Auxetic metamaterials offer various novel abilities, one of the abilities is to deform into a dome-shape under out-of-plane deformation. Contrary to a material with a positive Poisson's ratio, which deforms into a saddle-shape. A dome-shape is named synclastic deformation and a saddle-shape is named anticlastic deformation. Under out-of-plane deformation, the magnitude and sign of the Poisson's ratio influence the curvature of the material, and hence the final shape. Starting from a flat plane, manipulation of the Poisson's ratio can create various unusual shapes, such as an egg or a wave-shape. A desired shape might require a uniform Poisson's ratio or a varying Poisson's ratio distribution. Most of the current estimations on the relation between an auxetic material and the deformation shape are performed experimentally. This paper presents an analytical approach which shows the influence of a varying Poisson's ratio on the out-of-plane deformation of a material under pure bending conditions. Four Poisson's ratio distributions are applied which follow the formulas: S-curve, parabolic and cosine in one and two directions. The same model is build in the FEM software COMSOL which serves as the reference model. Comparison of the COMSOL model shows a Mean Absolute Percentage Error between 0.30% and 11.93% for the analytical model. Remarkably, the accuracy of the analytical model is high if a Poisson's ratio distribution varies in one direction, resulting in a Mean Absolute Percentage Error lower than one percent point. A limitation of the analytical model is that the Mean Absolute Percentage Error increases to 0.69% till 11.93% when the Poisson's ratio varies in two directions. The presented analytical approach provides a first step in determining a varying Poisson's ratio distribution that can deform into any desired shape. The resulting shapes are synclastic and combinations of synclastic and anticlastic.

Origami structures are found in mechanical technology more and more often. A less strict derivative of origami are Hinging Rigid Panel Structures, which are not bound to be developable from a single flat sheet of planar material. These Hinging Rigid Panel Structures can be applied to many fields of mechanical design, and moreover are interesting for their kinematic behaviour. The benefits of using a structure that originates from pieces of flat material include but are not limited to being able to surface treat uninterrupted sections of material that can subsequently be folded into part of the structure’s configuration. In order to describe and programmatically manipulate Hinging Rigid Panel Structures and their kinematics adequately and systematically, this research takes a new and specific approach on modelling them. The Hinging Rigid Panel Structures are modelled as 1-DOF mechanisms, consisting of a base pyramid, to which 2 arms of a variable amount of pairs of triangles are attached. To sufficiently test the versatility of this method of describing Hinging Rigid Panel Structures, a classification has been set up to cover a range of kinematic input-output relations, which will be used to test algorithms against. This classification differentiates by dimension and displacement distribution over both the input and output curves, and captures all kinematic transmissions in 1545 cases. With a sample size of np = 10 randomly generated versions of each of these input-output relations and a motion path resolution of rc = 25, a data set was generated using this classification method. An evolutionary algorithm was created to navigate the solution space more efficiently than using conventional algorithms like (gradient based) hill climber algorithms. The main variables of the evolutionary algorithm like generation size (sg = 60), amount of generations (ng = 75), mutation rate amount (nm = 180) and parent splicing methods have empirically been determined. Running the optimisation for all the categories of the previously mentioned classification was done by adapting the code to be able to be run in crowd computational capacity across 17 contributors’ computers. The results show that Hinging Rigid Panel Structure mechanisms are to a certain extend able to be synthesised to generate requested transmissions, but some cases are harder to reach than others. Complex compound 3D paths are harder to optimise for than other categories, such as planar circular motions. This research lays out a valuable basis that contains all aspects to create a reasonable performing optimiser for 3-D Hinging Rigid Panel Structures that follow requested input-output relations. This research could for example be used as a starting point for developing a software package that allows designers to implement Hinging Rigid Panel Structures in their CAD designs for mechanical transmissions.

The interest in shape-shifting materials has increased over the past years. A part of this field concerns the shape-shifting of sheets from flat configuration into a double curved configuration, requiring nonuniform strain among the sheet. This functionality can be used for various purposes, in different application fields. For example, shape-changing properties are increasingly used in tangible user interfaces. For activating these sheets, shape memory alloys (SMAs) lend themselves well. That is why multiple shape-shifting sheets that are activated with SMAs already exist. However, a new design is developed and explored in this thesis, in which SMA springs are used as compressive bendable actuators. This is different from the designs that are found in literature, and the distributed low bending stiffness could potentially lead to smoother shapes. The goal of the project is to create a SMA spring network that can deform out-of-plane into a specific shape and to explore possible applications. The idea is to prescribe this shape by prescribing the related nonuniform strain via controlling the springs individually. Through an iterative prototyping process such a network is developed. Flexures are included to impose the out-of-plane bending direction. Antagonist hoses are included to prevent these flexures from interacting with the springs and to draw the network back in plane upon cooling. In the final prototype, the shape of the network can be adjusted via binary activating the springs with Joule heating. More possible future applications of the network are explored through brainstorm sessions. In addition, a finite element model (FEM) is set-up to calculate the resulting shape upon an activation scheme. The important network parameters are tested and integrated in simple elements. The demonstrator can successfully deform out of plane into different shapes upon different activation schemes, although the shape control is low, and the overall shape not very smooth due to excessive local bending of the network struts. This could be diminished by increasing the bending stiffness of the struts. However, this would lead to less overall deflection as well. The control over the strains or the bending should be improved for enhanced shape control. To evaluate the FEM, the prototype is 3Dscanned and compared with the result of the FEM. There is a significant difference in the amount of deformation, which may be due to inaccuracies in the model or in the prototype. The validity of these should be improved before further evaluating the effectiveness of the simplified model.

