Manufacturing and assembly (geometric) errors affect the positioning precision of manipulators. In six degrees-of-freedom (6DOF) manipulators, geometric error effects can be compensated through suitable calibration procedures. This, in general, is not possible in lower-mobility manipulators. Thus, methods that evaluate such effects must be implemented at the design stage to determine both which workspace region is less affected by these errors and which dimensional tolerances must be assigned to match given positioning-precision requirements. In the literature, such evaluations are mainly tailored on particular architectures, and the proposed techniques are difficult to extend. Here, a general discussion on how to take into account geometric error effects is presented together with a general method to solve this design problem. The proposed method can be applied to any nonoverconstrained architecture. Eventually, as a case study, the method is applied to the analysis of the geometric error effects of the translational parallel manipulator (TPM) Triflex-II.

References

References
1.
Liu
,
H.
,
Huang
,
T. T.
, and
Chetwynd
,
D. G.
,
2011
, “
A General Approach for Geometric Error Modeling of Lower Mobility Parallel Manipulators
,”
ASME J. Mech. Rob.
,
3
(
2
), p.
021013
.
2.
Huang
,
T.
,
Whitehouse
,
D. J.
, and
Chetwynd
,
D. G.
,
2002
, “
A Unified Error Model for Tolerance Design, Assembly and Error Compensation of 3-DOF Parallel Kinematic Machines With Parallelogram Struts
,”
CIRP Ann. Manuf. Technol.
,
51
(
1
), pp.
297
301
.
3.
Di Gregorio
,
R.
, and
Parenti-Castelli
,
V.
,
2002
, “
Geometric Errors Versus Calibration in Manipulators With Less Than 6 DOF
,”
RoManSy 14—Theory and Practice of Robots and Manipulators
,
G.
Bianchi
,
J.-C.
Guinot
, and
C.
Rzymkowski
, eds.,
Springer
,
New York
, pp.
31
38
.
4.
Fang
,
Y.
, and
Tsai
,
L.
,
2002
, “
Structure Synthesis of a Class of 4-DOF and 5-DOF Parallel Manipulators With Identical Limb Structures
,”
Int. J. Rob. Res.
,
21
(
9
), pp.
799
810
.
5.
Kong
,
X.
, and
Gosselin
,
C. M.
,
2007
,
Type Synthesis of Parallel Mechanisms
,
Springer-Verlag
,
Berlin
.
6.
Klimchik
,
A.
,
Chablat
,
D.
, and
Pashkevich
,
A.
,
2014
, “
Stiffness Modeling for Perfect and Non-Perfect Parallel Manipulators Under Internal and External Loadings
,”
Mech. Mach. Theory
,
79
, pp.
1
28
.
7.
Caro
,
S.
,
Wenger
,
P.
,
Bennis
,
F.
, and
Chablat
,
D.
,
2006
, “
Sensitivity Analysis of the Orthoglide: A 3-DOF Translational Parallel Kinematic Machine
,”
ASME J. Mech. Des.
,
128
(
2
), pp.
392
402
.
8.
Liu
,
X.-J.
, and
Wang
,
J.
,
2014
,
Parallel Kinematics: Type, Kinematics, and Optimal Design
(Springer Tracts in Mechanical Engineering),
Springer
,
Berlin
.
9.
Gosselin
,
C.
, and
Angeles
,
J.
,
1991
, “
A Global Performance Index for the Kinematic Optimization of Robotic Manipulators
,”
ASME J. Mech. Des.
,
113
(
3
), pp.
220
226
.
10.
Tian
,
W.
,
Gao
,
W.
,
Chang
,
W.
, and
Nie
,
Y.
,
2014
, “
Error Modeling and Sensitivity Analysis of a Five-Axis Machine Tool
,”
Math. Probl. Eng.
,
2014
, p.
745250
.
11.
Merlet
,
J.-P.
,
2005
, “
Jacobian, Manipulability, Condition Number, and Accuracy of Parallel Robots
,”
ASME J. Mech. Des.
,
128
(
1
), pp.
199
206
.
12.
Li
,
Y.
,
Li
,
C.
,
Qu
,
D.
,
Duan
,
S.
,
Bai
,
X.
, and
Shen
,
H.
,
2012
, “
Errors Modeling and Sensitivity Analysis for a Novel Parallel Manipulator
,”
International Conference on Mechatronics and Automation
(
ICMA
), Aug. 5–8, pp.
755
760
.
13.
Mei
,
J.
,
Ni
,
Y.
,
Li
,
Y.
,
Zhang
,
L.
, and
Liu
,
F.
,
2009
, “
The Error Modeling and Accuracy Synthesis of a 3-DOF Parallel Robot Delta-s
,”
International Conference on Information and Automation (ICIA’09)
, pp.
289
294
.
14.
Frisoli
,
A.
,
Solazzi
,
M.
