Synthesis of mechanisms with prescribed elastic load-displacement characteristics

In this dissertation a collection of concepts to synthesise nonlinear springs is presented. Such springs can be useful in various application domains where, e.g., multi-stability or static balancing is desired. These behaviors are often sought to alleviate the effort required for actuation. The explored concepts are presented by showing the design methods, numerical or analytical models, and assessing their viability with experimental evaluations.

In part~I two concepts show how the linear moment characteristic of torsion bars can be reshaped into a nonlinear one. Torsion bars are often suitable energy storage elements because they can be conveniently integrated within the hinge of a mechanism. In both examples the synthesised nonlinear characteristic is determined such that it counteracts the moment of a turning pendulum. The way how the characteristic is reshaped is, however, very different. In the first concept multiple springs are employed, but activated or deactivated by mechanical stops in order to create a piecewise linear characteristic. In the second concept the characteristic is reshaped by a set of non-circular gears. These gears are arranged in a planetary way to obtain a compact transmission.

In part~II the focus is on planar compliant mechanisms that by virtue of their optimized shape exhibit the desired behavior. A few examples demonstrate that, even with relatively simple topologies, complex characteristics can be synthesised accurately. For example, a single beam clamped at one end and pivoted at the other end, is able to match a sinusoidal moment characteristic for a half period. In a second example we were able to produce a constant force by a doubly clamped optimally shaped beam. The constant force of this minimalistic design can be applied to balance a weight over a range of motion approximately equal to the largest dimension of the design. In another example it is shown that an optimized beam shape can emulate the behavior of zero free-length springs. These springs have ideal properties but are in practice difficult to make. We also show that a meta-material constituted by a lattice of zero free-length springs, exhibits very peculiar properties as zero Poisson's ratio, isotropy, and constant Young's modulus, up to large strains. Obtaining the required spring bahaviour at such small scale would become possible by the use of optimally shaped beam springs.
In the last example of part~II a design consisting of four symmetric beams that move over a straight line of continuous static equilibrium is shown. As an aid to the design process, a representation of the elastokinematic behavior is introduced, based on the potential energy field (PEF). The PEFs characterise the behavior of compliant systems not only instantaneously, but over an area of possible displacement locations of the endpoint of the system.

Part~III of this dissertation is dedicated to compliant shell mechanisms. The design of compliant mechanisms as spatial, thin walled, and possibly double curved structures has some interesting and promising aspects. Because of their inherent nonlinear behavior, for example, they lend themselves good for synthesising the nonlinear equilibrium path. With compliant shell mechanisms it is also possible to conveniently create anisotropic stiffness, such that some motion directions are travelled much easier with respect to others. This type of effects can be tailored to create a desired kinematic function. In applications as wearable devices and interactive structures, compliant shell mechanisms can yield to slender, lightweight, aesthetically pleasing, and highly functional solutions. In this dissertation some progresses are made in this infant field of research. As a showcase, in the first chapter of this part, a self-balanced shell is designed. The optimized doubly curved shape of this shell is in continuous equilibrium with its own weight over a fairly large range of motion. In the subsequent two chapters, a tailored moment-angle characteristic is realized by optimizing the parameters of a basic origami mechanism. In the last chapter of this part a spiral spring with various cross-sections is analyzed to understand the anisotropic stiffness behaviors that can be achieved. In particular, the out-of-plane spatial behavior is studied. This is done by using the PEFs, for the first time in three dimensions.

In part~IV two application examples are shown. First a shell mechanism, designed to provide a constant force, is applied to the tip of a heart ablation catheter. The constant force at the tip of the catheter helps maintaining contact with the heart wall while preventing dangerously high forces. The second example shows the concept of a large scale collapsible wall, consisting of a doubly curved shell that balances its own weight. Such wall, employed as e.g. a sound barrier, could be hidden flat when not in use, and be lifted upright when it is needed.

The concepts presented in this dissertation are applied to selected examples. However, they can be applied to synthesise a broader scope of desired characteristics. Also, the ideas can be generalised by moving from springs to mechanisms, i.e. where input and output have distinct locations. A step even further is to apply distributed actuation, sensing, and control on the deforming bodies such to obtain real automata, where advantage is taken of the synthesised elastic behavior. It is also advisable to direct future research into the use of composites as spring material. It can be expected that their high strength, their tailorable anisotropy, and the possibility to deliberately introduce prestress will lead to springs with increased performance and improved control of the behavior. Future research should also be directed towards improving the available design aids, including PEFs, for compliant mechanism designers. Furthermore, it is expected that the developments of this dissertation can be beneficially applied in an increasing number of application areas.