This paper introduces a fully compliant spherical joint with a stiffness profile specifically optimized for balancing a pendulum. The design builds on previous work where a fully compliant spherical joint was created using tetrahedron-shaped elements connected in series. Using a numerical simulation, optimizations are conducted for two different ranges of spherical motion. Based on one of the optimized results, a prototype is fabricated and experimentally validated, achieving a moment reduction of 90.5%. The deformation calculated by the computational tool closely matches the prototype’s deformation with an accuracy of 89.6%, demonstrating its potential for application in the development of shoulder exoskeletons.

This paper presents a novel prestressing method for polymeric compliant zero-stiffness mechanisms to obtain neutral stability. The method utilizes stress relaxation as an actor for imprinting a permanent elevated internal stress state. The method in question does not require a complex mechanical setup for application of the prestress. An existing zero-torsional stiffness mechanism is presented as a case study to demonstrate the working principle. Simulations have been performed and experimentally validated to present how stress relaxation can induce neutrally stable behavior in zero-stiffness compliant mechanisms. A sensitivity analysis is performed for the relaxation time to see its influence on the shift of the moment-angular deflection curve.

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.

Orthotic wrist supports will be beneficial for people with muscular weakness to keep their hand in a neutral rest position and prevent potential wrist contractures. Compensating the weight of the hands is complex since the level of support depends on both wrist and forearm orientations. To explore simplified approaches, two different weight compensation strategies (constant and linear) were compared to the theoretical ideal sinusoidal profile and no compensation in eight healthy subjects using a mechanical wrist support system. All three compensation strategies showed a significant reduction of 47–53% surface electromyography activity in the anti-gravity m. extensor carpi radialis. However, for the higher palmar flexion region, a significant increase of 44–61% in the m. flexor carpi radialis was found for all compensation strategies. No significant differences were observed between the various compensation strategies. Two conclusions can be drawn: (1) a simplified torque profile (e.g., constant or linear) for weight compensation can be considered as equally effective as the theoretically ideal sinusoidal profile and (2) even the theoretically ideal profile provides no perfect support as other factors than weight, such as passive joint impedance, most likely influence the required compensation torque for the wrist joint.

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.

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.

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.

Het boek Werktuigkundige Systemen is een compacte inleiding op het systeemdenken in de werktuigbouwkunde, met nadruk op inzicht en grafische methoden, gelardeerd met prikkelende werkingsprincipes en constructie-elementen. Velen merken dat ze nog lang nadat ze het vak gedaan hebben dit boek als naslagwerk gebruiken en het steeds meer gaan waarderen, ook omdat het boek de basis legt voor veel vervolgvakken en projecten.

Het boek is al jarenlang in gebruik bij eerstejaars studenten Werktuigbouwkunde aan de TU Delft. Diverse docenten gebruiken het bij vakken of ontwerp­projecten.

De oorsprong van dit boek in de tachtiger jaren is een college geweest, waarin op eenvoudige wijze de werking van bestaande apparaten en machines werd geanalyseerd. In een later stadium is deze stof uitgebreid met een aantal constructieve bijzonderheden. Daarbij heeft de systeemleer en de modelvorming een belangrijke basis gevormd.

Meer uitgebreid: De fundamentele principes bij ontwerpen komen in dit boek ‘Werktuigkundige Systemen’ naar voren. Zo wordt de systeemleer toegepast op werktuigkundige constructies en wordt in het hoofdstuk over modelvorming de weg aangegeven om de complexe fysische werkelijkheid om te zetten in een overzichtelijk werkingsinzicht. Ook onder meer mechanische versterkers komen aan bod en is een hoofdstuk gewijd aan de belangrijke begrippen sterkte en stijfheid. Er is ruim aandacht gegeven aan wrijving en weerstand, alsmede aan de middelen om deze te vergroten of te verkleinen. Omdat veren tot de essentiële werktuigonderdelen behoren is een hoofdstuk gewijd aan de toepassing van veren in een ontwerp. Hier is het belangrijke begrip voorspanning behandeld. Het onderwerp Aandrijving wordt behandeld en daarin wordt aangegeven op welke wijze een motor met een last moet worden gekoppeld. Het hoofdstuk over comparalogie laat de problemen zien bij het verkleinen of vergroten van reeds bestaande constructies en bij de vaak noodzakelijke modelproeven. Het hoofdstuk over energie ten slotte, geeft een inleiding in de ‘warme werktuigbouwkunde’. Hierin is een technologisch rendement beschreven dat aangeeft in welke mate een machine warmtetechnisch goed is geconstrueerd.

