Research Papers

Accuracy Analysis of Redundantly Actuated and Overconstrained Parallel Mechanisms With Actuation Errors

[+] Author and Article Information
Jianzhong Ding

School of Mechanical
Engineering and Automation,
Beihang University,
Beijing 100191, China
e-mail: jianzhongd@buaa.edu.cn

Chunjie Wang

School of Mechanical
Engineering and Automation,
Beihang University,
Beijing 100191, China
e-mail: wangcj@buaa.edu.cn

Hongyu Wu

School of Mechanical
Engineering and Automation,
Beihang University,
Beijing 100191, China
e-mail: hongyu@buaa.edu.cn

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received March 20, 2017; final manuscript received August 9, 2018; published online September 25, 2018. Assoc. Editor: Raffaele Di Gregorio.

J. Mechanisms Robotics 10(6), 061010 (Sep 25, 2018) (7 pages) Paper No: JMR-17-1070; doi: 10.1115/1.4041212 History: Received March 20, 2017; Revised August 09, 2018

A general accuracy analysis method of redundantly actuated and overconstrained parallel mechanisms is proposed. Coupled effects of actuation errors and internal elastic forces arose from the elastic deformation are both considered. The accuracy analysis approach is based on the Lie-group theory and screw theory, and it includes three steps. First, stiffness matrices of serial legs are obtained. Second, the movement of each leg is modeled based on group theory and the elastic forces arose from the deformation are represented using the stiffness matrices, following which the multiclosed-loop structure constraint and self-balanced force constraint are modeled. Finally, the error pose is estimated. The proposed method is illustrated by the accuracy study of a redundantly actuated and overconstrained Stewart platform. The error modeling is easy as the use of stiffness matrix can model the passive joint motions and deformation together. Moreover, the proposed method is computationally cheap as all computations are linear.

