Current design methods for flexure (or compliant) mechanisms regard stress as a secondary, limiting factor. This is remarkable because stress is also known as a useful design parameter. In this paper we propose the Stress And Geometry (STAGE) method, to design the geometry of a flexure mechanism together with a desired stress field. From this design, the stress-free to-be-fabricated geometry is computed using the inverse finite element method. To demonstrate the potential of the method, the geometry of the well-known crossed-flexure pivot is taken as example. We first show how this mechanism can be redesigned for the same functional geometry with various internal stresses. This results for a specific choice of stress field in a design of a crossed-flexure pivot with 23% lower peak stresses during motion as compared to the known designs, for a ±45° rotation. We then present a second example, of a Folded Leaf Spring (FLS). With a parameter sweep the optimal stress field is calculated, showing a peak stress reduction of 28% during motion. This result was validated with an experiment, showing a normalized mean absolute error of 5.5% between experiment and theory. With a second experiment it was verified that the functional geometry of the FLS with internal stresses was equal to the one without internal stresses, with geometric deviations smaller than half the thickness of the flexures.

Current design methods for flexure (or compliant) mechanisms regard stress as a secondary, limiting factor. This is remarkable because stress is also known as a useful design parameter. In this paper we propose the Stress And Geometry (STAGE) method, to design the geometry of a flexure mechanism together with a desired stress field. From this design, the stress-free to-be-fabricated geometry is computed using the inverse finite element method. To demonstrate the potential of the method, the geometry of the well-known crossed-flexure pivot is taken as example. We first show how this mechanism can be redesigned for the same functional geometry with various internal stresses. This results for a specific choice of stress field in a design of a crossed-flexure pivot with 23% lower peak stresses during motion as compared to the known designs, for a ±45° rotation. We then present a second example, of a Folded Leaf Spring (FLS). With a parameter sweep the optimal stress field is calculated, showing a peak stress reduction of 28% during motion. This result was validated with an experiment, showing a normalized mean absolute error of 5.5% between experiment and theory. With a second experiment it was verified that the functional geometry of the FLS with internal stresses was equal to the one without internal stresses, with geometric deviations smaller than half the thickness of the flexures.

In this study, a flexure-based (compliant) linear guide with a motion range comparable to its footprint is presented. The design consists of two-folded leaf springs on which torsion reinforcement structures are added. Due to these structures, only two-folded leaf springs are needed instead of a minimum of five as in preexisting designs. The new design is compared to such a preexisting design, after optimizing both on a support stiffness metric. The new design scores over twice as high on the support stiffness metric, while occupying a smaller (-33%) and a less obstructive build volume. Stress, build volume, and manufacturing limitations are taken into account. In addition, a variation on the new design using three torsion reinforced folded leaf springs is presented and optimized. This design occupies a build volume similar to the preexisting design, but scores four times higher on the support stiffness metric. A prototype of the new design is built and its parasitic eigenfrequencies are measured, validating the theoretical models (normalized mean absolute error of 4.3%).

In this paper we present two new designs of spherical flexure joints, which are the compliant equivalent of a traditional ball-and-socket joint. The designs are formed by tetrahedron-shaped elements, each composed of three blade flexures with a trapezoidal shape, that are connected in series without intermediate bodies. This is new with respect to the designs currently found in literature and helps to increase the range of motion. We also present two planar (x-y-θ_z) flexure joint designs which were derived as special versions of the spherical designs. In these designs the tetrahedron elements have degenerated to a triangular prisms. For detailed investigation we developed equivalent representations of the tetrahedron and triangular prism elements and proved that three of the four constraint stiffness terms depend solely on the properties of the main blade flexure. Furthermore, we derived equations for these stiffness terms which are compared to finite-element simulations, showing a good correspondence for the prism element with a Normalized Mean Absolute Error (NMAE) of 1.9%. For the tetrahedron element, the equations showed to only capture the qualitative behaviour with a NMAE of 34.9%. Also, we derived an equation for the optimal width of the prism element regarding rotational stiffness.

For steel flexures, complex geometries are required to reach high support stiffness and limit axis drift over large ranges of motion. These complex flexures are expensive and difficult to manufacture. This paper presents a method of designing short, polymer wire flexures with high support stiffness and modelling their axis drift using a novel method, the arc method. The arc method is validated against finite element methods (FEM) and physical tests, showing at least a factor 10 lower error than existing pseudo-rigid-body models (PRBM) at 70° deflection, while maintaining a simple modelling approach. The use of polymers increases support stiffness of wire flexures by a factor 7800 with respect to steel at 70° deflection, even though the material stiffness is substantially lower. This is due to the large allowed strain of polymers increasing the possible diameter by a factor 110.

For steel flexures, complex geometries are required to reach high support stiffness and limit axis drift over large ranges of motion. These complex flexures are expensive and difficult to manufacture. This paper presents a method of designing short, polymer wire flexures with high support stiffness and modelling their axis drift using a novel method, the arc method. The arc method is validated against finite element methods (FEM) and physical tests, showing at least a factor 10 lower error than existing pseudo-rigid-body models (PRBM) at 70° deflection, while maintaining a simple modelling approach. The use of polymers increases support stiffness of wire flexures by a factor 7800 with respect to steel at 70° deflection, even though the material stiffness is substantially lower. This is due to the large allowed strain of polymers increasing the possible diameter by a factor 110.

While compact folding is desirable for applications such as deployable mechanisms, achieving this with compliant mechanisms can be challenging. One reason for this is that the relaxed and stressed states of the mechanism are known and the loads producing the transition are unknown. The relaxed state is determined by the desired, deployed state and the stressed geometry is determined by the storage space. Approaches for solving this problem often require significant software development or cannot address problems in three dimensions. To address this problem, this work describes a method for designing 3D compliant mechanisms that can fold compactly. If the stressed and relaxed geometry are specified, an algebraic method can be used to find loads which best approximate the desired geometry. A least-squares approach is used to minimize error. A simplification of this method in two dimensions is also described. To further enhance the accuracy of the shape approximation, a method for varying the beam bending stiffness is described. For comparison, an inverse finite-element solver was implemented and paired with an optimizer and used to solve the same problem. Both methods were used to design a compliant, compactly folding beam. These results were compared with results from a commercial, finite-element software package.

Compliant (flexure) elements provide highly precise motion guiding because they do not suffer from friction or backlash. However, their support stiffness drops dramatically when they are actuated from their home position. In this paper, we show that the existing Inverse Finite Element (IFE) method can be used to efficiently design flexure elements such that they have a high support stiffness in their actuated state. A folded leaf spring element was redesigned using an IFE code written in Matlab™. The design was validated using the commercial Finite Element software package Ansys™, showing the desired high support stiffness in the actuated state. The proposed method could aid in the design of more compact flexure mechanisms with a larger useful range of motion.