Two of the main sources of position error in parallel manipulators are clearances at joints and elastic deformations of the links. The former are usually necessary in order to produce a smooth movement between the pin and the hub of a joint. The latter are unavoidable and they tend to be greater in manipulators designed for pick-and-place tasks due to the need of light links. It can be stated that the end-effector pose error depends on the mechanism configuration, the applied external wrenches, the nature and magnitude of clearances, and the rigidity of the mechanical components. This paper proposes a procedure to calculate position error in parallel manipulators due to both clearances and elastic deformations. Although the procedure is applicable to any planar or spatial parallel manipulator, a planar 5R mechanism is used as an illustrative example in order to make it easier to understand.

References

References
1.
Merlet
,
J.-P.
,
2006
, “
Jacobian, Manipulability, Condition Number, and Accuracy of Parallel Robots
,”
ASME J. Mech. Des.
128
(
1
), pp.
199
205
.10.1115/1.2121740
2.
Briot
,
S.
, and
Bonev
,
I. A.
,
2008
, “
Accuracy Analysis of 3-DOF Planar Parallel Robots
,”
Mech. Mach. Theory
43
(
4
), pp.
445
458
.10.1016/j.mechmachtheory.2007.04.002
3.
Briot
,
S.
, and
Bonev
,
I. A.
,
2010
, “
Accuracy Analysis of 3T1R Fully Parallel Robots
,”
Mech. Mach. Theory
45
, pp.
695
706
.10.1016/j.mechmachtheory.2009.04.002
4.
Altuzarra
,
O.
,
Pinto
,
C.
,
Sandru
,
B.
, and
Hernández
,
A.
,
2011
, “
Optimal Dimensioning for Parallel Manipulators: Workspace, Dexterity, and Energy
,”
ASME J. Mech. Des.
,
133
(
4
), p.
041007
.10.1115/1.4003879
5.
Gosselin
,
C. M.
,
1990
, “
Stiffness Mapping for Parallel Manipulators
,”
IEEE Trans. Robot. Auto.
,
6
(
3
), pp.
281
290
.10.1109/70.56660
6.
Xu
,
Q.
, and
Li
,
Y.
,
2008
, “
An Investigation on Mobility and Stiffness of a 3-DOF Translational Parallel Manipulator via Screw Theory
,”
Robot. CIM Int. Manuf.
,
24
(
3
), pp.
402
411
.10.1016/j.rcim.2007.02.022
7.
Ceccarelli
,
M.
, and
Carbone
,
G.
,
2008
, “
A Stiffness Analysis for CaPaMan (Cassino Parallel Manipulator)
,
Mech. Mach. Theory
37
(
5
), pp.
427
439
.10.1016/S0094-114X(02)00006-X
8.
Deblaise
,
D.
,
Hernot
,
X.
, and
Maurine
,
P.
,
2006
, “
A Systematic Analytical Method of PKM Stiffness Matrix Calculation
,”
Proceedings of the IEEE International Conference on Robotics and Automation
, 4213–4219, Orlando, FL, May 2006.
9.
Corradini
,
C.
,
Faroux
,
J. C.
,
Krut
,
S.
, and
Company
,
O.
,
2003
, “
Evaluation of a 4-Degree of Freedom Parallel Manipulator Stiffness
,”
Proceedings of the 11th World Congress in Mechanism and Machine Science
, IFTOMM’2003, Tianjin, China, August 2003.
10.
Aginaga
,
J.
,
Zabalza
,
I.
,
Altuzarra
,
O.
, and
Nájera
,
J.
,
2012
, “
Improving Static Stiffness of the 6-RUS Parallel Manipulator Using Inverse Singularities
,”
Robot. CIM Int. Manuf.
,
28
(
4
), pp.
458
471
.10.1016/j.rcim.2012.02.003
11.
Farahanchi
,
F.
, and
Shaw
,
S. W.
,
1994
, “
Chaotic and Periodic Dynamics of a Slider-Crank Mechanism With Slider Clearance
,”
J. Sound Vib.
,
177
(
3
), pp.
307
324
.10.1006/jsvi.1994.1436
12.
Muvengei
,
O.
,
Kihiu
,
J.
, and
Ikua
,
B.
,
2012
, “
Numerical Study of Parametric Effects on the Dynamic Response of Planar Multi-Body Systems With Differently Located Frictionless Revolute Clearance Joints
,”
Mech. Mach. Theory
,
53
, pp.
30
49
.10.1016/j.mechmachtheory.2012.02.007
13.
Majarena-Bello
,
A. C.
,
Santolaria-Mazo
,
J.
,
Samper-Carnicer
,
D.
, and
Aquilar-Martín
,
J. J.
,
2011
, “
Análisis del Juego, Repetibilidad de Posicionamiento y Precarga de un Mecanismo Paralelo
,”
Dyna
,
86
(
6
), pp.
676
685
.10.6036/4082
14.
Bauchau
,
O. A.
, and
Rodríguez
,
J.
,
2002
, “
Modeling of Joints With Clearance in Flexible Multibody Systems
,”
Int. J. Solid. Struct.
,
39
(
1
), pp.
41
63
.10.1016/S0020-7683(01)00186-X
15.
Liu
,
C.-S.
,
Zhang
,
K.
, and
Yang
,
R.
,
2007
, “
The FEM Analysis and Approximate Model for Cylindrical Joints With Clearances
,”
Mech. Mach. Theory
,
42
(
2
), pp.
