The aim of this paper is to describe a general and systematic methodology to make controllable transitions between different solutions of the direct kinematic problem (DKP) from the joint space. This work is focused on parallel manipulators and the goal is the usage of just the input variables domain. This way, such transitions can be made controlling all the inputs simultaneously at all times. To do so, it is necessary to analyze the locus of direct kinematics singularities, where different direct kinematic solutions coalesce. It is necessary to specify which portions of such a locus specifically affect each solution. This analysis requires obtaining the locus of triple coalescence singularities. Having done this, all the information can be processed in order to obtain several maps in the joint space. Finally, it will establish the strategy on how to use these maps to connect desired solutions, including the application to a representative example.

References

References
1.
Merlet
,
J.
, 1992, “
Direct Kinematic and Assembly Modes of Parallel Manipulators
,”
Int. J. Robot. Res.
,
11
(
2
), pp.
150
162
.
2.
Altuzarra
,
O.
,
Pinto
,
C.
,
Aviles
,
R.
, and
Hernandez
,
A.
, 2004, “
A Practical Procedure to Analyze Singular Configurations in Closed Kinematic Chains
,”
IEEE Trans. Rob.
,
20
(
6
), pp.
929
940
.
3.
Gosselin
,
C.
, and
Angeles
,
J.
, 1990, “
Singularity Analysis of Closed Loop Kinematic Chains
,”
IEEE Trans. Rob. Autom.
,
6
(
3
), pp.
281
290
.
4.
Hunt
,
K.
, and
Primrose
,
E.
, 1993, “
Assembly Configurations of Some In-Parallel-Actuated Manipulators
,”
Mech. Mach. Theory
,
28
(
1
), pp.
31
42
.
5.
Innocenti
,
C.
, and
Parenti-Castelli
,
V.
, 1992, “
Singularity Free Evolution From One Configuration to Another in Serial and Fully Parallel Manipulators
,”
ASME J. Mech. Des.
,
120
, pp.
73
99
.
6.
McAree
,
P.
, and
Daniel
,
R.
, 1999, “
An Explanation of the Never-Spacial Assembly Changing Motions for 3-3 Parallel Manipulators
,”
Int. J. Robot. Res.
,
18
(
6
), pp.
556
574
.
7.
Zein
,
M.
,
Wenger
,
P.
, and
Chablat
,
D.
, 2006, “
Singular Curves and Cusp Points in the Joint Space of 3-RPR Parallel Manipulators
,” IEEE International Conference on Robotics and Automation 2006, Orlando, FL, May 15–19, pp. 1–6
8.
Zein
,
M.
,
Wenger
,
P.
, and
Chablat
,
D.
, 2008, “
Non-Singular Assembly Mode Changing Motions for 3-RPR Parallel Manipulators
,”
Mech. Mach. Theory
,
43
(
4
), pp.
480
490
.
9.
Macho
,
E.
,
Altuzarra
,
O.
,
Pinto
,
C.
, and
Hernandez
,
A.
, 2008, “
Transitions Between Solutions of the Direct Kinematic Problem
,” Proceedings of the 11th International Symposium on Advances in Robot Kinematics, 2008, Batz-sur-Mer France, pp.
301
310
.
10.
Macho
,
E.
,
Altuzarra
,
O.
,
Petuya
,
V.
, and
Hernndez
,
A.
, 2008, “
Workspace Enlargement Merging Assembly Modes. Application to the 3-RRR Planar Platform
,” Proceedings of the 17th International Workshop on Robotics in Alpe-Adria-Danube Region.
11.
Bamberger
,
H.
,
Wolf
,
A.
, and
Shoham
,
M.
, 2008, “
Assembly Mode Changing in Parallel Mechanisms
,”
IEEE Trans. Rob.
,
24
(
4
), pp.
765
772
.
12.
Macho
,
E.
,
Altuzarra
,
O.
,
Pinto
,
C.
, and
Hernandez
,
A.
, 2007, “
Singularity Free Change of Assembly Mode in Parallel Manipulators. Application to the 3-RPR Planar Platform
,” Proceedings of 12th World Congress in Mechanism and Machine Science.
13.
Collins
,
C.
, and
McCarthy
,
J.
, 1998, “
The Quartic Singularity Surfaces of Planar Platforms in the Clifford Algebra of the Projective Plane
,”
Mech. Mach. Theory
,
33
(
7
), pp.
931
944
.
14.
Degani
,
A.
, and
Wolf
,
A.
, 2006, “
Graphical Singularity Analysis of Planar Parallel Manipulators
,” IEEE International Conference on Robotics and Automation, pp.
751
756
.
15.
Li
,
H.
,
Gosselin
,
C.
, and
Richard
,
M.
, 2006, “
Determination of Maximal Singularity-Free Zones in the Workspace of Planar Three-Degree-of-Freedom Parallel Mechanisms
,”
Mech. Mach. Theory
,
41
(
10
), pp.
1157
1167
.
16.
Murray
,
A.
, and
Pierrot
,
F.
, 1998, “
N-Position Synthesis of Parallel Planar RPR Platforms
,”
Adv. Robot Kinemat.
, pp.
67
78
.
17.
Zein
,
M.
,
Wenger
,
P.
, and
Chablat
,
D.
, 2007, “
Singular Curves in the Joint Space and Cusp Points of 3-RPR Parallel Manipulators
,”
Robotica
,
25
(
6
), pp.
717
724
.
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