New 3D Cartesian Flexible Hinge and Tripod Mechanism: Stress-Based Maximum Load and Displacement with Compliance Model

Authors

  • Nicolae Lobontiu University of Alaska Anchorage, USA
  • Jozef Hunter University of Alaska Anchorage, USA
  • Brian Robles University of Alaska Anchorage, USA

Keywords:

Flexible, hinge, three-dimensional, Cartesian, stress, concentrator

Abstract

The paper develops an analytical model to assess the maximum levels of external loads and displacements of a new three-dimensional (3D) Cartesian flexible hinge and of a tripod mechanism that uses such hinges. The small-displacement compliance model is based on the allowable stresses and includes the stress concentration effect at the filleted end of the circular cross-section 3D flexible hinges. The analytical compliances of the new hinge are confirmed by finite element simulation, while the tripod piston-motion stiffness is validated by experimental testing of a prototype. The analytical model is utilized to numerically analyze the maximum loads and displacements of the new hinge and the tripod mechanism in terms of defining geometric parameters and a set of load participation factors.

References

KYUSOJIN, A., SAGAWA, D., Development of Linear and Rotary Movement Mechanism by Using Flexible Strips, Bull. Jpn. Soc. Precis. Eng., 22, 4, pp. 309-314, 1988.

CHOI, Y.M. et al., A High-Bandwidth Electromagnetic MEMS Motion Stage for Scanning Applications, J. Micromech. Microeng., 22, 10, pp. 105012-1 - 9, 2012.

SHANG, J. et al., A Novel Voice Coil Motor-Driven Compliant Micropositioning Stage Based on Flexure Mechanism, Rev. Sci. Instrum., 86, 9, pp. 095001-1 - 10, 2015.

CLARK, L. et al., Design and Analysis of Compact Flexure-Based Precision Pure Rotation Stage without Actuator Redundancy, Mech. Mach. Theory, 105, pp. 129-144, 2016.

AL-JODAH, A. et al., Modeling and a Cross-Coupling Compensation Control Methodology of a Large Range 3-DOF Micropositioner with Low Parasitic Motions, Mech. Mach. Theory, 162, pp. 104334-1 - 32, 2021.

VUKOBRATOVICH, D. et al., Slit Diaphragm Flexures for Optomechanics, Proc. SPIE Int. Soc. Opt. Eng., 2542, pp. 2-10, 1995.

YONG, Y.K., REZA MOHEMANI, S.O., A z-Scanner Design for High-Speed Scanning Probe Microscopy, Proc. IEEE Int. Conf. Rob. Autom., Saint-Paul, Minnesota, USA, May 14-18, 4780, 2012.

REBEIZ, G.M., RF MEMS: Theory, Design and Technology, Wiley, New Jersey, 2003.

ROOPA, R., NAVIN KARANTH, P., KULKARNI, S.M., Modeling of Compliant Flexure Diaphragm for Micropump, Procedia Comput. Sci., 133, pp. 1035-1039, 2018.

WANG, G. et al., Design, Test and Control of a Compact Scanner Based on a Compound Compliant Amplification Mechanism, Mech. Mach. Theory, 139, pp. 460-475, 2019.

ZHANG, X., XU, Q., Design and Development of a New 3-DOF Active-Type Constant-Force Compliant Parallel Stage, Mech. Mach. Theory, 140, pp. 654-665, 2019.

LOBONTIU, N., Compliant Mechanisms: Design of Flexure Hinges, Second Edition, CRC Press, Boca Raton, 2020.

LOBONTIU, N., WESTENSKOW, J., KEEFE, J., HUNTER, J., New Series and Parallel 3D Cartesian Right Circularly Corner-Filleted Flexible Hinges, Precis. Eng., 72, pp. 653-663, 2021.

LOBONTIU, N., HUNTER, J., KEEFE, J., WESTENSKOW, J., Tripod Mechanisms with Novel Spatial Cartesian Flexible Hinges, Mech. Mach. Theory, 167, pp. 1-16, 2022.

ISIDA, M., On the Tension of the Strip with Semi-Circular Notches, Trans. Jpn. Soc. Mech. Eng., 19, pp. 5-10, 1953.

NEUBER, H., Theory of Stress Concentration for Shear-Strained Prismatic Bodies with Arbitrary Non-Linear Stress-Strain Law, J. Appl. Mech., 28, pp. 545-550, 1961.

PILKEY, W.D., PILKEY, D.F., Peterson’s Stress Concentration Factors, Third Edition, John Wiley & Sons, Inc., Hoboken, NJ, 2008.

GOMEZ, F.J. et al., A Generalized Notch Stress Intensity Factor for U-Notched Components Loaded Under Mixed Mode, Eng. Fract. Mech., 75, pp. 4819-4833, 2008.

TAYLOR, D. et al., The Variable-Radius Notch: Two Methods for Reducing Stress Concentration, Eng. Fail. Anal., 18, pp. 1009-1017, 2011.

ZAPPALORTO, M., BERTO, F., LAZZARIN, P., Practical Expressions for The Notch Stress Concentration Factors of Round Bars under Torsion, Int. J. Fatigue, 33, pp. 382-395, 2011.

PANASYUK, V.V., SAVRUK, M.P., KAZBERUK, A., Stress Concentration Near Sharp and Rounded V-Notches, Mater. Sci., 49, 6, pp. 711-722, 2014.

RADAJ, D., State-of-the-Art Review of Extended Stress Intensity Factor Concepts, Fatigue Fract. Eng. Mater. Struct., 37, pp. 1-28, 2014.

CHEN, G., WANG, J., LIU, X., Generalized Equations for Estimating Stress Concentration Factors of Various Notch Flexure Hinges, ASME J. Mech. Des., 136, pp. 031009-1 - 8, 2014.

ZELENIKA, S., MUNTEANU, M.GH., DE BONA, F., Optimized Flexural Hinge Shapes for Microsystems and High-Precision Applications, Mech. Mach. Theory, 44, 10, pp. 1826-1839, 2009.

DIRKSEN, F., ANSELMANN, M., ZOHDI, T., LAMMERING, R. Incorporation of Flexural Hinge Fatigue-Lifecycle Criteria into the Topological Design of Compliant Small-Scale Devices, Precis. Eng., 37, 3, pp. 531-541, 2013.

https://www.stratasysdirect.com, Between the Layer Lines: Understanding 3D Printing Metal Material Nuances.

Published

2022-02-13

Issue

Vol. 67 No. 1 (2022): Flexure Hinges and Flexure-Hinge Mechanisms

Section

Articles

Copyright (c) 2022 The Romanian Journal of Technical Sciences. Applied Mechanics.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.