Compliant mechanisms have the potential to be utilized in numerous applications where the use of conventional mechanisms is unfeasible. These mechanisms have inherent stiffness in their range of motion as they gain their mobility from elastic deformations of elements. In most systems, however, complete control over the elasticity is desired. Therefore, compliant mechanisms with variable, including zero, stiffness can have a great advantage. We present a novel concept based on the prestressing of open thin-walled multi-symmetric beams. It is demonstrated that by changing the prestress on the center-axis of these beams, a range of variable torsional stiffness can be achieved. For beams with a large warping constant, the stiffness changes from positive to zero and negative as the prestress increases, while for beams with a near-zero warping constant, the range of neutrally stable twisting motion increases. A planar equivalent is shown in this work to elucidate the notion, and numerical and experimental analyses are performed to validate the prestress-related behavior.

This paper presents a novel shape morphing concept, which exploits neutral stability to achieve reversible shape morphing. The concept is based on actively changing the material stiffness on a local level in order to perturb the neutral stability and thus induce the shell to deform. This concept is realized by embedding Ni-Ti wires in a neutrally stable shell. These wires undergo a significant increase in stiffness upon being heated beyond their Austenite transition temperature. The wires are locally heated by forced convection. The results show that the shape of the shell can be controlled freely along the neutrally stable elastic deformation path by changing the location of the heat stimulus. In contrast to existing shape morphing structures, the presented structure is capable of fully reversible (two-way) shape morphing, while also preserving its shape after removing the stimulus. This allows for positioning without continuous actuation. The shell achieves a significant range of motion and, since the elastic deformation reaction forces do not need to be overcome, it is capable of generating actuation force. Since the actuation concept does not require a complex patterning of active materials to achieve the desired deformation, it can potentially also be applied to other neutrally stable structures.

Continuously Variable Transmissions (CVT) can serve as subsystems for a variety of machineries and robotic systems. A compliant CVT mechanism based on the warping of twisting beams is presented here. The design works based on the demonstrated fact that the twist on one side of a beam can be transferred via sectional warping and propagate across a rotational constraint in the middle of the beam to create a reverse twist on the opposite side. In the proposed compliant CVT the transmission ratio is dependent on the position of the middle rotational constraint which can vary in a continuous range. We have demonstrated this concept and its relation to the twisting beam's warping constant, as well as its functionality for different transmission ratios of 1:4 to 4:1. An analytical model as well as a Finite Element Analysis (FEA) and experiments are employed to characterize and verify the concept and its relation to the warping constant.

Elastic structures that can deflect without springback, known as neutrally stable structures, form a remarkable group within their field, since they require the energetic state to remain unchanged during elastic deformation. Several examples in the literature obtain this state of neutral stability by the application of pre-stress, either as a result of manufacturing processes or the application of imposed boundary conditions. In this paper, we present a new class of neutrally stable structure that exhibits neutral stability as part of a continuous deformation process, while also allowing a stress-free configuration to exist. The transition of a double-curved compliant shell from its stress-free stable equilibrium towards its second stable equilibrium, through a range of neutrally stable equilibrium configurations forms the basis of this investigation. To design this neutrally stable shell, an optimization is employed to obtain an ideal set of variables that defines a varying thickness profile. Numerical analysis of the resulting optimized shell structure predicts a substantial region of near-constant energy and associated near-zero loads within this unique deformation mode. Additively manufactured prototypes demonstrate the validity of the modeled results by featuring a continuous equilibrium within the range of motion. These results lay the foundation for compliant beam elements with a neutrally stable bending degree of freedom.

A cantilevered rod's endpoint has a symmetric stiffness profile throughout its range of motion. Generally, this is not the case for spatially curved compliant beams, particularly if they are asymmetric, i.e., their fixation is not in the symmetry plane of their endpoint operating field. This paper discusses a technique for obtaining symmetric kinetostatic behavior from this type of asymmetric compliant beam over a relatively large range of motion. To accomplish this, a parametrization scheme was used to base the geometry of the beam on a limited number of control parameters. These parameters were then used as inputs for optimization in order to create beams with symmetric endpoint behavior. This process was further investigated using different sets of parameters. To validate the method's performance, experiments on prototypes were conducted. The results demonstrated a high degree of congruence with simulations of the anticipated behavior. Comparing to the non-optimized benchmark beam, the experimental performance of the resulting shapes demonstrated up to a 68% improvement in the desired symmetric behavior.

Compliant mechanisms (CM) with adaptive stiffness have been widely used in robotics and machine design applications. This paper proposes adapting the endpoint stiffness of a spatially curved compliant beam using a movable torsional stiffener and a new graphical characterization method for the resulting anisotropic stiffness of the endpoint for large deflections. A slender clamped-free cruciform beam with a predetermined spatial shape was utilized as the main compliant part, and a shorter sliding bellow was served as the torsional stiffener. The beam's endpoint displacements are mainly determined by its bending and torsional deformations. Therefore, the relocation of a bellow stiffener with high torsion and low bending stiffness along the described beam with relatively low torsion and high bending stiffness led to notable changes in the kinetostatic behavior at the endpoint. The share of bending and torsional stiffness of elements along the beam to endpoint stiffness varies depending on the direction. Experiments with arbitrarily chosen parameters of the current design reveal an anisotropically adaptive stiffness with 21.5 times more stiffness variations in one direction compared to the other. Effective characteristics for this behavior, such as the length and position of the bellow, were explored in an effort to improve it. To capture the effect of these parameters, the Isoforce Displacement Closed Surface (IDCS) was introduced as a new characterization method to visualize the nonlinear kinetostatic behavior of a CM throughout its three-dimensional range of motion. The IDCS was further used to elucidate how individual components of the current mechanism contribute to the system's overall kinetostatic behavior. Experiments were done on prototypes to confirm the changes in endpoint stiffness that were predicted by simulations.

