Research Papers

Characterization of Spatial Parasitic Motions of Compliant Mechanisms Induced by Manufacturing Errors

[+] Author and Article Information
Zhiwei Zhu

State Key Laboratory of Ultra-Precision
Machining Technology,
Department of Industrial and
System Engineering,
The Hong Kong Polytechnic University,
Kowloon, Hong Kong SAR 999077, China
e-mail: wsjdzzw-jx@163.com

Suet To

State Key Laboratory of Ultra-Precision
Machining Technology,
Department of Industrial and
System Engineering,
The Hong Kong Polytechnic University,
Kowloon, Hong Kong SAR 999077, China;
Shenzhen Research Institute of the
Hong Kong Polytechnic University,
Shenzhen 518052, China
e-mail: sandy.to@polyu.edu.hk

Xiaoqin Zhou

School of Mechanical Science and Engineering,
Jilin University,
Changchun 130022, China
e-mail: xqzhou@jlu.edu.cn

Rongqi Wang

School of Mechanical Science and Engineering,
Jilin University,
Changchun 130022, China
e-mail: gzzjwrq@163.com

Xu Zhang

School of Mechanical Science and Engineering,
Jilin University,
Changchun 130022, China
e-mail: zhangxu8613@163.com

1Corresponding author.

Manuscript received March 19, 2015; final manuscript received April 26, 2015; published online August 18, 2015. Assoc. Editor: Larry L. Howell.

J. Mechanisms Robotics 8(1), 011018 (Aug 18, 2015) (9 pages) Paper No: JMR-15-1065; doi: 10.1115/1.4030586 History: Received March 19, 2015

This paper proposes a theoretical model for characterizing manufacturing error induced spatial parasitic motions (MESPM) of compliant mechanisms (CM), and investigates the inherent statistic features of MESPM using Monte Carlo simulation. It also applies and extends a novel finite beam based matrix modeling (FBMM) method to theoretically derive the elastic deformation behavior of an imperfect flexural linkage (IFL), which is a basic element of a wide spectrum of compliant mechanisms. A case study of a well-known double parallelogram compliant mechanism (DPCM) is also conducted, and the practical parasitic motions of a prototype DPCM are characterized by laser interferometer based measurements.

