Abstract
In this paper, a generalized method for error modeling of the spatial 1T2R three degrees-of-freedom kinematically redundant parallel mechanism with a closed-loop chain is proposed, which is based on the matrix differential method. First, the detailed process of generalized error modeling and error analysis are described. Based on the proposed method, the error model of the spatial 3PRR(RR)S-P (P—prismatic joint, R—revolute joint, S—spherical joint, and the underline indicates that the joint is the actuator) kinematically redundant parallel mechanism is established as an example, and the correctness of the error model is verified by combining forward with inverse kinematics. Then, the patterns affecting the output error of the moving platform are discussed for the case where the mechanism contains only static error or dynamic error, respectively. In addition, the error sensitivity indices are defined to evaluate the error sensitivity of the moving platform to different redundant parameters L4 under a certain pose. Finally, in order to identify the key error terms, the sensitivity of the output error of the mechanism to a single error term is analyzed. The results show that the error sensitivity of the spatial kinematically redundant parallel mechanism can be effectively reduced by adjusting the kinematically redundant parameters, so that the mechanism can maintain a low error sensitivity in a certain pose.
Issue Section:
Design of Mechanisms and Robotic Systems
Topics:
Errors
References
1.
Xue
, Y.
, Qu
, H.
, Li
, X.
, and Guo
, S.
, 2023
, “Stiffness Performance Analysis of a 3-PRPS Kinematically Redundant Parallel Mechanism
,” Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci.
, 237
(3
), pp. 589
–602
. 2.
Xie
, Z.
, Xie
, F.
, Zhu
, L.
, and Liu
, X.
, 2022
, “Robotic Mobile and Mirror Milling of Large-Scale Complex Structures
,” Natl. Sci. Rev.
, 10
(5
), p. nwac188
. 3.
Meng
, Q.
, Xie
, F.
, and Liu
, X.
, 2018
, “Conceptual Design and Kinematic Analysis of a Novel Parallel Robot for High-Speed Pick-and-Place Operations
,” Front. Mech. Eng.
, 13
(2
), pp. 211
–224
. 4.
Stewart
, D.
, 2016
, “A Platform With Six Degrees of Freedom
,” Proc. Inst. Mech. Eng.
, 180
(1
), pp. 371
–386
. 5.
Dehghani
, M.
, Mohammadi Moghaddam
, M.
, and Torabi
, P.
, 2018
, “Analysis, Optimization and Prototyping of a Parallel RCM Mechanism of a Surgical Robot for Craniotomy Surgery
,” Ind. Robot
, 45
(1
), pp. 78
–88
. 6.
Neumann
, K.
, “Adaptive In-Jig High Load Exechon Machining Technology & Assembly.”7.
Gosselin
, C.
, and Schreiber
, L.
, 2018
, “Redundancy in Parallel Mechanisms: A Review
,” ASME Appl. Mech. Rev.
, 70
(1
), p. 010802
. 8.
Cui
, H.
, Zhu
, Z.
, Gan
, Z.
, and Brogardh
, T.
, 2005
, “Kinematic Analysis and Error Modeling of TAU Parallel Robot
,” Rob. Comput. Integr. Manuf.
, 21
(6
), pp. 497
–505
. 9.
Wang
, J.
, and Masory
, O.
, 1993
, “On the Accuracy of a Stewart Platform. I. The Effect of Manufacturing Tolerances
,” Proceedings of IEEE International Conference on Robotics and Automation
, Atlanta, GA
, May 2–6
, pp. 114
–120
.10.
Wang
, S.-M.
, and Ehmann
, K. F.
, 2002
, “Error Model and Accuracy Analysis of a Six-DOF Stewart Platform
,” ASME J. Manuf. Sci. Eng.
, 124
(2
), pp. 286
–295
. 11.
Binaud
, N.
, Caro
, S.
, and Wenger
, P.
, 2010
, “Sensitivity Comparison of Planar Parallel Manipulators
,” Mech. Mach. Theory
, 45
(11
), pp. 1477
–1490
. 12.
Zhan
, Z.
, Zhang
, X.
, Jian
, Z.
, and Zhang
, H.
, 2018
, “Error Modelling and Motion Reliability Analysis of a Planar Parallel Manipulator With Multiple Uncertainties
,” Mech. Mach. Theory
, 124
, pp. 55
–72
. 13.
Tang
, T.
, Chi
, C.
, Fang
, H.
, and Zhang
, J.
, 2022
, “Geometric Error Propagation Model-Based Accuracy Synthesis and Its Application to a 1T2R Parallel Manipulator
,” ASME J. Mech. Des.
, 144
(7
), p. 073304
. 14.
Shan
, X.
, and Cheng
, G.
, 2019
, “Structural Error Identification and Kinematic Accuracy Analysis of a 2(3PUS + S) Parallel Manipulator
,” Measurement
, 140
(9
), pp. 22
–28
. 15.
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
. 16.
Yuan
, X.
, Meng
, Q.
, Xie
, F.
, Liu
, X.
, and Wang
, J.
, 2023
, “Error Modeling and Accuracy Evaluation of Parallel Manipulators With Mixed DOFs Based on Motion/Force Transmissibility and Constrainability
,” Mech. Mach. Theory
, 186
, p. 105346
. 17.
