Compliant shell mechanisms are defined as spatially curved thin-walled structures able to transfer or transform motion, force or energy through elastic deflection. They are a sub-category of compliant mechanisms which also gain there motion from elastic deformation. As such they store energy during motion, in addition to providing desired kinematics. One major benefit of this attribute is that several functions of a mechanism or a machine can be integrated into a single monolithic part; this is often called function integration. Certain force-deflection behaviour can be purposefully designed by tailoring the energy storage over the range of motion. This is useful for passive exoskeletons where shell mechanisms are used to compensate the user's body weight and thereby decrease the fatigue accumulated during work. Other applications can be medical devices which often need specific kinetics while operating in a small environment. Shell mechanisms or shell flexures provide different kinetic behaviour than their flat counterparts: the wire flexure and leaf spring flexure. These properties of shell flexures can be leveraged to create more compact force generators. Shell mechanism research is a relatively new field, with articles introducing novel designs with a specific behaviour in mind, such as constant force or moment generators. The state of the art presents what shell mechanisms are capable of. However, the state of the art provides little guidance in how to analyse and design shell mechanisms in general. The objective of this thesis is to propose tools for the analysis and design of compliant shell mechanisms or flexures and to develop understanding of this class of mechanisms. This thesis is divided into three parts. Part I presents the eigenscrew decomposition as a tool to understand and design the kinetics of all compliant (shell) mechanisms. Part II discusses the properties of a buckled tape spring and a method to synthesise a wide array of force-deflection behaviour. In Part III, a novel category of shell mechanisms is introduced. A curved surface is patterned with a lattice, which is able to deform in the membrane of the shell. This is opposed to other shell mechanism that work primarily through the bending of the membrane.@en

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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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.

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The primary compliance vector (PCV) captures the dominant kinematic behavior of a compliant mechanism. Its trajectory describes large deformation mechanism behavior and can be integrated in an optimization objective in detailed compliant mechanism design. This paper presents a general framework for the optimization of the PCV path, the mechanism trajectory of lowest energy, using a unified stiffness characterization and piecewise curve representation. We present a meaningful objective formulation for the PCV path that evaluates path shape, location, orientation, and length independently and apply the framework to two design examples. The framework is useful for design of planar and shell compliant mechanisms that traverse a specified mechanism trajectory and that are insensitive to load perturbations.

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The use of overconstrained mechanisms is often avoided in precision mechanics. Misalignments in the mechanism can cause deteriorated system behaviour, such as buckling. Overconstrained designs do have several advantages, such as higher load bearing capacity and higher natural frequencies. However, these advantages are only present if the mechanism is aligned within certain tolerances. In this paper a method is introduced to identify the limits of these alignment tolerances. The method allows the calculation of the forces in the mechanism due to misalignment. The internal forces are compared to the buckling loads of the mechanism yielding the critical misalignments; the method is corroborated using a multibody simulations. Subsequently, both analyses are compared to an experimental setup; this setup measures the first three modal frequencies and identifies the buckling modes. The proposed method and multibody simulation match with each other and the experiment. However, the critical misalignments are about 20% larger in the experiment; this is mainly attributed to hardware imperfections. Due to misalignment and flatness limitations of the flexures, the undeflected stiffness in the experiment is lower than modelled. The deterioration of the support stiffness is smaller in the experiment. In the most serious case, it retains 80% of the modal frequency in the support directions. The proposed method can be used as a guideline to estimate the manufacturing and assembly tolerances of an overconstrained flexure-based mechanism.

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The primary compliance vector captures the predominant kinematic degree of freedom of a mechanism. Its displacement describes large deformation mechanism behavior and can be an optimization objective in detailed compliant mechanism design. This paper presents a general framework for the optimization of the PCV path of compliant mechanisms using unified stiffness characterization, Fourier descriptors, and surrogate-based optimization. We found a meaningful objective formulation that evaluates PCV path shape independently. Furthermore, we reason that design variables should effect mechanism shape. Lastly, we apply the framework to a design example.@en

Tape springs are thin-walled structures with zero longitudinal and constant transverse curvature. Folding them twice and connecting both ends creates a tape loop which acts as a linear guide. At this time, there is insufficient understanding of the influence of the tape spring's cross section on its behavior. This study investigates the influence of the subtended angle on the tape spring's behavior, especially the energy distribution and the fold radius. First, some key aspects in the design of a twofold tape loop are discussed. By performing a curvature analysis of this folded geometry, the different regions within a tape spring are identified. This information is used to identify the influence of the subtended angle on the geometry and energy state of the tape loop. The fold radius and fold angle are determined by analyzing the geometry of the fold region. The analysis showed that the energy within the transition regions cannot be neglected. The energy within these regions and the length of the transition regions both increase with the subtended angle. It is also shown that the fold radius is not constant when the subtended angle is small. The subtended angle should be above 100 deg to ensure a constant radius.

