This paper presents novel 2DOF and 3DOF closed-chain orientational manipulators, whose end-effector motion is actuated in a decoupled and homokinetic way by frame-located motors via holonomic transmissions based on constant-velocity couplings. The functioning of these couplings is investigated and the conditions applying for homokinetic transmission to be preserved during simultaneous motor drive are revealed and implemented. As a result, decoupled and configuration-independent relations between the motor rates and the time-derivatives of the variables describing the end-effector orientation are achieved. The attainment of analogous relations between the motor speeds and the components of the end-effector angular velocity is conversely proven to be unfeasible. The problem of singularities is furthermore examined, showing that input-output homokinesis is not a sufficient condition for a globally uniform kinetostatic behavior of the mechanism, which may, indeed, possibly reach uncertainty singular configurations. The connecting chains of the most typical constant-velocity couplings are analyzed, in order to obtain analytical expressions for the functions on which such singularities depend. The influence of design parameters is accordingly inspected. The results are valuable for the type and dimension synthesis of closed-chain wrists free from direct kinematic singularities, and characterized by simple kinematics and regular input-output kinetostatic relations.

1.
Gosselin
,
C. M.
, and
Angeles
,
J.
, 1990, “
Singularity Analysis of Closed-Loop Kinematic Chains
,”
IEEE Trans. Rob. Autom.
1042-296X,
6
(
3
), pp.
281
290
.
2.
Carricato
,
M.
, and
Parenti-Castelli
,
V.
, 2002, “
Singularity-Free Fully-Isotropic Translational Parallel Mechanisms
,”
Int. J. Robot. Res.
0278-3649,
21
(
2
), pp.
161
174
.
3.
Kong
,
X.
, and
Gosselin
,
C. M.
, 2002, “
Kinematics and Singularity Analysis of a Novel Type of 3-CRR 3-DOF Translational Parallel Manipulator
,”
Int. J. Robot. Res.
0278-3649,
21
(
9
), pp.
791
798
.
4.
Kong
,
X.
, and
Gosselin
,
C. M.
, 2004, “
Type Synthesis of Input-Output Decoupled Parallel Manipulators
,”
Trans. Can. Soc. Mech. Eng.
0315-8977,
28
(
2A
), pp.
185
196
.
5.
Carricato
,
M.
, 2005, “
Fully Isotropic Four-Degrees-of-Freedom Parallel Mechanisms for Schoenflies Motion
,”
Int. J. Robot. Res.
0278-3649,
24
(
5
), pp.
397
414
.
6.
Carricato
,
M.
, and
Parenti-Castelli
,
V.
, 2004, “
A Novel Fully Decoupled Two-Degrees-of-Freedom Parallel Wrist
,”
Int. J. Robot. Res.
0278-3649,
23
(
6
), pp.
661
667
.
7.
Gogu
,
G.
, 2005, “
Fully-Isotropic Over-Constrained Parallel Wrists With Two Degrees of Freedom
,”
2005 IEEE International Conference on Robotics and Automation
, Barcelona, Spain, pp.
4025
4030
.
8.
Hervé
,
J. M.
, 2006, “Uncoupled Actuation of Pan-Tilt Wrists,” IEEE Trans. Rob., 22(1), pp. 56–64.
9.
Vertechy
,
R.
, and
Parenti-Castelli
,
V.
, 2006, “
Synthesis of 2-DOF Spherical Fully Parallel Mechanisms
,”
Advances in Robot Kinematics
,
J.
Lenarčič
and
B.
Roth
, eds.,
Springer
,
Dordrecht, The Netherlands
, pp.
385
394
.
10.
Dudiţă
,
F.
, 1974,
Cuplaje mobile homocinetice
,
Editura Tehnică
,
Bucharest, Romania
, in Romanian.
11.
Zagatti
,
E.
, 1983,
Giunti: criteri di scelta e proporzionamento
,
Tecniche Nuove
,
Milano, Italy
, pp.
39
188
, in Italian.
12.
Matschinsky
,
W.
, 2000,
Road Vehicle Suspensions
,
Professional Engineering
,
London, UK
, pp.
42
50
.
13.
Seherr-Thoss
,
H. C.
,
Schmelz
,
F.
