By drawing on the duality of twist space and wrench space, this paper presents a general and systematic approach for force/motion transmissibility analysis of lower mobility nonredundant and nonoverconstrained parallel manipulators. This leads to the formulation of a complete and justifiable model that enables the force/motion transmissibility analysis to be integrated into a unified framework under the umbrella of a homogenous and decoupled linear transformation that maps the coordinates of the platform wrench/twist in the joint space to its natural coordinates in the operation space. Utilizing the penalty method to avoid the indeterminate form “0/0” when the local maximum of a virtual coefficient approaches zero, a set of dimensionally homogeneous transmission indices is proposed which can be employed for precisely representing the closeness to different types of singularities defined in twist space as well as for dimensional optimization. An example is given to illustrate the effectiveness of this approach.

References

References
1.
Merlet
,
J.-P.
,
2006
, “
Jacobian, Manipulability, Condition Number, and Accuracy of Parallel Robots
,”
ASME Mech. Des.
,
128
(
1
), pp.
199
206
.10.1115/1.2121740
2.
Merlet
,
J.-P.
, and
Gosselin
,
C. M.
,
2008
, “
Parallel Mechanisms and Robots
,”
Springer Handbook of Robotics
,
S.
Bruno
, and
K.
Oussama
, eds.,
Springer-Verlag
,
Heidelberg
, Chap. 12.
3.
Doty
,
K. L.
,
Melchiorri
,
C.
,
Schwartz
,
E. M.
, and
Bonivento
,
C.
,
1995
, “
Robot Manipulability
,”
IEEE J. Rob. Autom.
,
11
(
3
), pp.
462
468
.10.1109/70.388791
4.
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
.10.1115/1.2912810
5.
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
.10.1115/1.2826896
6.
Chen
,
C.
, and
Angeles
,
J.
,
2007
, “
Generalized Transmission Index and Transmission Quality for Spatial Linkages
,”
Mech. Mach. Theory
,
42
(
9
), pp.
1225
1237
.10.1016/j.mechmachtheory.2006.08.001
7.
Ball
,
R. S.
,
1900
,
A Treatise on the Theory of Screws
,
Cambridge University Press
,
Cambridge, UK
.
8.
Yuan
,
M. S. C.
,
Freudenstein
,
F.
, and
Woo
,
L. S.
,
1971
, “
Kinematic Analysis of Spatial Mechanism by Means of Screw Coordinates. Part 2—Analysis of Spatial Mechanisms
,”
ASME J. Eng. Ind., Ser. B
,
91
(
1
), pp.
67
73
.10.1115/1.3427919
9.
Sutherland
,
G.
, and
Roth
,
B.
,
1973
, “
A Transmission Index for Spatial Mechanisms
,”
ASME J. Eng. Ind.
,
95
(
2
), pp.
589
597
.10.1115/1.3438195
10.
Tsai
,
M. J.
, and
Lee
,
H. W.
,
1994
, “
The Transmissivity and Manipulability of Spatial Mechanisms
,”
ASME J. Mech. Des.
,
116
(
1
), pp.
137
143
.10.1115/1.2919337
11.
Tsai
,
M. J.
, and
Lee
,
H. W.
,
1994
, “
Generalized Evaluation for the Transmission Performance of Mechanisms
,”
Mech. Mach. Theory
,
29
(
4
), pp.
607
618
.10.1016/0094-114X(94)90098-1
12.
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
.10.1016/j.mechmachtheory.2013.12.012
13.
Takeda
,
Y.
, and
Funabashi
,
H.
,
2001
, “
A Transmission Index for In-Parallel Wire-Driven Mechanisms
,”
JSME Int. J., Ser. C
,
44
(
1
), pp.
180
187
.10.1299/jsmec.44.180
14.
Chang
,
W.-T.
,
Lin
,
C.-C.
, and
Lee
,
J.-J.
,
2003
, “
Force Transmissibility Performance of Parallel Manipulators
,”
J. Rob. Syst.
,
20
(
11
), pp.
659
670
.10.1002/rob.10115
15.
Wang
,
J.-S.
,
Wu
,
C.
, and
Liu
,
X.-J.
,
2010
, “
Performance Evaluation of Parallel Manipulators: Motion/Force Transmissibility and Its Index
,”
Mech. Mach. Theory
,
45
(
10
), pp.
1462
1476
.10.1016/j.mechmachtheory.2010.05.001
16.
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
.10.1115/1.4007004
17.
Liu
,
X.-J.
,
Chen
,
X.
, and
Nahon
,
M.
,
2014
, “
Motion/Force Constrainability Analysis of Lower-Mobility Parallel Manipulators
,”
ASME J. Mech. Rob.
,
6
(
3
), p.
031006
.10.1115/1.4026632
18.
Briot
,
S.
,
Glazunov
,
V.
, and
Arakelian
,
V.
,
2013
, “
Investigation on the Effort Transmission in Planar Parallel Manipulators
,”
ASME J. Mech. Rob.
,
5
(
1
), p.
011011
.10.1115/1.4023325
19.
Huang
,
T.
,
Wang
,
M.
,
Yang
,
S.
,
Sun
,
T.
,
Chetwynd
,
D. G.
, and
Xie
,
F.
,
2014
, “
Force/Motion Transmissibility Analysis of Six Degree of Freedom Parallel Mechanisms
,”
ASME J. Mech. Rob
,
6
(
3
), p.
031010
.10.1115/1.4026631
20.
Davidson
,
J. K.
, and
Hunt
,
K. H.
,
2004
,
Robots and Screw Theory: Applications of Kinematics and Statics to Robotics
,
Oxford University Press
,
Oxford, UK
.
21.
Huang
,
T.
,
Yang
,
S.
,
Wang
,
M.
,
Sun
,
T.
, and
Chetwynd
,
D. G.
,
2015
, “
An Approach to Determining the Unknown Twist/Wrench Subspaces of Lower Mobility Serial Kinematic Chain
,”
ASME J. Mech. Rob.
,
7
(
3
), p.
031003
.10.1115/1.4028622
22.
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
.10.1016/j.mechmachtheory.2011.01.009
23.
Tsai
,
L.-W.
,
1999
,
Robot Analysis: The Mechanics of Serial and Parallel Manipulators
,
Wiley
,
New York
.
24.
Mohamed
,
M. G.
, and
Duffy
,
J.
,
1985
, “
A Direct Determination of the Instantaneous Kinematics of Fully Parallel Robot Manipulators
,”
ASME J. Mech. Des.
,
107
(
2
), pp.
226
229
.10.1115/1.3258713
25.
Zlatanov
,
D.
,
Bonev
,
I. A.
, and
Gosselin
,
C. M.
,
2002
, “
Constraint Singularities of Parallel Mechanisms
,”
IEEE International Conference Robotics Automation
(
ICRA’02
), Washington, DC, May 11–15, pp.
496
502
.10.1109/ROBOT.2002.1013408
26.
Joshi
,
S.
, and
Tsai
,
L. W.
,
2002
, “
Jacobian Analysis of Limited-DOF Parallel Manipulators
,”
ASME J. Mech. Des.
,
124
(
2
), pp.
254
258
.10.1115/1.1469549
27.
Di Gregorio
,
R.
, and
Parenti-Castelli
,
V.
,
2002
, “
Mobility Analysis of the 3-UPU Parallel Mechanism Assembled for a Pure Translational Motion
,”
ASME J. Mech. Des.
,
124
(
2
), pp.
259
264
.10.1115/1.1471530
You do not currently have access to this content.