Articles | Volume 9, issue 1
https://doi.org/10.5194/ms-9-71-2018
https://doi.org/10.5194/ms-9-71-2018
Research article
 | 
16 Feb 2018
Research article |  | 16 Feb 2018

Determining the range of allowable axial force for the third-order Beam Constraint Model

Fulei Ma, Guimin Chen, and Guangbo Hao

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Cited articles

Awtar, S. and Sen, S.: A Generalized Constraint Model for Two-Dimensional Beam Flexures: Nonlinear Load-Displacement Formulation, ASME J. Mechan. Des., 132, 081008, https://doi.org/10.1115/1.4002005, 2010a.
Awtar, S. and Sen, S.: A Generalized Constraint Model for Two-Dimensional Beam Flexures: Nonlinear Strain Energy Formulation, ASME J. Mechan. Des., 132, 081009, https://doi.org/10.1115/1.4002006, 2010b.
Awtar, S. and Slocum, A.: Constraint-Based Design of Parallel Kinematic XY Flexure Mechanisms, ASME J. Mech. Des., 129, 816–830, 2007.
Awtar, S., Slocum, A., and Sevincer, E.: Characteristics of Beam-Based Flexure Modules, ASME J. Mechan. Des., 129, 625–639, 2007.
Awtar, S., Shimotsu, K., and Sen, S.: Elastic Averaging in Flexure Mechanisms – A Three-Beam Parallelogram Flexure Case Study, ASME J. Mech. Robot., 2, 041006, https://doi.org/10.1115/1.4002204, 2010.
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Short summary
The Beam Constraint Model (BCM) may yield large predicting errors (> 5 %) when the applied axial force goes beyond a certain boundary. We mathematically determine the nondimensional boundary of the axial force by the conditions of the positive definite quadratic form of the strain energy expression and the buckling load expressions. If the axial force is beyond the boundary, the Chained Beam Constraint Model (CBCM) can be used instead.