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Sugimoto, K. , 1990, “ Existence Criteria for Over-Constrained Mechanisms: An Extension of Motor Algebra,” ASME J. Mech. Des., 112(3), pp. 295–298. [CrossRef]
Li, Y. , Sun, Y. , Peng, B. , and Hu, F. , 2016, “ Dynamic Modeling of a High-Speed Over-Constrained Press Machine,” J. Mech. Sci. Technol., 30(7), pp. 3051–3059. [CrossRef]
Maaroof, O. W. , and Dede, M. İ. C. , 2014, “ Kinematic Synthesis of Over-Constrained Double-Spherical Six-Bar Mechanism,” Mech. Mach. Theory, 73, pp. 154–168. [CrossRef]
Fu, J. , Gao, F. , Chen, W. , Pan, Y. , and Lin, R. , 2016, “ Kinematic Accuracy Research of a Novel Six-Degree-of-Freedom Parallel Robot With Three Legs,” Mech. Mach. Theory, 102, pp. 86–102. [CrossRef]
Ropponen, T. , and Arai, T. , 1995, “ Accuracy Analysis of a Modified Stewart Platform Manipulator,” IEEE International Conference on Robotics and Automation (ICRA), Nagoya, Japan, May 21–27, pp. 521–525.
Hao, F. , and Merlet, J.-P. , 2005, “ Multi-Criteria Optimal Design of Parallel Manipulators Based on Interval Analysis,” Mech. Mach. Theory, 40(2), pp. 157–171. [CrossRef]
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. [CrossRef]
Ma, X. , Zhang, L. , Zhu, L. , Yang, W. , and Hu, P. , 2016, “ The Slider Motion Error Analysis by Positive Solution Method in Parallel Mechanism,” Proc. SPIE, 99603, p. 99030.
Patel, A. J. , and Ehmann, K. , 1997, “ Volumetric Error Analysis of a Stewart Platform-Based Machine Tool,” CIRP Ann.-Manuf. Technol., 46(1), pp. 287–290. [CrossRef]
Li, H. , Zhang, X. , Zeng, L. , and Wu, H. , 2017, “ Vision-Aided Online Kinematic Calibration of a Planar 3 R RR Manipulator,” Mechanism and Machine Science (Lecture Notes in Electrical Engineering, Vol. 408), Springer, Singapore, pp. 963–972.
Liu, H. , Huang, 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. [CrossRef]
Briot, S. , and Bonev, I. A. , 2008, “ Accuracy Analysis of 3-DOF Planar Parallel Robots,” Mech. Mach. Theory, 43(4), pp. 445–458. [CrossRef]
Briot, S. , and Bonev, I. A. , 2010, “ Accuracy Analysis of 3T1R Fully-Parallel Robots,” Mech. Mach. Theory, 45(5), pp. 695–706. [CrossRef]
Wang, Y. , and Chirikjian, G. S. , 2006, “ Error Propagation on the Euclidean Group With Applications to Manipulator Kinematics,” IEEE Trans. Rob., 22(4), pp. 591–602. [CrossRef]
Li, X. , Ding, X. , and Chirikjian, G. S. , 2015, “ Analysis of Angular-Error Uncertainty in Planar Multiple-Loop Structures With Joint Clearances,” Mech. Mach. Theory, 91, pp. 69–85. [CrossRef]
Chen, G. , Wang, H. , and Lin, Z. , 2013, “ A Unified Approach to the Accuracy Analysis of Planar Parallel Manipulators Both With Input Uncertainties and Joint Clearance,” Mech. Mach. Theory, 64, pp. 1–17. [CrossRef]
Pucheta, M. A. , and Gallardo, A. G. , 2017, “ Synthesis of Precision Flexible Mechanisms Using Screw Theory With a Finite Elements Validation,” International Symposium on Multibody Systems and Mechatronics, pp. 3–14.
Jiang, Y. , Li, T. , Wang, L. , and Chen, F. , 2018, “ Improving Tracking Accuracy of a Novel 3-Dof Redundant Planar Parallel Kinematic Machine,” Mech. Mach. Theory, 119, pp. 198–218. [CrossRef]
Shang, W. , and Cong, S. , 2014, “ Motion Control of Parallel Manipulators Using Acceleration Feedback,” IEEE Trans. Control Syst. Technol., 22(1), pp. 314–321. [CrossRef]
Wang, K. , Luo, M. , Mei, T. , Zhao, J. , and Cao, Y. , 2013, “ Dynamics Analysis of a Three-DOF Planar Serial-Parallel Mechanism for Active Dynamic Balancing With Respect to a Given Trajectory,” Int. J. Adv. Rob. Syst., 10(1), p. 23. [CrossRef]
Ciblak, N. , and Lipkin, H. , 1994, “ Centers of Stiffness, Compliance, and Elasticity in the Modelling of Robotic Systems,” Robotics: Kinematics, Dynamics and Control, Minneapolis, MN, pp. 185–194.
Ciblak, N. , 1994, “ Asymmetric Cartesian Stiffness for the Modeling of Compliant Robotic Systems,” 23rd Biennial ASME Mechanisms Conference, Minneapolis, MN, pp. 197–204.
Selig, J. , and Ding, X. , 2001, “ A Screw Theory of Static Beams,” IEEE/RSJ International Conference on Intelligent Robots and Systems, Maui, HI, Oct. 29–Nov. 3, pp. 312–317.
Ciblak, N. , and Lipkin, H. , 1999, “ Synthesis of Cartesian Stiffness for Robotic Applications,” IEEE International Conference on Robotics and Automation, Detroit, MI, May 10–15, pp. 2147–2152.
Liu, H. , Huang, T. , Chetwynd, D. G. , and Kecskeméthy, A. , 2017, “ Stiffness Modeling of Parallel Mechanisms at Limb and Joint/Link Levels,” IEEE Trans. Rob., 33(3), pp. 734–741. [CrossRef]
Ding, X. , and Selig, J. , 2002, “ Analysis of Spatial Compliance Behavior of Coiled Springs Via Screw Theory,” Chin. J. Mech. Eng., 15(4), pp. 293–297. [CrossRef]
Ding, X. , and Mark, S. J. , 2005, “ Lie Groups and Lie Algebras on Dynamic Analysis of Beam With Spatial Compliance,” Chin. J. Mech. Eng., 41(1), pp. 16–23. [CrossRef]
Li, Y. , and Xu, Q. , 2008, “ Stiffness Analysis for a 3-PUU Parallel Kinematic Machine,” Mech. Mach. Theory, 43(2), pp. 186–200. [CrossRef]
Kim, H. S. , and Lipkin, H. , 2014, “ Stiffness of Parallel Manipulators With Serially Connected Legs,” ASME J. Mech. Rob., 6(3), p. 031001. [CrossRef]
Sun, T. , Lian, B. , and Song, Y. , 2016, “ Stiffness Analysis of a 2-DOF Over-Constrained Rpm With an Articulated Traveling Platform,” Mech. Mach. Theory, 96, pp. 165–178. [CrossRef]
Liu, H. , Huang, T. , Kecskeméthy, A. , Chetwynd, D. G. , and Li, Q. , 2017, “ Force/Motion Transmissibility Analyses of Redundantly Actuated and Overconstrained Parallel Manipulators,” Mech. Mach. Theory, 109, pp. 126–138. [CrossRef]


Grahic Jump Location
Fig. 2

Parallel mechanism with n legs

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Fig. 1

Euler–Bernoulli beam

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Fig. 3

Manipulator pose actuated independently by the leg 1

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Fig. 5

Schematic diagrams of Stewart mechanism: (a) general and (b) active overconstrained

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Fig. 8

Elastic model of the nominal leg 2

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Fig. 9

Constraint space of the leg 7

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Fig. 6

Elastic model of the overconstrained Stewart mechanism

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Fig. 7

Elastic model of the leg 1

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Fig. 10

Closed-loop constraint and the error pose



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