Abstract
Sensitivity analysis of manipulators aims at studying the influence of variations in its own geometric parameters on its performance. This information is useful for evaluating the position error of the end-effector as well as for the synthesis of tolerances. Indeed, the synthesis of tolerances is a very important issue in the design and manufacturing of robot manipulators. In this paper, a sequential procedure for modeling, dimensioning, and tolerance synthesis of the Parallel Kinematic Manipulator (PKM) PAR2 is proposed. For optimal dimensional design, an approach based on the optimization of the workspace is proposed, taking into account several constraints, followed by a numerical matrix analysis-based deterministic method for sensitivity analysis whose performance is studied in terms of accuracy. To calculate the optimal dimensional tolerances, a new tolerance synthesis method is used. The effect of geometric tolerance on accuracy is analyzed.
Issue Section:
Research Papers
References
1.
Taguchi
, G.
, 1978
, “Off-Line and On-Line Quality Control Systems
,” Proceedings of International Conferences on Quality Control
, Tokyo, Japan
, pp. B4-1
–5
.2.
Al-Widyan
, K.
, Angeles
, J.
, and Cervantes-Sanchez
, J.
, 2003
, “A Model-Based Framework for Robust Design,” Recent Advances in Integrated Design and Manufacturing in Mechanical Engineering
, Gogu
, G.
, Coutellier
, D.
, Chedmail
, P.
, and Ray
, P.
, eds., Springer
, Dordrecht
, pp. 431
–442
.3.
Lian
, B.
, Sun
, T.
, and Song
, Y.
, 2017
, “Parameter Sensitivity Analysis of a 5-dof Parallel Manipulator
,” Rob. Comput. Int. Manuf.
, 46
(C
), pp. 1
–14
. 4.
Sun
, T.
, and Lian
, B.
, 2018
, “Stiffness and Mass Optimization of Parallel Kinematic Machine
,” Mech. Mach. Theory
, 120
, pp. 73
–88
. 5.
Sun
, T.
, Lian
, B.
, Song
, Y.
, and Feng
, L.
, 2019
, “Elastodynamic Optimization of a 5-dof Parallel Kinematic Machine Considering Parameter Uncertainty
,” IEEE/ASME Trans. Mech.
, 24
(1
), pp. 315
–325
. 6.
Lian
, B.
, Wang
, X. V.
, and Wang
, L.
, 2019
, “Static and Dynamic Optimization of a Pose Adjusting Mechanism Considering Parameter Changes During Construction
,” Rob. Comput. Int. Manuf.
, 59
, pp. 267
–277
. 7.
Ting
, K.-L.
, and Long
, Y.
, 1996
, “Performance Quality and Tolerance Sensitivity of Mechanisms
,” ASME J. Mech. Des.
, 118
(1
), pp. 144
–150
. 8.
Zhu
, J.
, and Ting
, K.-L.
, 2000
, “Performance Distribution Analysis and Robust Design
,” ASME J. Mech. Des.
, 123
(1
), pp. 11
–17
. 9.
Caro
, S.
, Bennis
, F.
, and Wenger
, P.
, 2005
, “Tolerance Synthesis of Mechanisms: A Robust Design Approach
,” ASME J. Mech. Des.
, 127
(1
), pp. 86
–94
. 10.
Caro
, S.
, 2004
, “Conception robuste de mécanismes
,” Ph.D. thesis
, IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes
, Nantes, France.11.
Caro
, S.
, Wenger
, P.
, Bennis
, F.
, and Chablat
, D.
, 2005
, “Sensitivity Analysis of the Orthoglide: A Three-DOF Translational Parallel Kinematic Machine
,” ASME J. Mech. Des.
, 128
(2
), pp. 392
–402
. 12.
Rout
, B.
, and Mittal
, R.
, 2006
, “Tolerance Design of Robot Parameters Using Taguchi Method
,” Mech. Syst. Signal Process.
, 20
(8
), pp. 1832
–1852
. 13.
Rout
, B. K.
, and Mittal
, R.
, 2007
, “Tolerance Design of Manipulator Parameters Using Design of Experiment Approach
,” Struct. Multidiscipl. Optim.
, 34
, pp. 445
–462
. 14.
Rout
, B.
, and Mittal
, R.
, 2008
, “Optimal Manipulator Parameter Tolerance Selection Using Evolutionary Optimization Technique
,” Eng. Appl. Artif. Intell.
, 21
(4
), pp. 509
–524
. 15.
Kim
, J.
, Song
, W.-J.
, and Kang
, B.-S.
, 2010
, “Stochastic Approach to Kinematic Reliability of Open-Loop Mechanism With Dimensional Tolerance
,” Appl. Math. Model.