183
197
.10.1016/j.mechmachtheory.2006.02.006
16.
Tian
,
Q.
,
Zhang
,
Y.
,
Chen
,
L
, and
Flores
,
P.
,
2009
, “
Dynamics of Spatial Flexible Multibody Systems With Clearance and Lubricated Spherical Joints
,”
Comput. Struct.
,
87
(
13–14
), pp.
913
929
.10.1016/j.compstruc.2009.03.006
17.
Ravn
,
P.
,
1998
, “
A Continuous Analysis Method for Planar Multibody Systems With Joint Clearance
,”
Multibody System Dynamics
,
2
, pp.
1
24
.10.1023/A:1009759826529
18.
Flores
,
P.
, and
Ambrósio
,
J.
,
2004
, “
Revolute Joints With Clearance in Multibody Systems
,”
Comput. Struct.
,
82
(
17–19
), pp.
1359
1369
.10.1016/j.compstruc.2004.03.031
19.
Flores
,
P.
,
Ambrósio
,
J.
,
Claro
,
H. C. P.
,
Lankarani
,
H. M.
, and
Koshy
,
C. S.
,
2006
, “
A Study on Dynamics of Mechanical Systems Including Joints With Clearance and Lubrication
,”
Mech. Mach. Theory
,
41
(
3
), pp.
247
261
.10.1016/j.mechmachtheory.2005.10.002
20.
Flores
,
P.
, and
Lankarani
,
H. M.
,
2012
, “
Dynamic Response of Multibody Systems With Multiple Clearance Joints
,”
J. Comput. Nonlinear Dyn.
,
7
(
3
), p.
031003
.10.1115/1.4005927
21.
Khemili
,
I.
, and
Romdhane
,
L.
,
2008
, “
Dynamic Analysis of a Flexible Slider-Crank Mechanism With Clearance
,”
Eur. J. Mech. A
,
27
(
5
), pp.
882
898
.10.1016/j.euromechsol.2007.12.004
22.
Ting
,
K.-L.
,
Zhu
,
J.
, and
Watkins
,
D.
,
2000
, “
The Effects of Joint Clearances on Position and Orientation Deviation of Linkages and Manipulators
,”
Mech. Mach. Theory
,
35
(
3
), pp.
391
401
.10.1016/S0094-114X(99)00019-1
23.
Zhu
,
J.
, and
Ting
,
K.-L.
,
2000
, “
Uncertainty Analysis of Planar and Spatial Robots With Joint Clearances
,”
Mech. Mach. Theory
,
35
(
9
), pp.
1239
1256
.10.1016/S0094-114X(99)00076-2
24.
Jawale
,
H. P.
, and
Thorat
,
H. T.
,
2012
, “
Investigation of Positional Error in Two Degree of Freedom Mechanism With Joint Clearance
,”
ASME J. Mech. Robot.
,
4
, p.
011002
.10.1115/1.4005523
25.
Venanzi
,
S.
, and
Parenti-Castelli
,
V.
,
2005
, “
A New Technique for Clearance Influence Analysis in Spatial Mechanisms
,
ASME J. Mech. Des.
,
127
(
3
), pp.
446
455
.10.1115/1.1867512
26.
Tischer
,
C. R.
, and
Samuel
,
A. E.
,
1999
, “
Prediction of the Slop in General Spatial Linkages
,”
Int. J. Robot. Res.
,
18
, pp.
845
858
.10.1177/02783649922066600
27.
Meng
,
J.
,
Zhang
,
D.
, and
Li
,
Z.
,
2009
, “
Accuracy Analysis of Parallel Manipulators With Joint Clearance
,”
ASME J. Mech. Des.
,
131
(
1
), p.
011013
.10.1115/1.3042150
28.
Innocenti
,
C.
,
2002
, “
Kinematic Clearance Sensitivity Analysis of Spatial Linkages With Revolute Joints
,”
ASME J. Mech. Des.
,
124
(
1
), pp.
50
58
.10.1115/1.1436088
29.
Lim
,
S. R.
,
Kang
,
K.
,
Park
,
S.
,
Choi
,
W. C.
,
Song
,
J.-B.
,
Hong
,
D.
, and
Shim
,
J. K.
,
2002
, “
Error Analysis of a Parallel Mechanism Considering Link Stiffness and Joint Clearances
,
KSME Int. J.
,
16
(
6
), pp.
799
809
.10.1007/BF02939339
30.
Tsai
,
M.-J.
, and
Lai
,
T.-H.
,
2008
, “
Accuracy Analysis of a Multi-Loop Linkage With Joint Clearances
,”
Mech. Mach. Theory
,
43
(
9
), pp.
1141
1157
.10.1016/j.mechmachtheory.2007.09.001
31.
Altuzarra
,
O.
,
Aginaga
,
J.
,
Hernández
,
A.
, and
Zabalza
,
I.
,
2011
, “
Workspace Analysis of Positioning Discontinuities due to Clearances in Parallel Manipulators
,”
Mech. Mach. Theory
,
46
(
5
), pp.
577
592
.10.1016/j.mechmachtheory.2011.01.005
32.
Company
,
O.
,
Pierrot
,
F.
,
Krut
,
S.
,
Baradat
,
C.
and
Nabat
,
V.
,
2011
, “
Par2: A Spatial Mechanism for Fast Planar Two-Degree-of-Freedom Pick-and-Place Applications
,”
Meccanica
,
46
, pp.
239
248
.10.1007/s11012-010-9413-x
You do not currently have access to this content.