,
Pellegrinetti
,
D.
, and
Bergamasco
,
M.
,
2011
, “
A New Screw Theory Method for the Estimation of Position Accuracy in Spatial Parallel Manipulators With Revolute Joint Clearances
,”
Mech. Mach. Theory
,
46
(
12
), pp.
1929
1949
.
15.
Yu
,
Z.
,
Tiemin
,
L.
, and
Xiaoqiang
,
T.
,
2011
, “
Geometric Error Modeling of Machine Tools Based on Screw Theory
,”
Proc. Eng.
,
24
, pp.
845
849
.
16.
Kumaraswamy
,
U.
,
Shunmugam
,
M.
, and
Sujatha
,
S.
,
2013
, “
A Unified Framework for Tolerance Analysis of Planar and Spatial Mechanisms Using Screw Theory
,”
Mech. Mach. Theory
,
69
, pp.
168
184
.
17.
Chen
,
Y.
,
Xie
,
F.
,
Liu
,
X.
, and
Zhou
,
Y.
,
2014
, “
Error Modeling and Sensitivity Analysis of a Parallel Robot With Scara (Selective Compliance Assembly Robot Arm) Motions
,”
Chin. J. Mech. Eng.
,
27
(
4
), pp.
693
702
.
18.
Angeles
,
J.
, and
Rojas
,
A.
,
1987
, “
Manipulator Inverse Kinematics Via Condition-Number Minimization and Continuation
,”
Int. J. Rob. Autom.
,
2
(
2
), pp.
61
69
.
19.
Campos
,
A. A.
,
Guenther
,
R.
, and
Martins
,
D.
,
2009
, “
Differential Kinematics of Parallel Manipulators Using Assur Virtual Chains
,”
Proc. Inst. Mech. Eng., Part C
,
223
(
7
), pp.
1697
1711
.
20.
Davies
,
T. H.
,
1981
, “
Kirchhoff's Circulation Law Applied to Multi-Loop Kinematic Chain
,”
Mech. Mach. Theory
,
16
(
3
), pp.
171
173
.
21.
Tsai
,
L.-W.
,
1999
,
Robot Analysis: The Mechanics of Serial and Parallel Manipulators
,
Wiley
,
New York
.
22.
Hervé
,
J. M.
,
1994
, “
The Mathematical Group Structure of the Set of Displacements
,”
Mech. Mach. Theory
,
29
(
1
), pp.
73
81
.
23.
Meyer
,
C. D.
,
2000
,
Matrix Analysis and Applied Linear Algebra
,
Society for Industrial and Applied Mathematics
,
Philadelphia, PA
.
24.
Gosselin
,
C. M.
, and
Angeles
,
J.
,
1990
, “
Singularity Analysis of Closed-Loop Kinematic Chains
,”
IEEE Trans. Rob. Autom.
,
6
(
3
), pp.
281
290
.
25.
Ma
,
O.
, and
Angeles
,
J.
,
1991
, “
Architecture Singularities of Platform Manipulators
,”
IEEE
International Conference on Robotics and Automation
, Sacramento, CA, Apr. 9–11, pp.
1542
1547
.
26.
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
.
27.
Simas
,
H.
,
Martins
,
D.
, and
Simoni
,
R.
,
2013
, “
Uma Classe de Manipuladores Paralelos de Configuração Variável com Autoalinhamento
,” Instituto Nacional da Propriedade Industrial (INPI), Rio de Janeiro, Brazil, Patent No. BR1020130267716.
28.
Simoni
,
R.
,
Simas
,
H.
, and
Martins
,
D.
,
2014
, “
TRIFLEX: Design and Prototyping of a 3-DOF Variable-Configuration Parallel Manipulator With Self-Aligning
,”
Int. J. Mech. Eng. Autom.
,
1
(
2
), pp.
77
82
.
29.
Simoni
,
R.
,
Simas
,
H.
, and
Martins
,
D.
,
2013
, “
Uma Classe de Manipuladores Paralelos de Configuração Variável
,” Instituto Nacional da Propriedade Industrial (INPI), Rio de Janeiro, Brazil, Patent No. BR102013026774.
30.
Gosselin
,
C. M.
,
Kong
,
X.
,
Foucault
,
S.
, and
Bonev
,
I. A.
,
2004
, “
A Fully Decoupled 3-DOF Translational Parallel Mechanism
,”
4th Chemnitz Parallel Kinematics Seminar, Parallel Kinematic Machines International Conference
, Chemnitz, Germany, pp.
595
610
.
31.
Lecours
,
A.
, and
Gosselin
,
C.
,
2009
, “
Determination of the Workspace of a 3-PRPR Parallel Mechanism for Human-Robot Collaboration
,”
Trans. Can. Soc. Mech. Eng.
,
33
(
4
), pp.
609
618
.
This content is only available via PDF.
You do not currently have access to this content.