Zhang
, J.
, Lian
, B.
, and Song
, Y.
, 2019
, “Geometric Error Analysis of an Over-Constrained Parallel Tracking Mechanism Using the Screw Theory
,” Chin. J. Aeronaut.
, 32
(6
), pp. 1541
–1554
. 18.
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
. 19.
Tian
, W.
, Shen
, Z.
, Lv
, D.
, and Yin
, F.
, 2020
, “A Systematic Approach for Accuracy Design of Lower-Mobility Parallel Mechanism
,” Robotica
, 38
(12
), pp. 2173
–2188
. 20.
Tannous
, M.
, Caro
, S.
, and Goldsztejn
, A.
, 2014
, “Sensitivity Analysis of Parallel Manipulators Using an Interval Linearization Method
,” Mech. Mach. Theory
, 71
, pp. 93
–114
. 21.
Chebbi
, A.
, Chouaibi
, Y.
, Affi
, Z.
, and Romdhane
, L.
, 2018
, “Sensitivity Analysis and Prediction of the Orientation Error of a Three Translational Parallel Manipulator
,” Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci.
, 232
(1
), pp. 140
–161
. 22.
Guo
, S.
, Wang
, N.
, Fang
, Y.
, and Li
, X.
, 2011
, “Error Sensitivity of 3-UPU Parallel Manipulator Based on Probability Distribution
,” Chin. J. Mech. Eng.
, 47
(21
), pp. 14
–21
. 23.
Cai
, S.
, Peng
, L.
, and Huang
, W.
, 2013
, “Error Analysis of a 2-PRS/2-UPS 4-DOF Parallel Platform
,” Advanced Materials Research
, 605-607
, pp. 1511
–1514
. www.scientific.net/AMR.605-607.151124.
Wu
, G.
, Bai
, S.
, Kepler
, J.
, and Caro
, S.
, 2012
, “Error Modeling and Experimental Validation of a Planar 3-PPR Parallel Manipulator With Joint Clearances
,” ASME J. Mech. Rob.
, 4
(4
), p. 041008
. 25.
Zhuang
, X.
, 2022
, “Time-Dependent Kinematic Reliability of a Dual-Axis Driving Mechanism for Satellite Antenna Considering Non-Uniform Planar Revolute Joint Clearance
,” Acta Astronaut.
, 197
, pp. 91
–106
. 26.
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
. 27.
Kotlarski
, J.
, Abdellatif
, H.
, and Heimann
, B.
, 2008
, “Improving the Pose Accuracy of a Planar 3RRR Parallel Manipulator Using Kinematic Redundancy and Optimized Switching Patterns
,” Proceedings of IEEE International Conference on Robotics and Automation
, Pasadena, CA
, May 9–13
, pp. 3863
–3868
.28.
Kotlarski
, J.
, Heimann
, B.
, and Ortmaier
, T.
, 2011
, “Experimental Validation of the Influence of Kinematic Redundancy on the Pose Accuracy of Parallel Kinematic Machines
,” Proceedings of IEEE International Conference on Robotics and Automation
, Shanghai, China
, May 9–13
, pp. 1923
–1929
.29.
Li
, G.
, Qu
, H.
, and Guo
, S.
, 2020
, “Sensitivity Analysis of a Planar Parallel Manipulator With Kinematic Redundancy
,” Chin. J. Mech. Eng.
, 56
(23
), pp. 45
–57
. 30.
Li
, X.
, Qu
, H.
, Li
, G.
, Guo
, S.
, and Dong
, G.
, 2023
, “Optimal Design of a Kinematically Redundant Planar Parallel Mechanism Based on Error Sensitivity and Workspace
,” ASME J. Mech. Des.
, 145
(2
), p. 023305
. 31.
Zeng
, C.-D.
, Qiu
, Z.-C.
, Zhang
, F.-H.
, and Zhang
, X.-M.
, 2023
, “Error Modelling and Motion Reliability Analysis of a Multi-DOF Redundant Parallel Mechanism With Hybrid Uncertainties
,” Reliab. Eng. Syst. Saf.
, 235
(3
), p. 109259
. 32.
Qu
, H.
, and Guo
, S.
, 2016
, “Topology and Mobility Variations of a Novel Redundant Reconfigurable Parallel Mechanism,” Advances in Reconfigurable Mechanisms and Robots II
, Vol. 36
, X.
Ding
, X.
Kong
, and J.
Dai
, eds., Springer, Cham
, Switzerland
, pp. 223
–233
. 33.
Shen
, C.
, Qu
, H.
, Guo
, S.
, and Li
, X.
, 2021
, “Kinematics Analysis and Singularity Avoidance of a Parallel Mechanism With Kinematic Redundancy
,” Chin. J. Mech. Eng.
, 35
(1
), p. 113
. 34.
Qu
, H.
, Guo
, S.
, and Zhang
, Y.
, 2017
, “A Novel Relative Degree-of-Freedom Criterion for a Class of Parallel Manipulators With Kinematic Redundancy and Its Applications
,” Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci.
, 231
(22
), pp. 4227
–4240
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