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TECHNICAL PAPERS

A Finite-Element-Based Method to Determine the Spatial Stiffness Properties of a Notch Hinge

[+] Author and Article Information
Shilong Zhang, Ernest D. Fasse

Dept. of Aerospace and Mechanical Engineering, The University of Arizona, Tucson, Arizona

J. Mech. Des 123(1), 141-147 (Nov 01, 1998) (7 pages) doi:10.1115/1.1342157 History: Received November 01, 1998
Copyright © 2001 by ASME
Topics: Hinges , Stiffness
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References

Paros, J., and Weisbord, L., 1965, “How to Design Flexure Hinges,” Mach. Des., Nov., pp. 151–156.
Smith,  S., Chetwynd,  D., and Bowen,  D., 1987, “The Design and Assessment of High Precision Monolithic Translation Mechanisms,” J. Phys. E, 20, pp. 977–983.
Smith, S., and Chetwynd, D., 1992, Foundations of Ultraprecision Mechanism Design, Gordon and Breach, New York.
Koster, M., 1998, Constructieprincipes voor het nauwkeurig bewegen en positioneren (second ed.), Twente University Press (in Dutch).
Braak, L., 1999. personal communication.
Fasse,  E., and Breedveld,  P., 1998, “Modelling of Elastically Coupled Bodies: Part 1: General Theory and Geometric Potential Function Method,” ASME J. Dyn. Syst., Meas., Control, 120, pp. 496–500.
Fasse,  E., and Breedveld,  P., 1998, “Modelling of Elastically Coupled Bodies: Part II: Exponential and Generalized Coordinate Methods,” ASME J. Dyn. Syst., Meas., Control, 120, pp. 501–506.
Zhang,  S., and Fasse,  E., 2000, “Spatial Compliance Modeling Using a Quaternion-Based Potential Function Method,” Multibody System Dynamics, 4, pp. 75–101.
Griffis,  M., and Duffy,  J., 1991, “Kinestatic Control: A Novel Theory for Simultaneously Regulating Force and Displacement,” ASME J. Mech. Des., 113, pp. 508–515.
Patterson,  T., and Lipkin,  H., 1993, “Structure of Robot Compliance,” ASME J. Mech. Des., 115, pp. 576–580.
Patterson,  T., and Lipkin,  H., 1993, “A Classification of Robot Compliance,” ASME J. Mech. Des., 115, pp. 581–584.
Huang,  S., and Schimmels,  J., 1998, “Achieving an Arbitrary Spatial Stiffness With Springs Connected in Parallel,” ASME J. Mech. Des., 120, pp. 520–526.
Huang,  S., and Schimmels,  J., 1998, “The Bounds and Realization of Spatial Stiffness Achieved With Simple Springs Connected in Parallel.” IEEE Trans. Rob. Autom., 14, pp. 466–475.
Žefran, M., and Kumar, V., 1997, “Affine Connections for the Cartesian Stiffness Matrix,” in Proc. IEEE Int. Conf. on Robotics and Automation, pp. 1376–1381.
Žefran, M., and Kumar, V., 1999, “A Geometric Approach to the Study of the Cartesian Stiffness Matrix,” ASME J. Mech. Des., accepted for publication.
Ciblak, N., 1998, “Analysis of Cartesian Stiffness and Compliance with Application,” Ph.D. thesis, Georgia Institute of Technology.
Ciblak, N., and Lipkin, H., 1996, “Centers of Stiffness, Compliance, and Elasticity in the Modelling of Robotic Systems,” in Proc. ASME Design Engineering Technical Conf., 26 , pp. 185–195.
Ciblak, N., and Lipkin, H., 1996, “Remote Center of Compliance Reconsidered,” in Proc. ASME Design Engineering Technical Conf., Number 96-DETC-MECH-1167, CD-ROM.
Lončarić,  J., 1987, “Normal Forms of Stiffness and Compliance Matrices,” IEEE Trans. Rob. Autom., 3, pp. 567–572.
Zhang, S., 1999, “Lumped-Parameter Modelling of Elastically Coupled Bodies: Derivation of Constitutive Equations and Determination of Stiffness Matrices,” Ph.D. thesis, The University of Arizona.

Figures

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Pair of ideally rigid bodies mutually supported by an elastic notch hinge, shown in (a) undeformed, relaxed configuration and (b) deformed, strained configuration
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An elastic section couples two rigid bodies. Distinguished nodes on the mobile rigid body define frame b.
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Finite element mesh with contours of constant strain ε13
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Nondimensional stiffness plots. Dashed lines plot finite element data. Solid lines plot curves fitted to this data. Parameters κ2t and κ1o decrease as t/D increases. Asterisks plot fitted data and analytical predictions of Braak. Crosses plot fitted data of Smith and Chetwynd. Dotted lines plot analytical predictions of Paros and Weisbord.
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Initial and final, near-equilibrium configurations. The initial configuration is indicated by dotted lines. The final configuration is indicated by solid lines.

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