Differential mechanisms are remarkable mechanical elements that are widely utilized in various systems; nevertheless, conventional differential mechanisms are heavy and difficult to use in applications with limited design space. In this paper, a curved lightweight compliant type of differential mechanism is presented. This mechanism acquires its differential characteristic by having a high rotational stiffness when the mechanism is symmetrically actuated on two sides, while having a low rotational stiffness when actuated only on one side. The intrinsic elastic strain energy required for deformation of the compliant differential is compensated for by reintroduction of potential energy to make the mechanism neutrally stable. For the storage of potential energy, two preloaded linear springs were used. The rotational stiffness of the one-sided actuation around the neutral position of the compliant differential mechanism is hypothesized to be adjustable by changing the preload of the springs. The stiffness can be positive, zero, and negative, meaning that the mechanism can have neutral stability and bistability. The hypothesis is investigated using a simulated model in Ansys Parametric Design Language using optimized parameters to achieve the desired stiffness for the mechanism. The simulated model is validated using an experimental setup for both the one-sided and symmetrical actuation stages. The experimental results showed a high correlation with the simulations. The mechanism with optimized dimensions and preload showed neutral stability for a range of 16°. Bistability was found for preloads higher than the aforementioned optimized preload. A linear trend was found between the preload of the springs and the rotational stiffness of the mechanism at θ = 0. Furthermore, an output/input kinematic performance of 0.97 was found for the simulated results and 0.95 for the experimental results.

Passive and active exoskeletons have been used over recent decades. However, regarding many physiological systems, we see that the majority explore both active and passive elements to minimize energy consumption while retaining proper motion control. In light of this, we propose a design that combines compliant mechanisms as passive support for gravity balancing of the hand's weight and soft actuators as active support for wrist flexion-extension. Our approach offers a safe, lightweight solution that intrinsically complements and supports the wrist's degrees of freedom. We hypothesize that the proposed soft wearable device is able to increase the range of motion and reduce muscle fatigue while being energy-conservative by balancing of the passive and active subsystems. In this work, we perform a design feasibility study for such soft wrist exoskeletons, particularly focused on wrist flexion-extension rehabilitation. Through optimization, geometries for the required functionality of the compliant beam and soft actuator are obtained, and their performance as separate subsystems is evaluated by simulations and experiments. Under the appropriate inputs, we show that the system can introduce a controllable bifurcation. Through experiments, we investigate such bi-stability and explore its usefulness for rehabilitative support of wrist flexion-extension. In short, the proposed wearable can offer a viable, energy-efficient alternative to traditional rehabilitation technologies.

A design tool for passive wrist support using compliant spatial beams as gravity balancer is presented. The aim of this assistive device is to reduce required effort for pronation-supination and flexion-extension by 70% to help patients with muscular weakness keeping their hand’s posture and doing daily tasks, while the forearm is rested. To reach this goal, a setup with three connection points to the user’s hand, and two optimized spatial beams as elastic gravity compensators, are developed. The overall shape and cross-sectional dimensions of the compliant beams are attained using an optimization technique. The objective is reaching a desired endpoint kinetostatic behaviour which is determined based on the hand’s weight and available muscular forces. A design case is presented to show the ability of the method, and the final errors from the desired behaviour are clarified. In the end, possible further applications of the design tool are discussed.

Elastic neutral stability in compliant mechanisms is a remarkable appearance since it requires the energetic state of the structure to remain unchanged during a deformation mode. Several examples in literature require either plastic deformation or external constraints to be enforced to obtain a state of pre-stress and often require the use of anisotropic materials. This paper presents a new type of compliant shell structure featuring a neutrally stable deformation mode without requiring one of the aforementioned conditions. The shell structure is composed of two initially flat compliant facets that are connected via a curved crease. The structure can be reconfigured into a second zero-energy state via propagation of a transition region, without any apparent effort. Both the structure's local width and local crease curvature can be tuned to reach neutral stability during transition. The modelled results are verified by several prototypes that match the modelled predictions qualitatively, as well as by measurement results that show quantitative agreement. The new type of structure introduced here features neutral stability without relying on the application of pre-stress during manufacturing or externally applied boundary conditions. Moreover, it shows potential for combining geometric simplicity with complex and highly tune-able behaviour.

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.

A method to achieve symmetric kinetostatic behaviour in an extensive working range at the endpoint of an asymmetric spatial beam, using cross-section optimization, is presented. The objective function of the optimization is defined as expanding the beam working range to the desired region, simultaneously maximizing symmetric behaviour in it. To reach this goal, a beam with predefined spatial global shape and an ‘I’ cross-section selected. The cross-sectional dimensions throughout the beam are used as input values for the optimization. The endpoint displacements under symmetric loadings are attained using a nonlinear co-rotational beam element based on the Euler-Bernoulli beam formulation. The optimized beams are compared to a circular cross-section beam with the same global shape to show the efficacy of the method. Isoforce diagrams are investigated for the optimized beams to show the symmetry behaviour of the beam endpoint and the effect of changing different parameters in cross-sectional optimization is discussed.