Performance Optimization of Polymer Fibre Actuators for Soft Robotics.

Analytical modeling of soft pneumatic actuators constitutes a powerful tool for the systematic design and characterization of these key components of soft robotics. Here, we maximize the quasi-static bending angle of a soft pneumatic actuator by optimizing its cross-section for a fixed positive pressure inside it. We begin by formulating a general theoretical framework for the analytical calculation of the bending angle of pneumatic actuators with arbitrary cross-sections, which is then applied to an actuator made of a circular polymer tube and an asymmetric patch in the shape of a hollow-cylinder sector on its outer surface. It is shown that the maximal bending angle of this actuator can be achieved using a wide range of patches with different optimal dimensions and approximately the same cross-sectional area, which decreases with pressure. We also calculate the optimal dimensions of thin and small patches in thin pneumatic actuators. Our analytical results lead to clear design guidelines, which may prove useful for engineering and optimization of the key components of soft robotics with superior features.

Dynamic similarity of oscillatory flows induced by nanomechanical resonators.

Rarefied gas flows generated by resonating nanomechanical structures pose a significant challenge to theoretical analysis and physical interpretation. The inherent noncontinuum nature of such flows obviates the use of classical theories, such as the Navier-Stokes equations, requiring more sophisticated physical treatments for their characterization. In this Letter, we present a universal dynamic similarity theorem: The quality factor of a nanoscale mechanical resonator at gas pressure P0 is α times that of a scaled-up microscale resonator at a reduced pressure α P0, where α is the ratio of nanoscale and microscale resonator sizes. This holds rigorously for any nanomechanical structure at all degrees of rarefaction, from continuum through to transition and free molecular flows. The theorem is demonstrated for a series of nanomechanical cantilever devices of different size, for which precise universal behavior is observed. This result is of significance for research aimed at probing the fundamental nature of rarefied gas flows and gas-structure interactions at nanometer length scales.

Velocity gradient singularity and structure of the velocity profile in the Knudsen layer according to the Boltzmann equation.

Rarefied gas flow modeling presents significant challenges in the characterization of nanoscale devices and their applications. An important feature of such flows is the Knudsen layer, which is known to exhibit non-Newtonian viscosity behavior. Significantly, recent research has suggested that the effective viscosity at the surface is about half the standard dynamic viscosity. We examine these claims using numerical solutions of the linearized Boltzmann equation and direct simulation Monte Carlo calculations and discover that (i) the flow exhibits a striking power-law dependence on distance from the solid surface and (ii) the velocity gradient is singular at this surface. This finding contradicts these recent claims and has direct implications for gas flow modeling and the design of nanoscale devices.