Constraint-force-based approach of modelling compliant mechanisms: principle and application

Numerous works have been conducted on modelling basic compliant elements such as wire beams, and closed-form analytical models of most basic compliant elements have been well developed. However, the modelling of complex compliant mechanisms is still a challenging work. This paper proposes a constraint-force-based (CFB) modelling approach to model compliant mechanisms with a particular emphasis on modelling complex compliant mechanisms. The proposed CFB modelling approach can be regarded as an improved free-body- diagram (FBD) based modelling approach, and can be extended to a development of the screw-theory-based design approach. A compliant mechanism can be decomposed into rigid stages and compliant modules. A compliant module can offer elastic forces due to its deformation. Such elastic forces are regarded as variable constraint forces in the CFB modelling approach. Additionally, the CFB modelling approach defines external forces applied on a compliant mechanism as constant constraint forces. If a compliant mechanism is at static equilibrium, all the rigid stages are also at static equilibrium under the influence of the variable and constant constraint forces. Therefore, the constraint force equilibrium equations for all the rigid stages can be obtained, and the analytical model of the compliant mechanism can be derived based on the constraint force equilibrium equations. The CFB modelling approach can model a compliant mechanism linearly and nonlinearly, can obtain displacements of any points of the rigid stages, and allows external forces to be exerted on any positions of the rigid stages. Compared with the FBD based modelling approach, the CFB modelling approach does not need to identify the possible deformed configuration of a complex compliant mechanism to obtain the geometric compatibility conditions and the force equilibrium equations. Additionally, the mathematical expressions in the CFB approach have an easily understood physical meaning. Using the CFB modelling approach, the variable constraint forces of three compliant modules, a wire beam, a four-beam compliant module and an eight-beam compliant module, have been derived in this paper. Based on these variable constraint forces, the linear and non-linear models of a decoupled XYZ compliant parallel mechanism are derived, and verified by FEA simulations and experimental tests.

Towards the design of monolithic decoupled XYZ compliant parallel mechanisms for multi-function applications

This paper deals with the monolithic decoupled XYZ compliant parallel mechanisms (CPMs) for multi-function applications, which can be fabricated monolithically without assembly and has the capability of kinetostatic decoupling. At first, the conceptual design of monolithic decoupled XYZ CPMs is presented using identical spatial compliant multi-beam modules based on a decoupled 3-PPPR parallel kinematic mechanism. Three types of applications: motion/positioning stages, force/acceleration sensors and energy harvesting devices are described in principle. The kinetostatic and dynamic modelling is then conducted to capture the displacements of any stage under loads acting at any stage and the natural frequency with the comparisons with FEA results. Finally, performance characteristics analysis for motion stage applications is detailed investigated to show how the change of the geometrical parameter can affect the performance characteristics, which provides initial optimal estimations. Results show that the smaller thickness of beams and larger dimension of cubic stages can improve the performance characteristics excluding natural frequency under allowable conditions. In order to improve the natural frequency characteristic, a stiffness-enhanced monolithic decoupled configuration that is achieved through employing more beams in the spatial modules or reducing the mass of each cubic stage mass can be adopted. In addition, an isotropic variation with different motion range along each axis and same payload in each leg is proposed. The redundant design for monolithic fabrication is introduced in this paper, which can overcome the drawback of monolithic fabrication that the failed compliant beam is difficult to replace, and extend the CPM’s life.

Beyond simple imaging with energetic beams – nanopatterning, correlative microscopy and statistical analysis of inclusions

Electron microscopy (EM) has advanced in an exponential way since the first transmission electron microscope (TEM) was built in the 1930’s. The urge to ‘see’ things is an essential part of human nature (talk of ‘seeing is believing’) and apart from scanning tunnel microscopes which give information about the surface, EM is the only imaging technology capable of really visualising atomic structures in depth down to single atoms. With the development of nanotechnology the demand to image and analyse small things has become even greater and electron microscopes have found their way from highly delicate and sophisticated research grade instruments to key-turn and even bench-top instruments for everyday use in every materials research lab on the planet. The semiconductor industry is as dependent on the use of EM as life sciences and pharmaceutical industry. With this generalisation of use for imaging, the need to deploy advanced uses of EM has become more and more apparent. The combination of several coinciding beams (electron, ion and even light) to create DualBeam or TripleBeam instruments for instance enhances the usefulness from pure imaging to manipulating on the nanoscale. And when it comes to the analytic power of EM with the many ways the highly energetic electrons and ions interact with the matter in the specimen there is a plethora of niches which evolved during the last two decades, specialising in every kind of analysis that can be thought of and combined with EM. In the course of this study the emphasis was placed on the application of these advanced analytical EM techniques in the context of multiscale and multimodal microscopy – multiscale meaning across length scales from micrometres or larger to nanometres, multimodal meaning numerous techniques applied to the same sample volume in a correlative manner. In order to demonstrate the breadth and potential of the multiscale and multimodal concept an integration of it was attempted in two areas: I) Biocompatible materials using polycrystalline stainless steel and II) Semiconductors using thin multiferroic films. I) The motivation to use stainless steel (316L medical grade) comes from the potential modulation of endothelial cell growth which can have a big impact on the improvement of cardio-vascular stents – which are mainly made of 316L – through nano-texturing of the stent surface by focused ion beam (FIB) lithography. Patterning with FIB has never been reported before in connection with stents and cell growth and in order to gain a better understanding of the beam-substrate interaction during patterning a correlative microscopy approach was used to illuminate the patterning process from many possible angles. Electron backscattering diffraction (EBSD) was used to analyse the crystallographic structure, FIB was used for the patterning and simultaneously visualising the crystal structure as part of the monitoring process, scanning electron microscopy (SEM) and atomic force microscopy (AFM) were employed to analyse the topography and the final step being 3D visualisation through serial FIB/SEM sectioning. II) The motivation for the use of thin multiferroic films stems from the ever-growing demand for increased data storage at lesser and lesser energy consumption. The Aurivillius phase material used in this study has a high potential in this area. Yet it is necessary to show clearly that the film is really multiferroic and no second phase inclusions are present even at very low concentrations – ~0.1vol% could already be problematic. Thus, in this study a technique was developed to analyse ultra-low density inclusions in thin multiferroic films down to concentrations of 0.01%. The goal achieved was a complete structural and compositional analysis of the films which required identification of second phase inclusions (through elemental analysis EDX(Energy Dispersive X-ray)), localise them (employing 72 hour EDX mapping in the SEM), isolate them for the TEM (using FIB) and give an upper confidence limit of 99.5% to the influence of the inclusions on the magnetic behaviour of the main phase (statistical analysis).