, 34
(5
), pp. 1225
–1237
. 16.
Qi
, Y.
, Sun
, T.
, and Song
, Y.
, 2018
, “Multi-Objective Optimization of Parallel Tracking Mechanism Considering Parameter Uncertainty
,” ASME J. Mech. Rob.
, 10
(4
), p. 041006
. 17.
Huang
, X.
, and Zhang
, Y.
, 2010
, “Robust Tolerance Design for Function Generation Mechanisms With Joint Clearances
,” Mech. Mach. Theory
, 45
(9
), pp. 1286
–1297
. 18.
Goldsztejn
, A.
, Caro
, S.
, and Chabert
, G.
, 2015
, “A New Methodology for Tolerance Synthesis of Parallel Manipulators
,” Proceedings of the 14th IFToMM World Congress
, pp. 184
–193
.19.
Goldsztejn
, A.
, Caro
, S.
, and Chabert
, G.
, 2016
, “A Three-Step Methodology for Dimensional Tolerance Synthesis of Parallel Manipulators
,” Mech. Mach. Theory
, 105
, pp. 213
–234
. 20.
Trang Thanh Trung
, L. W. G.
, and Long
, P. T.
, 2017
, “Tolerance Design of Robot Parameters Using Generalized Reduced Gradient Algorithm
,” Int. J. Mater. Mech. Manuf.
, 5
(2
), pp. 96
–105
.21.
ASME
, 1994
, “Dimensioning and Tolerancing: ASME Y14.5M-1994 (Engineering Drawing and Related Documentation Practices)
.”22.
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
. 23.
Natal
, G. S.
, Chemori
, A.
, and Pierrot
, F.
, 2016
, “Nonlinear Control of Parallel Manipulators for Very High Accelerations Without Velocity Measurement: Stability Analysis and Experiments on Par2 Parallel Manipulator
,” Robotica
, 34
(1
), pp. 43
–70
. 24.
Kelaiaia
, R.
, Zaatri
, A.
, Company
, O.
, and Chikh
, L.
, 2016
, “Some Investigations Into the Optimal Dimensional Synthesis of Parallel Robots.
,” Int. J. Adv. Manuf. Technol.
, 83
, pp. 1525
–1538
. 25.
Baradat
, C.
, Nabat
, V.
, Krut
, S.
, Company
, O.
, and Pierrot
, F.
, 2009
, “Par2: A Spatial Mechanism for Fast Planar, 2-dof, Pick-and-Place Applications
,” Proceedings of the Second International Workshop on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators
, Montpellier, France
, September
, p. 10
.26.
Pierrot
, F.
, Baradat
, C.
, Nabat
, V.
, Company
, O.
, Krut
, S.
, and Gouttefarde
, M.
, 2009
, “Above 40g Acceleration for Pick-and-Place With a New 2-dof PKM
,” 2009 IEEE International Conference on Robotics and Automation
, pp. 1794
–1800
.27.
Lin
, J.
, 1976
, “Multiple-Objective Problems: Pareto-Optimal Solutions by Method of Proper Equality Constraints
,” IEEE Trans. Autom. Contr.
, 21
(5
), pp. 641
–650
. 28.
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
. 29.
Kelaiaia
, R.
, Company
, O.
, and Zaatri
, A.
, 2012
, “Multiobjective Optimization of a Linear Delta Parallel Robot
,” Mech. Mach. Theory
, 50
, pp. 159
–178
. 30.
Merlet
, J.
, 2006
, Parallel Robots
, 2nd ed., Vol. 128
, Springer Netherlands
.31.
Briot
, S.
, Caro
, S.
, and Germain
, C.
, 2017
, “Design Procedure for a Fast and Accurate Parallel Manipulator
,” ASME J. Mech. Rob.
, 9
(6
), p. 061012
.32.
Lee
, M.-Y.
, Erdman
, A. G.
, and Faik
, S.
, 1992
, “A Generalized Performance Sensitivity Synthesis Methodology for Four-Bar Mechanisms
,” 22nd Biennial Mechanisms Conference: Mechanism Design and Synthesis of International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, pp. 1
–4
.33.
Parkinson
, A.
, 1995
, “Robust Mechanical Design Using Engineering Models
,” ASME J. Vib. Acoust.
, 117
(B
), pp. 48
–54
. 34.
He
, J.
, 1991
, “Tolerancing for Manufacturing Via Cost Minimization
,” Int. J. Mach. Tools Manuf.
, 31
(4
), pp. 455
–470
. Copyright © 2021 by ASME
You do not currently have access to this content.
