Generalized model for conic-V-shaped flexure hinges

Abstract

This paper presents a new class of flexure hinges, namely, conic-V-shaped flexure hinges (CFHs), which can be used as a generalized model for flexure hinges with profiles such as parabolic-V-shape, elliptical-V-shape, and hyperbolic-V-shape. Compliance and precision equations for the CFHs were derived as a set of nonlinear equations using Castigliano’s second theorem. The parameters of the nonlinear equations inputted to the compliance and precision matrices were based on the generalized equations used for conic curves in polar coordinates. Furthermore, the compliance equations were verified by means of finite element analysis and experiments. The errors in the finite element and experimental results were within 10% and 8% compared to the analytical results, respectively. Finally, the effects of dimensional parameters on the analytical model could be effectively analyzed by numerical simulations and comparisons.

Development of novel multiple-axis flexure hinges based on hook function curve and a generalized model for multiple-axis flexure hinges

“…10 Notched flexure hinges can be classified into single-axis, double-axis and multiple-axis (multiple-axis flexure hinges are also called spherical flexure hinges) according to the implemented functions and the number of sensitive axes. 1 Many researchers have conducted extensive research on single-axis and double-axis flexure hinges, such as circular flexure hinges, 11 ellipticalarc flexure hinges, 12,13 conic-section flexure hinges, [14][15][16] corner-fileted flexure hinges, 17,18 fileted V-shaped flexure hinges, 19,20 exponent-sine-shaped flexure hinges, 21 double-axis elliptical flexure hinges, 22 etc. In contrast, there is less research on multiple-axis flexure hinges or spherical flexure hinges.…”

“…Many scholars directly define the center of rotation drift of flexure hinges as motion precision. [14][15][16][17][18][19][20] Lobontiu et al 25 defined a motion precision without material characteristics, and Wang et al 21 proposed a concept of relative precision. In response to the issue of nonuniform description of motion precision of flexure hinges, and in order to compare the motion performance of different notched flexure hinges more intuitively and fairly, this article redefines the motion precision matrix of flexure hinges, proposes a new precision model for flexure hinges, and verifies the accuracy of the proposed precision model through finite element analysis (FEA).…”

Theoretical Modeling and Experimental Verification of Elliptical Hyperbolic Hybrid Flexure Hinges

“…Xu et al compared the performance of the conic section flexure hinge from the three indexes of compliance, rotation accuracy, and hinge index [16], pointing out that the hyperbolic flexure hinge had the highest accuracy but a smaller range of rotation, and the elliptical flexure hinge had the largest compliance but lower accuracy. In addition to these flexure hinges, some other flexure hinges with notch profiles have been designed, such as filleted V-shaped [17,18], cycloid-shaped [19], power functionshaped [20], U-shaped flexure hinges [21], leaf flexure hinge [22], and so on. At present, the commonly used methods for modeling the compliance and rotation accuracy of flexure hinges include the direct integration method based on Castigliano's second theorem [12,13,[17][18][19], the Euler-Bernoulli beam theory [14,15], and the unit load method [20].…”

Theoretical, numerical, and experimental investigation on the compliance and natural frequency of sinusoidal flexure hinges

“…The generalized model of compliance and precision factor of the multi‐axis flexure hinge 23 is derived and verified by simulation. Kong et al 24 deduced the generalized model of compliance and precision factor of conic‐V‐shaped flexure hinges based on Castigliano's second theorem. The results are verified by simulation and experiment.…”