The majority of the manipulation tasks require the motion of the end-effector from an initial pose to a final one without any particular condition on the path. Thus, the reduction of the practicable paths between any two poses is a possible choice, exploitable at the design stage, for simplifying the manipulator hardware. This choice is adopted in underactuated manipulators. The (nS)-2SPU wrist is one out of the underactuated parallel wrists this author proposed in a previous paper. Here, the kinematic analysis of this wrist is studied: both its finite and its elementary kinematics are considered. It is shown that its control algorithms can be written by using simple closed-form formulas, which can take advantage from the wide literature on the spherical four-bar linkages. Moreover, the demonstration that its singular configurations can be avoided more easily than the ones of the fully parallel wrist is provided.

References

References
1.
Angeles
J.
, 2003,
Fundamentals of Robotic Mechanical Systems
,
Springer-Verlag
,
New York, NY
.
2.
O’Reilly
O. M.
, 2008,
Intermediate Dynamics for Engineers
,
Cambridge University Press
,
New York, NY.
3.
Pennestrì
E.
,
Cavacece
M.
, and
Vita
L.
, 2005, “
On the Computation of Degrees-of-Freedom: A Didactic Perspective
,”
Proceedings of ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, IDETC/CIE 2005, Sept. 24–28, Long Beach, CA, Paper No. DETC2005-84109.
4.
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.
5.
Murray
,
R. M.
,
Li
,
Z.
, and
Sastry
,
S. S.
, 1994,
A Mathematical Introduction to Robotic Manipulation
,
CRC Press
,
Boca Raton
.
6.
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
.
7.
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
.
8.
Ben-Horin
,
P.
, and
Thomas
,
F.
, 2008, “
A Nonholonomic 3-Motor Parallel Robot
,”
Advances in Robot Kinematics
,
J.
Lenarcic
and
P.
Wenger
, eds.,
Springer-Verlag
,
New York
.
9.
Chung
,
W.
, 2004,
Nonholonomic Manipulators
,
Springer-Verlag
,
Berlin, Heidelberg, New York
.
10.
Krysiak
B.
,
Pazderski
D.
, and
KozŁowski
K.
, 2011, “
Modelling and Experimental Research of Nonholonomic Ball Gear
,”
J. Autom. Mobile Rob. Intell. Syst.
,
5
(
3
), pp.
27
32
, Available at: http://www.jamris.org/issue_03_2011.php.
11.
Tan
Y.
, and
Li
L.
, 2012, “
Design of Three Joints Underactuated Manipulator With Nonholonomic Constraint
,”
Appl. Mech. Mater.
,
121–126
, pp.
810
814
.
12.
Di Gregorio
R.
, 2012, “
Position Analysis and Path Planning of the S-(nS)PU-SPU and S-(nS)PU-2SPU Underactuated Wrists
,”
ASME J. Mech. Rob.
,
4
(
2
), p.
021006
.
13.
Di Gregorio
R.
, 2012, “
Instantaneous Kinematics and Singularities of Two Types of Under-Actuated Parallel Wrists
,”
Proceedings of the ASME 2012 11th Biennial Conference On Engineering Systems Design And Analysis, ESDA 2012
, Nantes (France), July 2–4, Paper No.: ESDA2012-82084.
14.
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
.
15.
Stammers
C. W.
, 1993, “
Operation of a Two-Motor Robot Wrist to Achieve Three-Dimensional Manoeuvres With Minimum Total Rotation
,”
Proc. Inst. Mech. Eng., Part C
,
207
(
1
), pp.
33
39
.
16.
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
.
17.
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.
18.
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
.
19.
Thomas
,
F.
, 2010, private communication.
20.
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
.
21.
Yuegang
T.
,
Haifeng
Y.
, and
All-Bail
M.
, 2009, “
Motion Planning of Multi-joint Underactuated Manipulator Based on Trigonometric Function Input
,”
Proceedings of IEEE 2009 International Forum on Computer Science-Technology and Applications
, pp.
75
78
.
22.
Mazur
A.
,
Szakie
D.
, 2009, “
On Path Following Control of Nonholonomic Mobile Manipulators
,”
Int. J. Appl. Math. Comput. Sci.
,
19
(
4
), pp.
561
574
.
23.
Mazur
A.
, 2010, “
Trajectory Tracking Control in Workspace-Defined Tasks for Nonholonomic Mobile Manipulators
,”
Robotica
,
28
(
1
), pp.
57
68
.
24.
Jakubiak
J.
,
Tchoń
K.
, and
Magiera
W.
, 2010, “
Motion Planning in Velocity Affine Mechanical Systems
,”
Int. J. Control
,
83
(
9
), pp.
1965
1974
.
25.
Ma
,
O.
, and
Angeles
,
J.
, 1991, “
Architecture Singularities of Platform Manipulators
,”
Proceedings of the 1991 IEEE International Conference on Robotics and Automation
, Sacramento, CA, pp.
1542
1547
.
26.
Chiang
,
C. H.
, 1988,
Kinematics of Spherical Mechanisms
,
Cambridge University Press
,
New York
.
27.
Zhang
,
Y.
,
Crane
,
C. D.
III
, and
Duffy
,
J.
, 1998, “
Determination of the Unique Orientation of Two Bodies Connected by a Ball-and-Socket Joint From Four Measured Displacements
,”
J. Rob. Syst.
,
15
(
5
), pp.
299
308
.
28.
Gosselin
,
C. M.
, and
Angeles
,
J.
, 1990, “
Singularity Analysis of Closed-Loop Kinematic Chains
,”
IEEE Trans. Rob. Autom.
,
6
(
3
), pp.
281
290
.
29.
Zlatanov
,
D.
,
Fenton
,
R. G.
, and
Benhabib
,
B.
, 1995, “
A Unifying Framework for Classification and Interpretation of Mechanism Singularities
,”
ASME J. Mech. Des.
,
117
(
4
), pp.
566
572
.
30.
Di Gregorio
,
R.
, 2008, “
An Exhaustive Scheme for the Singularity Analysis of Three-Dof Parallel Manipulators
,”
Proceedings of the 17th International Workshop on Robotics in Alpe-Adria-Danube Region (RAAD 2008)
, Sept. 15–17, Ancona, Italy.
31.
Wang
,
J.
, and
Gosselin
,
C. M.
, 2004, “
Singularity Loci of a Special Class of Spherical 3-DOF Parallel Mechanisms With Prismatic Actuators
,”
ASME J. Mech. Des.
,
126
(
2
), pp.
319
326
.
32.
Hunt
,
K. H.
, 1978,
Kinematic Geometry of Mechanisms
,
Claredon Press
,
Oxford, UK
.
33.
Davidson
,
J. K.
,
Hunt
,
K. H.
, 2007, “
Robots and screw theory
,” Oxford University Press, Oxford, UK.
34.
Den Hartog
,
J. P.
, 1948,
Mechanics
,
Dover Publications, Inc.
,
New York
.
You do not currently have access to this content.