In this paper, the wrench accuracy for parallel manipulators is examined under variations in parameters and data. The solution sets of actuator forces/torques are investigated utilizing interval arithmetic (IA). Implementation issues of interval arithmetic to analyze the performance of manipulators are addressed, including the consideration of dependencies in parameters and the design of input vectors to generate the required wrench. Specifically, the effect of the dependency within and among the entries of the Jacobian matrix is studied, and methodologies for reducing and/or eliminating the overestimation of solution set are presented. In addition, the subset of solution set that produces platform wrenches within the required lower and upper bounds is modeled. Furthermore, the formulation of solutions that provide any platform wrench within the defined interval is examined. Intersection of these two sets, if any, results in the given interval platform wrench. Implementation of the methods to identify the solution for actuator forces/torques is presented on example parallel manipulators.

References

References
1.
Hansen
,
E.
,
1992
,
Global Optimization Using Interval Analysis
, 1st ed.,
Marcel Dekker
, New York.
2.
Moore
,
R.
,
Kearfott
,
R. B.
, and
Cloud
,
M. J.
,
2009
,
Introduction to Interval Analysis
,
SIAM
, Philadelphia, PA.
3.
Kearfott
,
R. B.
,
1996
,
Rigorous Global Search: Continuous Problems
,
Kluwer Academic
, Dordrecht, The Netherlands.
4.
Notash
,
L.
,
2015
, “
Analytical Methods for Solution Sets of Interval Wrench
,”
ASME
Paper No. DETC2015-47575.
5.
Shary
,
S. P.
,
1992
, “
A New Class of Algorithms for Optimal Solution of Interval Linear Systems
,”
Interval Comput.
,
2
(
4
), pp.
18
29
.
6.
Hartfiel
,
D.
,
1980
, “
Concerning the Solution Set of Ax = b Where P ≤ A ≤ Q and p ≤ b ≤ q
,”
Numer. Math.
,
35
(
3
), pp.
355
359
.
7.
Popova
,
E. D.
, and
Krämer
,
W.
,
2008
, “
Visualizing Parametric Solution Sets
,”
BIT Numer. Math.
,
48
(
1
), pp.
95
115
.
8.
Nazari
,
V.
, and
Notash
,
L.
,
2016
, “
Motion Analysis of Manipulators With Uncertainty in Kinematic Parameters
,”
ASME J. Mech. Rob.
,
8
(
2
), p.
021014
.
9.
Rao
,
R. S.
,
Asaithambi
,
A.
, and
Agrawal
,
S. K.
,
1998
, “
Inverse Kinematic Solution of Robot Manipulators Using Interval Analysis
,”
J. Mech. Des.
,
120
(
1
), pp.
147
150
.
10.
Merlet
,
J.
,
2004
, “
Solving the Forward Kinematics of a Gough-Type Parallel Manipulator With Interval Analysis
,”
Int. J. Rob. Res.
,
23
(
3
), pp.
221
235
.
11.
Daney
,
D.
,
Andreff
,
N.
,
Chabert
,
G.
, and
Papegay
,
Y.
,
2006
, “
Interval Method for Calibration of Parallel Robots: Vision-Based Experiments
,”
Mech. Mach. Theory
,
41
(
8
), pp.
929
944
.
12.
Carricato
,
M.
,
2013
, “
Direct Geometrico-Static Problem of Underconstrained Cable-Driven Parallel Robots With Three Cables
,”
ASME J. Mech. Rob.
,
5
(
3
), p.
031008
.
13.
Notash
,
L.
,
2016
, “
On the Solution Set for Positive Wire Tension With Uncertainty in Wire-Actuated Parallel Manipulators
,”
ASME J. Mech. Rob.
,
8
(
4
), p.
044506
.
14.
Fieldler
,
M.
,
Nedoma
,
J.
,
Ramik
,
J.
, and
Rohn
,
J.
,
2006
,
Linear Optimization Problems With Inexact Data
,
Springer
,
New York
.
15.
Elishakoff
,
I.
, and
Miglis
,
Y.
,
2012
, “
Overestimation-Free Computational Version of Interval Analysis
,”
Int. J. Comput. Methods Eng. Sci. Mech.
,
13
(
5
), pp.
319
328
.
16.
Popova
,
E. D.
,
2013
, “
On Overestimation-Free Computational Version of Interval Analysis
,”
Int. J. Comput. Methods Eng. Sci. Mech.
,
14
(
6
), pp.
491
494
.
17.
Shary
,
S. P.
,
1992
, “
On Controlled Solution Set of Interval Algebraic Systems
,”
Interval Comput.
,
4
(
6
), pp.
66
75
.
18.
Rump
,
S. M.
,
1999
, “
INTLAB—INTerval LABoratory
,”
Developments in Reliable Computing
,
T.
Csendes
, ed.,
Kluwer Academic Publishers
, Dordrecht, The Netherlands, pp.
77
104
.
19.
Notash
,
L.
,
2016
, “
Investigation of Wrench Accuracy for Parallel Manipulators
,”
ASME
Paper No. DETC2016-59425.
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