Graduation Year

2014

Document Type

Dissertation

Degree

Ph.D.

Degree Granting Department

Mechanical Engineering

Major Professor

CRAIG LUSK

Keywords

Compliant Mechanisms, Kinematics, Large Deflections, Non-Dimensional, Spatial Deflections

Abstract

This dissertation introduces a novel three-dimensional pseudo-rigid-body model (3-D PRBM) for straight cantilever beams with rectangular cross sections. The model is capable of capturing the behavior of the neutral axis of a beam loaded with an arbitrary force end-load. Numerical integration of a system of differential equations yields approximate displacement and orientation of the beam's neutral axis at the free end, and curvatures of the neutral axis at the fixed end. This data was used to develop the 3-D PRBM which consists of two torsional springs connecting two rigid links for a total of 2 degrees of freedom (DOF). The 3-D PRBM parameters that are comparable with existing 2-D model parameters are characteristic radius factor (mean: γ = 0.8322), bending stiffness coefficient (mean: KΘ = 2.5167) and parametric angle coefficient (mean: cΘ = 1.2501). New parameters are introduced in the model in order to capture the spatial behavior of the deflected beam, including two parametric angle coefficients (means: cΨ = 1.0714; cΦ = 1.0087). The model is verified in a few locations using ANSYSTM and its use in the design of compliant mechanisms is illustrated through spatial compliant versions of crank slider and double slider mechanisms.

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