Dit boek kan gebruikt worden bij verschillende soorten technisch hoger onderwijs; zowel door het globale overzicht van de gehele werktuigbouwkunde, de introductie van systeemleer en modelvorming, als door de specialistische behandeling van enkele bijzondere onderwerpen.

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.

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.

Inspired by phenomena in the plant world, a meteoro-sensitive rotational actuator is developed. The design uses a hygro-active shell, whose water-based swelling is restricted at selective locations to form a helicoid structure. The influence of geometrical parameters on the performance is investigated using a numerical analysis of various geometries, by looking at resulting rotation and torque during this rotation. Prototypes are built of five key geometries in the design space, to validate the simulations and to investigate the behaviour of the design experimentally. These prototypes are submerged in water to investigate their deformation, after which they are placed in a torsion machine to investigate the torque during rotation. The experiments result in similar rotations and torques as the simulations. The designed Hygromorphic Rotational Actuator is capable of passively rotating its own structure, thereby expanding the possibilities of engineers and designers when designing passive autonomous systems.

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.

Contact force management has been proven to have a positive effect on the outcome of cardiac ablation procedures. However, no method exists that allows maintaining a constant contact force within a required and effective range. This work aims to develop and evaluate such a constant force mechanism for use in an ablation catheter. A passive constant force mechanism was designed based on a tape loop. The tape loop consists of two tapered springs that work in parallel. A finite element analysis was carried out to verify the behavior and performance of the design. A design based on requirements for a constant force ablation tip showed an average force of about 7.8×10-2 N±8×10-3 N over 20 mm in simulation. A scaled prototype was built and evaluated to prove the validity of the concept; this prototype provides an average force of 1.3×10-1 N±1.6×10-2 N over 35 mm. The mechanism allows for controlled delivery of contact force within a desired and effective range. Based on these findings, it can be concluded that the approach is successful but needs to be optimized for future applications. Being able to control the delivery of contact force in a constant range may increase the effectivity of cardiac ablation procedures and improve clinical outcomes.

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.

Mechanisms that consist of many elements and are potentially small sized, benefit from kinematic elementary units like revolute joints that are compliant and monolithic, and therefore could be produced without need for assembly. We present a novel concept of a compliant revolute joint that features low axis drift, high support stiffness and a large range of motion. The concept is based on a helicoidal shell of which a portion reverses its twist direction upon application of a rotation. The reversed region increases gradually, resulting in a constant reaction moment. Analytical, numerical, and experimental analyses are presented to reveal and quantify the constant-moment behaviour. Prototypes of the concept are employed in exemplary linkages to demonstrate the ability to create a large variety of neutrally stable compliant linkages, which require extremely low actuation forces and exhibit large ranges of motion.

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.

It is expected that mobile robots can benefit from the exploitation of their resonance in terms of actuation and efficiency. Therefore, a study is conducted on the existing terrestrial mobile robots that use resonance to obtain or improve locomotion. An overview of these robots is provided, and their advantages over robots that do not use resonance are examined. A classification with fifteen subclasses is introduced based on the locomotion mechanisms that mobile robots use. In five of the fifteen subclasses, examples of mobile robots that use resonance are found. These robots prove that they can be up to 16 times more efficient and much simpler to actuate and control than their imposed counterparts. Four different methods to make use of the resonance of a mobile robot are distinguished. A systematic design approach that combines these four methods with the fifteen subclasses is proposed, which can be used to obtain unexplored concepts for mobile robots that benefit from the exploitation of their resonance.