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Compliant shell mechanisms utilize spatially curved thin-walled structures to transfer or transmit force, motion, or energy through elastic deformation. To design spatial mechanisms, designers need comprehensive nonlinear characterization methods, while the existing methods fall short of meaningful comparisons between rotational and translational degrees-of-freedom. This paper presents two approaches, both of which are based on the principle of virtual loads and potential energy, utilizing properties of screw theory, Plucker coordinates, and an eigen-decomposition. This leads to two unification lengths that can be used to compare and visualize all six degrees-of-freedom directions and magnitudes in a nonarbitrary, physically meaningful manner for mechanisms exhibiting geometrically nonlinear behavior.

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Dilational structures can change in size without changing their shape. Current dilational designs are only suitable for specific shapes or curvatures and often require parts of the structure to move perpendicular to the dilational surface, thereby occupying part of the enclosed volume. Here, we present a general method for creating dilational structures from arbitrary surfaces (2-manifolds with or without boundary), where all motions are tangent to the described surface. The method consists of triangulating the target curved surface and replacing each of the triangular faces by pantograph mechanisms according to a tiling algorithm that avoids collisions between neighboring pantographs. Following this algorithm, any surface can be made to mechanically dilate and could, theoretically, scale from the fully expanded configuration down to a single point. We illustrate the method with three examples of increasing complexity and varying Gaussian curvature.@en

Compliant shell mechanisms utilize spatially curved thin-walled structures to transfer or transmit force, motion or energy through elastic deformation. To design with spatial mechanisms designers need comprehensive characterization methods, while existing methods fall short of meaningful comparisons between rotational and translational degrees of freedom. This paper presents two approaches, both of which are based on the principle of virtual loads and potential energy, utilizing properties of screw theory, Plücker coordinates and an eigen-decomposition, leading to two unification lengths that can be used to compare and visualize all six degrees of freedom directions and magnitudes of compliant mechanisms in a non-arbitrary physically meaningful manner.@en

Dilational structures are one degree of freedom structures able to change their size without changing their global shape. In this paper, we present a method to create dilational shells with arbitrary curvature. For this, we designed triangular tiles, which can be placed on a triangulation of the desired surface. We present the method and illustrate it with the example of a dilational octahedron. Using this regular polygon, we demonstrate that the whole structure has a single degree of freedom, and that the maximum obtainable scaling factor is directly linked to the range of motion of the individual triangular tiles.

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Parasitic motion is undesired in precision mechanisms, it causes unwanted kinematics. These erroneous motions are especially apparent in compliant mechanisms. Usually an analysis of parasitic motion is only valid for one type of mechanism. Kinematic information is imbedded in the compliance matrix of any mechanism; an eigenscrew decomposition expresses this kinematic information as screws. It uses screw theory to identify the lines along which a force yields a parallel translation and a rotation yields a parallel moment. These lines are called eigenwrenches and eigentwists. Any other load on the compliant mechanism will lead to parasitic motion. This article introduces two parasitic motion metrics using eigenscrew decomposition: the parasitic resultant from an applied screw and the deviation of an actual degree of freedom from a desired degree of freedom. These metrics are applicable to all compliant mechanism and allow comparison between two compliant mechanisms. These metrics are applied to some common compliant mechanisms as an example.@en

Tape springs are thin-walled structures with zero longitudinal and constant transverse curvature. Folding them twice and connecting both ends creates a tape loop which acts as a linear guide. When using a tape spring with a non-constant cross-section, a force generator can be created. At this time there is insufficient understanding of the influence of the tape spring’s cross-section on its behavior. This study investigates the influence of the subtended angle on the tape spring’s behavior, especially the energy distribution and the fold radius. A tape spring is once folded in a finite element model. By performing a curvature analysis of this folded geometry, the different regions within a tape spring are identified. This information is used to identify the amount of strain energy of each region. Finally, the fold radius and fold angle are determined by analyzing the geometry of the bent region. The analysis showed that the energy within the transition regions cannot be neglected. The energy within these regions as ratio of the total energy and the length of the transition regions both increase with the subtended angle. It is also shown that the fold radius is not constant when the subtended angle is small. Therefore, when designing a force generator using tape loops, the energy within the transition regions should be taken into account. The subtended angle should not be small to ensure a constant radius.@en