, and
Aucktor
,
E.
, 2006,
Universal Joints and Driveshafts: Analysis, Design, Applications
,
Springer-Verlag
,
Berlin, Germany
.
14.
Dunlop
,
G. R.
, and
Jones
,
T. P.
, 1997, “
Position Analysis of a 3-DOF Parallel Manipulator
,”
Mech. Mach. Theory
0094-114X,
32
(
8
), pp.
903
920
.
15.
Tischler
,
C. R.
,
Hunt
,
K. H.
, and
Samuel
,
A. E.
, 1998, “
On Optimizing the Kinematic Geometry of a Dextrous Robot Finger
,”
Int. J. Robot. Res.
0278-3649,
17
(
10
), pp.
1055
1067
.
16.
Sone
,
K.
,
Isobe
,
H.
, and
Yamada
,
K.
, 2004, “
High Angle Active Link
,”
NTN Technical Review
,
71
, pp.
70
73
.
17.
Zlatanov
,
D.
, and
Gosselin
,
C. M.
, 2004, “
On the Kinematic Geometry of 3-RER Parallel Mechanisms
,”
11th World Congress in Mechanism and Machine Science
, Tianjin, China, pp.
226
230
.
18.
Rosheim
,
M. E.
, 1989,
Robot Wrist Actuators
,
Wiley
,
New York
.
19.
Milenkovic
,
V.
, 1990, “
Non-Singular Industrial Robot Wrist
,” U.S. Patent No. 4,907,937.
20.
Gogu
,
G.
, 2006, “
Fully-Isotropic Hexapods
,”
Advances in Robot Kinematics
,
J.
Lenarčič
and
B.
Roth
, ed.,
Springer
,
Dordrecht, The Netherlands
, pp.
323
330
.
21.
Gogu
,
G.
, 2007, “
Fully-Isotropic Three-Degree-of-Freedom Parallel Wrists
,”
2007 IEEE International Conference on Robotics and Automation
, Roma, Italy, pp.
895
900
.
22.
Porat
,
I.
, 1980, “
Moment Transmission by a Universal Joint
,”
Mech. Mach. Theory
0094-114X,
15
(
4
), pp.
245
254
.
23.
Hunt
,
K. H.
, 1973, “
Constant-Velocity Shaft Couplings: A General Theory
,”
ASME J. Eng. Ind.
0022-0817,
95B
(
2
), pp.
455
464
.
24.
Hunt
,
K. H.
, 1978,
Kinematic Geometry of Mechanisms
,
Clarendon
,
Oxford, UK
, pp.
389
402
.
25.
Zlatanov
,
D.
,
Fenton
,
R. G.
, and
Benhabib
,
B.
, 1995, “
A Unifying Framework for Classification and Interpretation of Mechanism Singularities
,”
ASME J. Mech. Des.
0161-8458,
117
(
4
), pp.
566
572
.
26.
Merlet
,
J. -P.
, 2006,
Parallel Robots
,
Springer
,
Dordrecht, The Netherlands
, pp.
153
155
.
27.
Wittenburg
,
J.
, 1977,
Dynamics of Systems of Rigid Bodies
,
Teubner
,
Stuttgart, Germany
, pp.
19
32
.
28.
Carricato
,
M.
, 2007, “
Homokinetic Transmission of Rotational Motion via Constant-Velocity Joints in Closed-Chain Wrists
,”
12th World Congress in Mechanism and Machine Science
, Besançon, France, pp.
284
290
.
29.
Robinson
,
J. D.
,
Holland
,
J. B.
,
Hayes
,
M. J. D.
, and
Langlois
,
R. G.
, 2005, “
Velocity-Level Kinematics of the Atlas Spherical Orienting Device Using Omni-Wheels
,”
Trans. Can. Soc. Mech. Eng.
0315-8977,
29
(
4
), pp.
691
700
.
30.
Kong
,
X.
, and
Gosselin
,
C. M.
, 2005, “
Type Synthesis of 3-DOF PPR-Equivalent Parallel Manipulators Based on Screw Theory and the Concept of Virtual Chain
,”
ASME J. Mech. Des.
0161-8458,
127
(
6
), pp.
1113
1121
.
31.
