In a previous work, this author showed that ten topologies for underactuated parallel wrists can be generated from a fully parallel wrist (FPW). Three of them are obtained by simply replacing a spherical pair (S) with a nonholonomic spherical pair (nS). The S-(nS)PU-SPU and S-(nS)PU-2SPU wrists are two among these three. The position analysis of these two wrists is studied here. In particular, all the four position-analysis problems, which are necessary for implementing their path planning, are addressed and solved in closed form. Despite their different topology, the position analysis of these two wrists can be practically solved by using the same formulas and algorithms. Based on the deduced formulas, a path-planning algorithm is proposed. The obtained results make the studied wrist topologies able to replace “ordinary” wrists in the manipulation tasks which do not require tracking.

References

References
1.
Ben-Horin
,
P.
, and
Thomas
,
F.
, 2008, “
A Nonholonomic 3-Motor Parallel Robot
,”
Advances in Robot Kinematics: Analysis and Design
,
J.
Lenarcic
and
P.
Wenger
, eds.,
Springer Science + Business Media B.V.
,
New York
, pp.
111
118
, ISBN: 978-1-4020-8599-4.
2.
Grosch
,
P.
,
Di Gregorio
,
R.
, and
Thomas
,
F.
, 2010, “
Generation of Under-Actuated Manipulators With Nonholonomic Joints From Ordinary Manipulators
,”
ASME J. Mech. Rob.
,
2
(
1
), p.
011005
.
3.
Di Gregorio
,
R.
, 2011, “
Under-Actuated Nonholonomic Parallel Wrists
,”
Proceedings of the 13th World Congress in Mechanism and Machine Science (IFToMM 2011)
, Guanajuato, México, June 19–25, Paper No. A12-264.
4.
Stammers
,
C. W.
,
Prest
,
P. H.
, and
Mobley
,
C. G.
, 1991, “
The Development of a Versatile Friction Drive Robot Wrist
,”
Proceedings of the 8th World Congress on the Theory of Machines and Mechanisms
, Prague, Czechoslovakia, Aug. 26–31, pp.
499
502
.
5.
Stammers
,
C. W.
,
Prest
,
P. H.
, and
Mobley
,
C. G.
, 1992, “
A Friction Drive Robot Wrist: Electronic and Control Requirements
,”
Mechatronics
,
2
(
4
), pp.
391
401
.
6.
Stammers
,
C. W.
, 1993, “
Operation of a Two-Motor Robot Wrist to Achieve Three-Dimensional Manoeuvres With Minimum Total Rotation
,”
Proc. IMechE, Part C: J. Mech. Eng. Sci.
,
207
(
1
), pp.
33
39
.
7.
Innocenti
,
C.
, and
Parenti-Castelli
V.
, 1993, “
Echelon Form Solution of Direct Kinematics for the General Fully-Parallel Spherical Wrist
,”
Mech. Mach. Theory
,
28
(
4
), pp.
553
561
.
8.
Di Gregorio
,
R.
, 2011, “
Kinematics of the (nS)-2SPU Wrist
,”
Proceedings of the ASME 2011 International Design Engineering Technical Conferences & Computer and Information in Engineering Conference, IDETC/CIE 2011
, Washington, DC, Aug. 28–31, Paper No. DETC2011-47103.
9.
Murray
,
R. M.
,
Li
,
Z.
, and
Sastry
,
S. S.
, 1994,
A Mathematical Introduction to Robotic Manipulation
,
CRC Press
,
Boca Raton
.
10.
Choset
,
H.
,
Lynch
,
K. M.
,
Hutchinson
,
S.
,
Kantor
,
G.
,
Burgard
,
W.
,
Kavraki
,
L. E.
, and
Thrun
,
S.
, 2005,
Principles of Robot Motion: Theory, Algorithms, and Implementations
,
MIT Press
,
Boston
.
11.
Rabier
,
P. J.
, and
Rheinboldt
,
W. C.
, 2000,
Nonholonomic Motion of Rigid Mechanical Systems From a DAE Viewpoint
,
Society for Industrial and Applied Mathematics (SIAM)
,
Philadelphia, PA
.
12.
Nakamura
,
Y.
,
Chung
,
W.
, and
Sørdalen
,
O. J.
, 2001, “
Design and Control of the Nonholonomic Manipulator
,”
IEEE Trans. Rob. Autom.
,
17
(
1
), pp.
48
59
.
13.
Jean
,
F.
, 2001, “
Complexity of Nonholonomic Motion Planning
,”
Int. J. Control
,
74
(
8
), pp.
776
782
.
14.
Cortés Monforte
,
J.
, 2002,
Geometric, Control and Numeric Aspects of Nonholonomic Systems
,
Springer-Verlag
,
Berlin, Heidelberg, New York
.
15.
Bloch
,
A. M.
, 2003,
Nonholonomic Mechanics and Control
,
Springer Science + Business Media, LLC
,
New York
.
16.
Chung
,
W.
, 2004,
Nonholonomic Manipulators
,
Springer-Verlag
,
Berlin, Heidelberg, New York
.
17.
Bloch
,
A. M.
,
Marsden
,
J. E.
, and
Zenkov
,
D. V.
, 2005, “
Nonholonomic Dynamics
,”
Not. AMS
,
52
(
3
), pp.
320
329
. Available at: http://www.ams.org/notices/200503/index.htmlhttp://www.ams.org/notices/200503/index.html
18.
Hussein
,
I. I.
, and
Bloch
,
A. M.
, 2008, “
Optimal Control of Underactuated Nonholonomic Mechanical Systems
,”
IEEE Trans. Autom. Control
,
53
(
3
), pp.
668
682
.
19.
Chaplygin
,
S. A.
, 2008, “
On the Theory of Motion of Nonholonomic Systems. The Reducing-Multiplier Theorem
,”
Regular Chaotic Dyn.
,
13
(
4
), pp.
369
376
. (Originally published in Russian on Matematicheskiĭ Sbornik (Mathematical Collection), 1911, 28(1))
20.
Fernandez
,
O. E.
,
Mestdag
,
T.
, and
Bloch
,
A. M.
, 2009, “
A Generalization of Chaplygin’s Reducibility Theorem
,”
Regular Chaotic Dyn.
,
14
(
6
), pp.
635
655
.
21.
Angeles
,
J.
, 2007,
Fundamentals of Robotic Mechanical Systems
,
Springer Science + Business Media, LLC
,
New York
.
You do not currently have access to this content.