detasFLEX – A computational design tool for the analysis of various notch flexure hinges based on non-linear modeling

Abstract

Abstract. Notch flexure hinges are commonly used in compliant mechanisms for precision engineering applications and yet important rotational properties of a hinge like the bending stiffness, maximum angular deflection and rotational precision are difficult to predict accurately and simultaneously. There exist some closed-form equations and a few design tool approaches for calculating flexure hinges with particular geometries, but apart from that no comprehensive calculation program for the contour-specific analysis is known to the authors. Developed in MATLAB, this paper presents a novel computational design tool using a non-linear analytical approach for large deflections of rod-like structures to calculate the elasto-kinematic flexure hinge properties by numerically solving a system of differential equations. Building on previous investigations, four certain hinge contours are implemented, the circular, the corner-filleted, the elliptical, and the power function-based contour with different exponents. In addition to the theoretical approach and the implementation it is exemplarily shown, that finite elements method (FEM) results correlate well with the analytical design tool results. For a given deflection angle of 10° and a corner-filleted contour as an example, the deviations of the bending stiffness are between 0.1 % and 9.4 % for typical parameter values. The presented design tool can be beneficial for the accelerated and systematic synthesis of compliant mechanisms with optimized flexure hinges.

Modeling and Design of Flexure Hinge-Based Compliant Mechanisms

“…variety of geometries, especially these contours offer high optimization potential, while a comparatively simple modeling is possible [35]. Thus, the advantages of the polynomial contour are implemented and extended to a power function contour to offer a wider range of possible hinges due to a rational exponent n [14], with…”

“…In the following, four certain flexure hinge contours are considered (see Figure 4): the semicircular contour, the corner-filleted contour with a stressoptimal and hinge length-related fillet radius r = 0.1 l [36], the semielliptical contour, and the power function-based contour. The remaining contour height functions and detailed information about the depicted segment-wise contour modeling are given in [14]. Many more notch geometries are classified in [32].…”

“…The boundary value problem is solved numerically with MATLAB [14]. At the end of this procedure, all four parameters κ, θ, u ξ , and u η are obtained for each point s along the deformed neutral axis, and further results for the considered hinge properties can be estimated.…”

“…The maximum absolute value of the strain always occurs at the outer fiber for the maximum ηcoordinate, which corresponds with the contour height function of the hinge. In addition, the absolute value of the rotational axis shift v, based on the fixed center approach, is put together from the axis shift of point C in ξ and η-direction [14].…”

“…However, optimizing the shapes of easy-to-manufacture and mainly used notch flexure hinges may prove useful in the synthesis of compliant mechanisms. Among many possible notch shapes, power function flexure hinges, based on the higher order polynomial hinges suggested in [13], are especially suitable because they are highly variable and allow a simplified modeling, too [14].…”