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Tian, Y. , Shirinzadeh, B. , and Zhang, D. , 2009, “A Flexure-Based Mechanism and Control Methodology for Ultra-Precision Turning Operation,” Precis. Eng., 33(2), pp. 160–166. [CrossRef]
Li, Y. , and Xu, Q. , 2009, “Design and Analysis of a Totally Decoupled Flexure-Based XY Parallel Micromanipulator,” IEEE Trans. Rob., 25(3), pp. 645–657 . [CrossRef]
Yong, Y. , Moheimani, S. , Kenton, B. J. , and Leang, K. , 2012, “Invited Review Article: High-Speed Flexure-Guided Nanopositioning: Mechanical Design and Control Issues,” Rev. Sci. Instrum., 83(12), p. 121101. [CrossRef] [PubMed]
Huang, H. , Zhao, H. , Mi, J. , Yang, J. , Wan, S. , Yang, Z. , Yan, J. , Ma, Z. , and Geng, C. , 2011, “Experimental Research on a Modular Miniaturization Nanoindentation Device,” Rev. Sci. Instrum., 82(9), p. 095101. [CrossRef] [PubMed]
Marinello, F. , Carmignato, S. , Voltan, A. , De Chiffre, L. , and Savio, E. , 2010, “Error Sources in Atomic Force Microscopy for Dimensional Measurements: Taxonomy and Modeling,” ASME J. Manuf. Sci. Eng., 132(3), p. 030903. [CrossRef]
Kashani, M. S. , and Madhavan, V. , 2011, “Analysis and Correction of the Effect of Sample Tilt on Results of Nanoindentation,” Acta Mater., 59(3), pp. 883–895. [CrossRef]
Huang, H. , Zhao, H. , Shi, C. , and Zhang, L. , 2013, “Using Residual Indent Morphology to Measure the Tilt Between the Triangular Pyramid Indenter and the Sample Surface,” Meas. Sci. Technol., 24(10), p. 105602. [CrossRef]
Huang, L. , Meyer, C. , and Prater, C. , 2007, “Eliminating Lateral Forces During AFM Indentation,” J. Phys.: Conf. Ser., 61, pp. 805–809 . [CrossRef]
Ren, J. , and Zou, Q. , 2014, “A Control-Based Approach to Accurate Nanoindentation Quantification in Broadband Nanomechanical Measurement Using Scanning Probe Microscope,” IEEE Trans. Nanotechnol., 13(1), pp. 46–54. [CrossRef]
Kim, J. H. , Kim, S. H. , and Kwak, Y. K. , 2004, “Development and Optimization of 3-D Bridge-Type Hinge Mechanisms,” Sens. Actuators, A, 116(3), pp. 530–538. [CrossRef]
Hwang, D. , Byun, J. , Jeong, J. , and Lee, M. G. , 2011, “Robust Design and Performance Verification of an In-Plane XYθ Micro-Positioning Stage,” IEEE Trans. Nanotechnol., 10(6), pp. 1412–1423. [CrossRef]
Li, Y. , and Xu, Q. , 2009, “Modeling and Performance Evaluation of a Flexure-Based XY Parallel Micromanipulator,” Mech. Mach. Theory, 44(12), pp. 2127–2152. [CrossRef]
Polit, S. , and Dong, J. , 2011, “Development of a High-Bandwidth XY Nanopositioning Stage for High-Rate Micro-/Nanomanufacturing,” IEEE/ASME Trans. Mechatronics, 16(4), pp. 724–733. [CrossRef]
Dibiasio, C. M. , and Hopkins, J. B. , 2012, “Sensitivity of Freedom Spaces During Flexure Stage Design Via FACT,” Precis. Eng., 36(3), pp. 494–499. [CrossRef]
Kang, D. , and Gweon, D. , 2013, “Analysis and Design of a Cartwheel-Type Flexure Hinge,” Precis. Eng., 37(1), pp. 33–43. [CrossRef]
Niaritsiry, T.-F. , Fazenda, N. , and Clavel, R. , 2004, “Study of the Sources of Inaccuracy of a 3 DOF Flexure Hinge-Based Parallel Manipulator,” IEEE International Conference on Robotics and Automation (ICRA '04), New Orleans, LA, Apr. 26–May 1, Vol. 4, pp. 4091–4096 .
Patil, C. B. , Sreenivasan, S. , and Longoria, R. G. , 2008, “Analytical and Experimental Characterization of Parasitic Motion in Flexure-Based Selectively Compliant Precision Mechanisms,” ASME Paper No. DETC2008-50111.
Li, S. , and Yu, J. , 2014, “Design Principle of High-Precision Flexure Mechanisms Based on Parasitic-Motion Compensation,” Chin. J. Mech. Eng., 27(4), pp. 663–672. [CrossRef]
Smith, S. , Chetwynd, D. , and Bowen, D. , 1987, “Design and Assessment of Monolithic High Precision Translation Mechanisms,” J. Phys. E: Sci. Instrum., 20(8), pp. 977–983. [CrossRef]
Hopkins, J. B. , and Culpepper, M. L. , 2010, “A Screw Theory Basis for Quantitative and Graphical Design Tools That Define Layout of Actuators to Minimize Parasitic Errors in Parallel Flexure Systems,” Precis. Eng., 34(4), pp. 767–776. [CrossRef]
Patil, C. B. , Sreenivasan, S. , and Longoria, R. G. , 2008, “Robust Design of Flexure Based Nano Precision Compliant Mechanisms With Application to Nano Imprint Lithography,” ASME Paper No. DETC2008-50114.
Patil, C. B. , Sreenivasan, S. , and Longoria, R. G. , 2007, “Analytical Representation of Nanoscale Parasitic Motion in Flexure-Based One DOF Translation Mechanism,” 22nd Annual Meeting of the American Society for Precision Engineering (ASPE 2007), Dallas, TX, Oct. 14–19.
