of Schoenflies Motion
,”
IEEE Trans. Rob.
,
25
(
1
), pp.
158
164
.
20.
Briot
,
S.
,
Arakelian
,
V.
, and
Guégan
,
S.
,
2009
, “
PAMINSA: A New Family of Partially Decoupled Parallel Manipulators
,”
Mech. Mach. Theory
,
44
(
2
), pp.
425
444
.
21.
Pierrot
,
F.
,
Reynaud
,
C.
, and
Fournier
,
A.
,
1990
, “
Delta: A Simple and Efficient Parallel Robot
,”
Robotica
,
8
(
2
), pp.
105
109
.
22.
Angeles
,
J.
,
Caro
,
S.
,
Khan
,
W.
, and
Morozov
,
A.
,
2006
, “
Kinetostatic Design of an Innovative Schönflies-Motion Generator
,”
Proc. Ins. Mech. Eng. Part C: J. Mech. Eng. Sci.
,
220
(
7
), pp.
935
943
.
23.
Lee
,
P.-C.
, and
Lee
,
J.-J.
,
2012
, “
Singularity and Workspace Analysis of Three Isoconstrained Parallel Manipulators With Schoenflies Motion
,”
Front. Mech. Eng.
,
7
(
2
), pp.
163
187
.
24.
Harada
,
T.
, and
Angeles
,
J.
,
2014
, “
Kinematics and Singularity Analysis of a CRRHHRRC Parallel Schönflies Motion Generator
,”
CSME Trans.
,
38
(
2
), pp.
173
183
.
25.
Kim
,
S. M.
,
Shin
,
K.
,
Yi
,
B.-J.
, and
Kim
,
W.
,
2015
, “
Development of a Novel Two-Limbed Parallel Mechanism Having Schönflies Motion
,”
Proc. Ins. Mech. Eng. Part C: J. Mech. Eng. Sci.
,
229
(
1
), pp.
136
154
.
26.
Wu
,
G.
,
2017
, “
Kinematic Analysis and Optimal Design of a Wall-Mounted Four-Limb Parallel Sch¨Nflies-Motion Robot for Pick-and-Place Operations
,”
J. Intell. Robot. Syst.
,
85
(
3–4
), pp.
663
677
.
27.
Merlet
,
J.-P.
,
2006
, “
Jacobian, Manipulability, Condition Number, and Accuracy of Parallel Robots
,”
ASME J. Mech. Des.
,
128
(
1
), pp.
199
206
.
28.
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
.
29.
Ranjbaran
,
F.
,
Angeles
,
J.
,
Gonzalez-Palacios
,
M. A.
, and
Patel
,
R. V.
,
1995
, “
The Mechanical Design of a Seven-Axes Manipulator With Kinematic Isotropy
,”
J. Intell. Rob. Syst.
,
14
(
1
), pp.
21
41
.
30.
Altuzarra
,
O.
,
Hernández
,
A.
Salgado
,
O.
, and
Angeles
,
J.
,
2009
, “
Multiobjective Optimum Design of a Symmetric Parallel Schönflies-Motion Generator
,”
ASME J. Mech. Des.
,
131
(
3
), p.
031002
.
31.
Pond
,
G.
, and
Carretero
,
J. A.
,
2006
, “
Formulating Jacobian Matrices for the Dexterity Analysis of Parallel Manipulators
,”
Mech. Mach. Theory
,
41
(
12
), pp.
1505
1519
.
32.
Wei
,
W.
, and
Simaan
,
N.
,
2010
, “
Design of Planar Parallel Robots With Preloaded Flexures for Guaranteed Backlash Prevention
,”
ASME J. Mech. Rob.
,
2
(
1
), p.
011012
.
33.
Angeles
,
J.
,
2006
, “
Is There a Characteristic Length of a Rigid-Body Displacement?
,”
Mech. Mach. Theory
,
41
(
8
), pp.
884
896
.
34.
Dresner
,
T. L.
, and
Buffinton
,
K. W.
,
1991
, “
Definition of Pressure and Transmission Angles Applicable to Multi-Input Mechanisms
,”
ASME J. Mech. Des.
,
113
(
4
), pp.
495
499
.
35.
Bawab
,
S.
,
Kinzel
,
G. L.
, and
Waldron
,
K. J.
,
1996
, “
Rectified Synthesis of Six-Bar Mechanisms With Well-Defined Transmission Angles for Four-Position Motion Generation
,”
ASME J. Mech. Des.
,
118
(
3
), pp.
377
383
.
36.
Balli
,
S. S.
, and
Chand
,
S.
