Notch flexure hinges are often used as revolute joints in high-precise compliant mechanisms, but their contour-dependent deformation and motion behaviour is currently difficult to predict. This paper presents general design equations for the calculation of the rotational stiffness, maximal angular elastic deflection and rotational precision of various notch flexure hinges in dependence of the geometric hinge parameters. The novel equations are obtained on the basis of a non-linear analytical model for a moment and a transverse force loaded beam with a variable contour height. Four flexure hinge contours are investigated, the semi-circular, the corner-filleted, the elliptical, and the recently introduced bi-quadratic polynomial contour. Depending on the contour, the error of the calculated results is in the range of less than 2 % to less than 16 % for the suggested parameter range compared with the analytical solution. Finite elements method (FEM) and experimental results correlate well with the predictions based on the comparatively simple and concise design equations.

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.

In soft robotics, there is still a great need for a universal but simple gripper that realizes a high level of adaptability as well as a gentle touch to a wide variety of unknown objects of different size, shape, stiffness, and weight without the use of sensors or vision. Various, mostly complex grippers already exist based on certain actuation concepts. However, each solution has specific limitations, especially regarding gripping different soft and delicate objects. Therefore, this paper introduces a new approach to design a simple, adaptive, and versatile soft robotic two-finger gripper that is based on compliant mechanisms. More specifically, an inherently gentle touch is realized by utilizing an optimally synthesized mechanism with distributed compliance in combination with a conventional linear actuator. It is shown by finite elements method (FEM) simulations that the gripper realizes a high force and motion transmission at the same time. Furthermore, it is demonstrated by tests with a gripper prototype that reliable, safe, and fast grasping as well as manipulation are possible for a wide variety of objects. It is shown that beside regular and stiff objects also very challenging objects can be easily gripped, e.g., small, irregular, soft, and squeezable objects like fruits, berries, and vegetables. Moreover, it is confirmed that the developed compliant two-finger gripper can be used beneficially without sensors and control for differently sized and shaped objects with a comparable weight.

A compliant mechanism gains its mobility fully or partially from the compliance of its elastically deformable parts rather than from conventional joints. Due to many advantages, in particular the smooth and repeatable motion, monolithic mechanisms with notch flexure hinges are state of the art in numerous precision engineering applications with required positioning accuracies in the low micrometer range. However, the deformation and especially motion behavior are complex and depend on the notch geometry. This complicates both the accurate modeling and purposeful design. Therefore, the chapter provides a survey of different methods for the general and simplified modeling of the elasto-kinematic properties of flexure hinges and compliant mechanisms for four hinge contours. Based on nonlinear analytical calculations and FEM simulations, several guidelines like design graphs, design equations, design tools, or a geometric scaling approach are presented. The obtained results are analytically and simulatively verified and show a good correlation. Using the example of a path-generating mechanism, it will be demonstrated that the suggested angle-based method for synthesizing a compliant mechanism with individually shaped hinges can be used to design high-precise and large-stroke compliant mechanisms. The approaches can be used for the accelerated synthesis of planar and spatial flexure hinge-based compliant mechanisms.