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.

Location dependence of a MEMS electromagnetic transducer with respect to an AC power source

A MEMS, silicon based device with a cantilever oscillationsand an integrated magnet is presented for magnetic to electrical transduction. The cantilever structure can be configured either as an energy harvester to harvest power from an AC power line or as an AC current sensor. The positioning of the transducer with respect to the AC conductor is critical in both scenarios. For the energy scavenger, correct positioning is required to optimize the harvested power. For the current sensor, it is necessary to optimise the sensitivity of the sensor. This paper considers the effect of the relative position of the transducer with respect to the wire on the resulting electromagnetic forces and torques driving the device. It is shown here that the magnetic torque acting on a cantilever beam with an integrated magnet and in the vicinity of an alternating electromagnetic field is a very significant driver of the cantilever oscillations.

Resist-substrate interface tailoring for generating high density arrays of Ge and Bi2Se3 nanowires by electron beam lithography

The authors report a chemical process to remove the native oxide on Ge and Bi2Se3 crystals, thus facilitating high-resolution electron beam lithography (EBL) on their surfaces using a hydrogen silsesquioxane (HSQ) resist. HSQ offers the highest resolution of all the commercially available EBL resists. However, aqueous HSQ developers such as NaOH and tetramethylammonium hydroxide have thus far prevented the fabrication of high-resolution structures via the direct application of HSQ to Ge and Bi2Se3, due to the solubility of components of their respective native oxides in these strong aqueous bases. Here we provide a route to the generation of ordered, high-resolution, high-density Ge and Bi2Se3 nanostructures with potential applications in microelectronics, thermoelectric, and photonics devices.