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. This paper presents a curved differential mechanism that utilizes a lightweight, compliant structure. 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. To make the mechanism neutrally stable, the intrinsic elastic strain energy required for deformation of the compliant differential is compensated for by the reintroduction of potential energy, which is provided by two preloaded springs. The rotational stiffness of the one-sided actuation of the compliant differential mechanism around the neutral position is hypothesized to be adjustable by changing the preload of the springs. The stiffness can be positive, zero, or negative, indicating that the mechanism can be neutral or bistable. This hypothesis is investigated using a simulated model in Ansys Parametric Design Language (APDL) 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 simulation results. The mechanism with optimized dimensions and preload demonstrated neutral stability over a 16deg range. Bistability was discovered for preloads greater than the optimized preload. At θ = 0, a linear relationship was discovered between the spring preload and the rotational stiffness of the mechanism. Furthermore, an output/input kinematic performance of 0.97 was found for the simulated results and 0.95 for the experimental results.@en

Compliant mechanisms (CMs), along with soft robotics devices formed therewith, may be defined as engineering systems achieving force and motion transmission via the deflection of flexible members. CMs have increasingly gained a strong foothold in the scientific arena owing to their hinge-less nature, shock resistance, potential single-piece manufacturability, safety in human–machine interaction, minimal maintenance requirements, and adaptability to work in unstructured environments. In parallel, current advances in the production of inherently compliant sensory-motor apparatus, as well as progresses in the development of robust control methods, are paving the way to practical CM adoption in a large variety of engineering fields, here including healthcare, manufacturing, inspection/maintenance, and agrifood.

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Auxetic metamaterials are architected structures that possess a unique property known as a negative Poisson's ratio. This remarkable characteristic enables them to expand or contract in a direction perpendicular to stretch or compression. Due to their exceptional attributes such as energy absorption and fracture resistance, these auxetic metamaterials hold great promise for various applications across multiple domains. However, the widespread development of these materials has been hindered by the absence of an efficient design method. Addressing this limitation, our work introduces a minimal 2D auxetic structure and a corresponding design approach that comprises two geometric transformations. This design method not only allows for the replication of existing auxetic structures but also facilitates the creation of novel structures. Additionally, it enables the classification of these structures into six distinct categories. To enhance the understanding and standardization of these structures, we propose a naming protocol and define their associated unit cell. Furthermore, we explore the possibilities of tessellations within this framework. Finally, we examine the auxetic structures from the perspective of surface strain, which is closely linked to the Poisson's ratio, the Bulk modulus and compressibility.

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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.

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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.

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We often interact with our environment through manual handling of objects and exploration of their properties. Object properties (OP), such as texture, stiffness, size, shape, temperature, weight, and orientation provide necessary information to successfully perform interactions. The human haptic perception system plays a key role in this. As virtual reality (VR) has been a growing field of interest with many applications, adding haptic feedback to virtual experiences is another step towards more realistic virtual interactions. However, integrating haptics in a realistic manner, requires complex technological solutions and actual user-testing in virtual environments (VEs) for verification. This review provides a comprehensive overview of recent wearable haptic devices (HDs) categorized by the OP exploration for which they have been verified in a VE. We found 13 studies which specifically addressed user-testing of wearable HDs in healthy subjects. We map and discuss the different technological solutions for different OP exploration which are useful for the design of future haptic object interactions in VR, and provide future recommendations.@en

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.

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In this paper, we present the ADAPT, a novel reconfigurable force-balanced parallel manipulator for spatial motions and interaction capabilities underneath a drone. The reconfigurable aspect allows different motion-based 3-DoF operation modes like translational, rotational, planar, and so on, without the need for disassembly. For the purpose of this study, the manipulator is used in translation mode only. A kinematic model is developed and validated for the manipulator. The design and motion capabilities are also validated both by conducting dynamics simulations of a simplified model on MSC ADAMS, and experiments on the physical setup. The force-balanced nature of this novel design decouples the motion of the manipulator’s end-effector from the base, zeroing the reaction forces, making this design ideally suited for aerial manipulation applications, or generic floating-base applications.@en

The ability to convert reciprocating, i.e., alternating, actuation into rotary motion using linkages is hindered fundamentally by their poor torque transmission capability around kinematic singularity configurations. Here, we harness the elastic potential energy of a linear spring attached to the coupler link of four-bar mechanisms to manipulate force transmission around the kinematic singularities. We developed a theoretical model to explore the parameter space for proper force transmission in slider-crank and rocker-crank four-bar kinematics. Finally, we verified the proposed model and methodology by building and testing a macro-scale prototype of a slider-crank mechanism. We expect this approach to enable the development of small-scale rotary engines and robotic devices with closed kinematic chains dealing with serial kinematic singularities, such as linkages and parallel manipulators.