Tsai
,
L. -W.
, 1988, “
The Kinematics of Spatial Robotic Bevel-Gear Trains
,”
IEEE J. Rob. Autom.
0882-4967,
4
(
2
), pp.
150
156
.
32.
Innocenti
,
C.
, and
Parenti-Castelli
,
V.
, 1993, “
Echelon Form Solution of Direct Kinematics for the General Fully-Parallel Spherical Wrist
,”
Mech. Mach. Theory
0094-114X,
28
(
4
), pp.
553
561
.
33.
Gosselin
,
C. M.
, and
St-Pierre
,
É.
, 1997, “
Development and Experimentation of a Fast 3-DOF Camera-orienting Device
,”
Int. J. Robot. Res.
0278-3649,
16
(
5
), pp.
619
630
.
34.
Vischer
,
P.
, and
Clavel
,
R.
, 2000, “
Argos: A Novel 3-DOF Parallel Wrist Mechanism
,”
Int. J. Robot. Res.
0278-3649,
19
(
1
), pp.
5
11
.
35.
Kong
,
X.
, and
Gosselin
,
C. M.
, 2004, “
Type Synthesis of Three-Degree-of-Freedom Spherical Parallel Manipulators
,”
Int. J. Robot. Res.
0278-3649,
23
(
3
), pp.
237
245
.
36.
Clemens
,
M.
, 1869, “
Improvement in Apparatus for Transmitting Rotary Motion
,” U.S. Patent No. 96,395.
37.
Rzeppa
,
A. H.
, 1953, “
Universal Joint Drives
,”
Mach. Des.
0024-9114,
25
(
4
), pp.
162
170
.
38.
Phillips
,
J.
, 1984,
Freedom in Machinery
,
Cambridge University Press
,
Cambridge, UK
, Vol.
I
, p.
130
.
39.
Phillips
,
J.
, 1984,
Freedom in Machinery
,
Cambridge University Press
,
Cambridge, UK
, Vol.
II
, p.
150
.
40.
Fenaille
,
P.
, 1927, “
Double cardan sphérique pour automobiles à roues avant motrices et directrices
,” French Patent No. 628,309.
41.
Carter
,
B. C.
, 1958, “
Universal Joints
,” U.S. Patent No. 2,828,615.
42.
Hervé
,
J. M.
1986, “
Le joint de Koenigs, ses variantes, son application possible en robotique
,”
Entraînements & systèmes
,
19
(
6
), pp.
4
6
. 0002-7820
43.
Culver
,
I. H.
, 1969, “
Constant Velocity Universal Joint
,” U.S. Patent No. 3,477,249.
44.
Herchenbach
,
P.
, 1981, “
Homokinetic Double Joint for Wide Bending Angles
,” U.S. Patent No. 4,257,243.
45.
Mohamed
,
M. G.
, and
Duffy
,
J.
, 1985, “
A Direct Determination of the Instantaneous Kinematics of Fully Parallel Robot Manipulators
,”
ASME J. Mech., Transm., Autom. Des.
0738-0666,
107
(
2
), pp.
226
229
.
46.
Conconi
,
M.
, and
Carricato
,
M.
, 2009, “A New Assessment of Singularities of Parallel Kinematic Chains,” IEEE Trans. Rob., 25(4), pp. 757–770.
47.
Gosselin
,
C. M.
, 1990, “
Stiffness Mapping for Parallel Manipulators
,”
IEEE Trans. Rob. Autom.
1042-296X,
6
(
3
), pp.
377
382
.
48.
Doty
,
K. L.
,
Melchiorri
,
C.
,
Schwartz
,
E. M.
, and
Bonivento
,
C.
, 1995, “
Robot Manipulability
,”
IEEE Trans. Robot. Autom.
,
11
(
3
), pp.
462
468
. 1042-296X
49.
Park
,
F. C.
, and
Kim
,
J. W.
, 1998, “
Manipulability of Closed Kinematic Chains
,”
ASME J. Mech. Des.
0161-8458,
120
(
4
), pp.
542
548
.
50.
Hunt
,
K. H.
, 2003, “
Review: Don’t Cross-Thread The Screw!
J. Rob. Syst.
0741-2223,
20
(
7
), pp.
317
339
.
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