Kirigami can be used to create objects with a nonzero Gaussian curvature. A mathematical method is presented that can be applied to join a single continuous and smooth cut of a kirigami sheet. This is realized by constraining additional discretized strips with origami. The mathematical model evaluates how the strips from both sides of the cut can be constrained. The mathematical model is validated with an experiment, which confirmed the direction of the constraints. However, due to physical elements which are not part of the presented mathematical model, the relative proportion between the constraints did not fully represent reality. Finally, this treatise shows the optimization of a crease pattern, by using this model, resulting in a joined kirigami object.

For more than 130 years there have been efforts to automate human services. One such automation is the use of computer-based solving methods to aid engineers in their search for their ideal goal, such as automated planar mechanism design. Contrary to creating mechanisms manually, automatic methods are able to create and evaluate mechanisms in quick succession. However, computers can often reach intricate designs which are not directly feasible in the physical domain. These programs do not focus on being able to manufacture the mechanisms, thus, the designs often have features that make it difficult or even impossible to create physically. Examples are inadequate spacing between joints or a mechanism consisting of many elements for which a good layer assignment is hard to find. To ensure these designs are physically feasible, a manufacturability check can be implemented. Sen et al. created a method to obtain manufacturable planar mechanisms for kinematic designs consisting of rigid bodies and revolute joints. This method identifies structural, kinematic or geometric infeasibilities for all layer assignments. When a mechanism is fully feasible, it can be manufactured. However, this method is still limited. It is only applicable for mechanisms consisting of rigid bodies and revolute joints. This restricts the application space of possible designs. Also, this method is not tested with physical examples. In this research, an extension of automatically created manufacturable mechanisms is developed. Firstly, it extends the method such that spring elements in a design can be checked for manufacturability and surrounding links can adapt their shape to accommodate for the springs, resulting in a wider field of applications. Secondly, a method is introduced to simplify the steps to manufacture the theoretical design. Four mechanism prototypes are built using the available methods and their manufacturability is evaluated. Lastly, this research can be used to find the layer assignment with the least amount of layers, resulting in thinner mechanisms for space-constrained applications.

This report presents the design of a 2-DOF compliant mechanism, capable of describing a closed spatial surface. The mechanism is designed with the intended application as leg in an omnidirectional walking machine. Therefore, a conceptual design of a way of coupling a multitude of these mechanisms is also presented. By means of a kinematic analysis it will be shown that the design is able to describe this surface, making it suitable for its intended purpose. Measurements of a physical prototype qualitatively confirm the functioning of the device without external loads, after production by means of additive manufacturing. Furthermore, an analysis of the deviations with respect to the created purely kinematic model is performed, indicating the most prominent improvement directions. This creates a first step towards a compliant walking machine, capable of translating in any direction over its supporting surface.

This thesis presents a transformable metamaterial, inspired by origami. Generally, metamaterials are build up following the periodicity of Bravais lattices. This study aims to design a structure not following the Bravais lattices, but rather a different type of symmetry which tiles a sphere, in order to expand on current design studies. In this report the different types of spherical symmetries are discussed and the icosahedral symmetry group is used to design a theorical model. Then a prototype is designed and 3D-printed. Lastly the prototype is discussed and recommendations for further research are made.

This thesis proposes the introduction of a metastable equilibrium state in a viscoelastic pre-curved beam. Generally, metamaterials with bistable unit cells need an external application of force to restore, leading to the contemplation of possible structures with self restorable behaviour. Such restorable nature is associated with metastable equilibrium, which is a time-dependent equilibrium state. The objective of the topic is to build a proof of concept for metastability in a pre-curved beam and identify the influence of geometric parameters on metastability. In the course of the thesis, various models of bistable designs are classified. A feasible bistable mechanism was selected, and the metastable nature is introduced through viscoelasticity. In this thesis, an analytical model is formulated by combining an equivalent Pseudo Rigid Body (PRB) model of the pre-curved beam (modelling the beam's compliance) with Standard Linear Solid (SLS) model (modelling the beam’s viscoelasticity). Prototypes are manufactured by using FDM printing of TPU material. Experimental studies are performed for the evaluation of material properties and testing for metastability in pre-curved beams with various shape factors. The results of experimental studies proved the possibility of metastable equilibrium in viscoelastic pre-curved beams. Later, discussions are offered to improve the predictability of metastability in pre-curved beams and the scope for future studies.