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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.

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This paper presents the design of a compliant spherical joint which is neutrally stable in two DoF and has a remote center of rotation. Such a joint can be used, for example, as an exoskeleton’s shoulder joint. The foundation of this paper lies in previous work that has succeeded in designing a compliant spherical joint with a remote center of rotation, but without neutral stability. The existing joint is simulated and its energy properties are analysed. Thereafter it is adapted and optimized for an axi-symmetrical energy field. A spring is introduced to the joint and optimized such that the combined energy field of both spring and joint, is neutrally stable. Experimental verification of the simulation was achieved with a prototype for which a moment reduction of 83.69% was achieved through the addition of the spring.

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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.

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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%).

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Passive shoulder supports show large potential for a wide range of applications, such as assisting activities of daily living and supporting work-related tasks. The rigid-link architecture used in currently available devices, however, may pose an obstacle to finding designs that offer low protrusion and close-to-body alignment. This study explores the use of mechanisms that employ a flexible element which connects the supported arm to an attachment at the back and acts as energy storage, transmission and part of the load bearing structure. Based on the synthesis method explained in this paper, a large scope investigation into possible flexure-based mechanism topologies is conducted. Thereby, many potential designs are discovered, which are presented, categorized and compared. Two promising designs are developed into prototypes, and are built and tested on a dedicated test bench. These two mechanisms reduce the necessary moment to lift the arm by more than 80 % throughout 85 % of the range of motion, while staying within 18 cm and 10 cm distance from the body, respectively. The study indicates that, due to its lower protrusion and interface loads, a design with a tapered flexure connecting the upper arm via a hinge to a spring-loaded slider at the back offers the most promising solution.

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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.

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The usually high eigenfrequencies of miniaturized oscillators can be significantly lowered by reducing the stiffness through stiffness compensation. In this work, a mechanical design for a compliant ortho-planar mechanism is proposed in which the stiffness is compensated to such a degree that it can be identified as statically balanced. The mechanism was fabricated using laser micro-machining and subsequently preloaded through packaging. The statically balanced property of the mechanism was experimentally validated by a measurement of the force-deflection relation. A piezoelectric version of the design was fabricated for the purpose of energy harvesting from low-frequency motion. For a sub 1 Hz excitation, the device demonstrated an average power output of 21.7 μW and an efficiency that compares favorably to piezoelectric energy harvesters reported in the literature. Therefore, it was found that stiffness compensation is a promising method for the design of piezoelectric energy harvesters for low-frequency motions.

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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.

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Weakness of the hip abduction muscles can result in a gait disorder named Trendelenburg gait, which can lead to problems in the hip joint, knees, and ankles. In this paper, the conceptual design of a compliant hip orthosis to prevent Trendelenburg gait is presented. A theoretical analysis and measurements on a technical prototype show a high stiffness ratio between adduction and flexion-extension of the leg, and minimal shear forces from the orthosis on the human body while staying close to the human body.

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A design approach for the quasi-static balancing of four-bar linkages with torsion springs is proposed. Such an approach is useful in the design of quasi-statically balanced fully compliant mechanisms by tuning the stiffness of the pseudo-rigid-body-model. Here, the positive stiffness exhibited by torsion springs at the R-joints is compensated by a negative stiffness function. The negative stiffness is created by a non-zero-free-length linear spring connected between the coupler link and the ground, and where both connecting points trace a line directed to the coupler link's instant center of rotation. A full example of the static balancing of two compliant linkages for approximate straight path generation is developed, where actuation energy of the compliant designs is reduced in 66% and 54%, respectively.

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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.

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