,
2002
, “
Transmission Angle in Mechanisms (Triangle in Mech)
,”
Mech. Mach. Theory
,
37
(
2
), pp.
175
195
.
37.
Takeda
,
Y.
, and
Funabashi
,
H.
,
2001
, “
A Transmission Index for in-Parallel Wire-Driven Mechanisms
,”
JSME Inter. J. Ser. C Mech. Syst., Mach. Elem. Manuf.
,
44
(
1
), pp.
180
187
.
38.
Wang
,
J.
,
Wu
,
C.
, and
Liu
,
X.
,
2010
, “
Performance Evaluation of Parallel Manipulators: Motion/Force Transmissibility and Its Index
,”
Mech. Mach. Theory
,
45
(
10
), pp.
1462
1476
.
39.
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
.
40.
Liu
,
H.
,
Wang
,
M.
,
Huang
,
T.
,
Chetwynd
,
D. G.
, and
Kecskeméthy
,
A.
,
2015
, “
A Dual Space Approach for Force/Motion Transmissibility Analysis of Lower Mobility Parallel Manipulators
,”
ASME J. Mech. Rob.
,
7
(
3
), p.
034504
.
41.
Zhao
,
Y.
,
Wang
,
J.
,
Cao
,
Y.
,
Liang
,
B.
, and
Zhao
,
T.
,
2017
, “
Constant Motion/Force Transmission Analysis and Synthesis of a Class of Translational Parallel Mechanisms
,”
Mech. Mach. Theory
,
108
, pp.
57
74
.
42.
Brinker
,
J.
,
Corves
,
B.
, and
Takeda
,
Y.
,
2018
, “
Kinematic Performance Evaluation of Highspeed Delta Parallel Robots Based on Motion/Force Transmission Indices
,”
Mech. Mach. Theory
,
125
, pp.
111
125
.
43.
Liu
,
H.
,
Huang
,
T.
,
Kecskeméthy
,
A.
, and
Chetwynd
,
D. G.
,
2014
, “
A Generalized Approach for Computing the Transmission Index of Parallel Mechanisms
,”
Mech. Mach. Theory
,
74
, pp.
245
256
.
44.
Gosselin
,
C.
, and
Angeles
,
J.
,
1990
, “
Singularity Analysis of Closed-Loop Kinematic Chains
,”
IEEE Trans. Robot. Autom
,
6
(
3
), pp.
281
290
.
45.
Merlet
,
J.-P.
,
1989
, “
Singular Configurations of Parallel Manipulators and Grassmann Geometry
,”
Int. J. Rot. Res
,
8
(
5
), pp.
45
56
.
46.
Amine
,
S.
,
Masouleh
,
M. T.
,
Caro
,
S.
,
Wenger
,
P.
, and
Gosselin
,
C.
,
2012
, “
Singularity Conditions of 3T1R Parallel Manipulators With Identical Limb Structures
,”
ASME J. Mech. Rob.
,
4
(
1
), p.
011011
.
47.
Amine
,
S.
,
Mokhiamar
,
O.
, and
Caro
,
S.
,
2017
, “
Classification of 3T1R Parallel Manipulators Based on Their Wrench Graph
,”
ASME J. Mech. Rob.
,
9
(
1
), p.
011003
.
48.
Wu
,
G.
,
Bai
,
S.
, and
Caro
,
S.
,
2018
, “
Transmission Quality Evaluation for a Class of Four-Limb Parallel Schönflies-Motion Generators With Articulated Platforms
,”
Mech. Mach. Sci.: Computational Kinematics
, Vol.
50
,
Springer
, Cham, Switzerland, pp.
282
290
.
49.
Wu
,
G.
,
Caro
,
S.
,
Bai
,
S.
, and
Kepler
,
J.
,
2014
, “
Dynamic Modeling and Design Optimization of a 3-DOF Spherical Parallel Manipulator
,”
Rob. Autom. Syst.
,
62
(
10
), pp.
1377
1386
.
50.
Maraje
,
S.
,
Nurahmi
,
L.
, and
Caro
,
S.
,
2016
, “
Operation Modes Comparison of a Reconfigurable 3-PRS Parallel Manipulator Based on Kinematic Performance
,”
ASME
Paper No. DETC2016-59804.
51.
Isaksson
,
M.
,
Marlow
,
K.
,
Brogårdh
,
T.
, and
Eriksson
,
A.
,
2016
, “
A Comparison of the Yaw Constraining Performance of SCARA-Tau Parallel Manipulator Variants Via Screw Theory
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), Stockholm, Sweden, May 16–21, pp.
888
893
.
You do not currently have access to this content.