Ryu, J. W. , and Gweon, D.-G. , 1997, “Error Analysis of a Flexure Hinge Mechanism Induced by Machining Imperfection,” Precis. Eng., 21(2), pp. 83–89. [CrossRef]
Huh, J. , Kim, K. , Kang, D. , Gweon, D. , and Kwak, B. , 2006, “Performance Evaluation of Precision Nanopositioning Devices Caused by Uncertainties Due to Tolerances Using Function Approximation Moment Method,” Rev. Sci. Instrum., 77(1), p. 015103. [CrossRef]
Valentini, P. P. , and Hashemi-Dehkordi, S.-M. , 2013, “Effects of Dimensional Errors on Compliant Mechanisms Performance by Using Dynamic Splines,” Mech. Mach. Theory, 70, pp. 106–115. [CrossRef]
Lobontiu, N. , Paine, J. S. , Garcia, E. , and Goldfarb, M. , 2001, “Corner-Filleted Flexure Hinges,” ASME J. Mech. Des., 123(3), pp. 346–352. [CrossRef]
Chen, G. , Liu, X. , and Du, Y. , 2011, “Elliptical-Arc-Fillet Flexure Hinges: Toward a Generalized Model for Commonly Used Flexure Hinges,” ASME J. Mech. Des., 133(8), p. 081002. [CrossRef]
Tian, Y. , Shirinzadeh, B. , and Zhang, D. , 2010, “Closed-Form Compliance Equations of Filleted V-Shaped Flexure Hinges for Compliant Mechanism Design,” Precis. Eng., 34(3), pp. 408–418. [CrossRef]
Zhu, Z. , Zhou, X. , Wang, R. , and Liu, Q. , 2015, “A Simple Compliance Modeling Method for Flexure Hinges,” Sci. China: Technol. Sci., 58(1), pp. 56–63. [CrossRef]
Wang, R. , Zhou, X. , and Zhu, Z. , 2013, “Development of a Novel Sort of Exponent-Sine-Shaped Flexure Hinges,” Rev. Sci. Instrum., 84(9), p. 095008. [CrossRef] [PubMed]
Cowper, G. , 1966, “The Shear Coefficient in Timoshenko's Beam Theory,” ASME J. Appl. Mech., 33(2), pp. 335–340. [CrossRef]
Chen, G. , and Howell, L. L. , 2009, “Two General Solutions of Torsional Compliance for Variable Rectangular Cross-Section Hinges in Compliant Mechanisms,” Precis. Eng., 33(3), pp. 268–274. [CrossRef]
Zhu, Z. , Zhou, X. , Liu, Z. , Wang, R. , and Zhu, L. , 2014, “Development of a Piezoelectrically Actuated Two-Degree-of-Freedom Fast Tool Servo With Decoupled Motions for Micro-/Nanomachining,” Precis. Eng., 38(4), pp. 809–820. [CrossRef]
Koseki, Y. , Tanikawa, T. , Koyachi, N. , and Arai, T. , 2000, “Kinematic Analysis of Translational 3-DOF Micro Parallel Mechanism Using Matrix Method,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2000), Takamatsu, Japan, Oct. 31–Nov. 5, Vol. 1, pp. 786–792 .
Tang, H. , and Li, Y. , 2013, “Design, Analysis, and Test of a Novel 2-DOF Nanopositioning System Driven by Dual Mode,” IEEE Trans. Rob., 29(3), pp. 650–662. [CrossRef]
Meijaard, J. , 2011, “Refinements of Classical Beam Theory for Beams With a Large Aspect Ratio of Their Cross-Sections,” IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments, Budapest, Hungary, June 7–11, pp. 285–292 .
Brouwer, D. , Meijaard, J. , and Jonker, J. , 2013, “Large Deflection Stiffness Analysis of Parallel Prismatic Leaf-Spring Flexures,” Precis. Eng., 37(3), pp. 505–521. [CrossRef]
Zhu, Z. , Zhou, X. , Liu, Q. , and Zhao, S. , 2011, “Multi-Objective Optimum Design of Fast Tool Servo Based on Improved Differential Evolution Algorithm,” J. Mech. Sci. Technol., 25(12), pp. 3141–3149. [CrossRef]


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Fig. 1

Schematic of a typical flexural linkage

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Fig. 2

Structure characteristic of the IFL

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Fig. 3

Schematic of the linkages derived from the mathematical model

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Fig. 5

Variations of the std of deformations in the y-axis direction

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Fig. 6

Characteristics of spatial parasitic motions, where the lines with circle marks and rectangle marks correspond to the PMU and the SPMU, respectively: (a) motions in the x-axis direction, (b) motions in the y-axis direction, (c) motions in the z-axis direction, (d) rotations around the x-axis, (e) rotations around the y-axis, and (f) rotations around the z-axis

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Fig. 7

SPMUs in terms of position uncertainties

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Fig. 8

SPMUs in terms of angle uncertainties

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Fig. 9

Experimental setup for measuring parasitic motions (1—capacitive displacement sensor, 2—linear interferometer, 3—reflector, 4—the DPCM, and 5—Piezoelectric actuator)

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Fig. 10

Parasitic motions of the mechanism in (a) the x-axis direction and (b) the z-axis direction




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