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BRIEF NOTES

Mitigating the Effects of Local Flexibility at the Built-In Ends of Cantilever Beams

[+] Author and Article Information
Jonathan W. Wittwer, Larry L. Howell

Department of Mechanical Engineering, Brigham Young University, 435 CTB, Provo, UT 84602

J. Appl. Mech 71(5), 748-751 (Nov 09, 2004) (4 pages) doi:10.1115/1.1782913 History: Received December 04, 2003; Revised April 23, 2004; Online November 09, 2004
Copyright © 2004 by ASME
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References

Smith, S. T., and Chetwynd, D. G., 1992, Foundations of Ultraprecision Mechanism Design, Gordon and Breach Science Publishers, New York.
Eastman,  F. S., 1937, “The Design of Flexure Pivots,” J. Aerosp. Sci., 5(1), pp. 16–21.
Howell, L. L., 2001, Compliant Mechanisms, John Wiley and Sons, New York.
Lobontiu, N., 2003, Compliant Mechanisms: Design of Flexure Hinges, CRC Press, Boca Raton, FL.
Smith, S. T., 2000, Flexures: Elements of Elastic Mechanisms, Gordon and Breach Science Publishers, New York.
Wittwer,  J. W., Gomm,  T., and Howell,  L. L., 2002, “Surface Micromachined Force Gauges: Uncertainty and Reliability,” J. Micromech. Microeng., 12(1), pp. 13–20.
Jaecklin,  V. P., Linder,  C., De Rooji,  N. F., and Moret,  J.-M., 1993, “Comb Actuators for XY-Microstages,” Sens. Actuators, 39(1), pp. 83–89.
Zhou,  G., Low,  D., and Dowd,  P., 2001, “Method to Achieve Large Displacements Using Comb Drive Actuators,” Proc. SPIE, Bellingham, WA, 4557, pp. 428–435.
O’Donnell,  W. J., 1960, “The Additional Deflection of a Cantilever due to the Elasticity of the Support,” ASME J. Appl. Mech., 27, pp. 461–464.
Small,  N. C., 1961, “Bending of a Cantilever Plate Supported From an Elastic Half-Space,” ASME J. Appl. Mech., 28, pp. 387–394.
O’Donnell,  W. J., 1963, “Stresses and Deflections in Built-in Beams,” J. Eng. Ind., 85(3), pp. 265–273.
Matusz,  J. M., O’Donnell,  W. J., and Erdlac,  R. J., 1969, “Local Flexibility Coefficients for the Built-In Ends of Beams and Plates,” J. Eng. Ind., 91(3), pp. 607–614.
Pilkey, W. D., 1997, Peterson’s Stress Concentration Factors, John Wiley and Sons, New York.

Figures

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Stress distribution at the juncture of a flexible beam and (a) an elastic half-plane and (b) an elastic quarter-plane
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(a) FEA model and (b) simplified model for simulating a constant-moment end-loaded cantilever beam of length, L, attached to an elastic half-plane
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(a) FEA model and (b) simplified model for simulating a vertically end-loaded cantilever beam of length, L, attached to an elastic quarter-plane
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Plot of the percent error versus the fillet ratio and slenderness for the (a) half-plane model, and (b) the quarter-plane model, under pure bending
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Schematic for a folded-beam linear suspension and the simplified model for applying Castigliano’s method to obtain the spring constant

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