Singularity Analysis for a 5-DoF FullySymmetrical Parallel Manipulator 5-RRR (RR

Abstract-A 5-DoF 3R2T (three dimensional rotation and two dimensional translation degrees of freedom) fully-symmetrical parallel manipulator can be adopted in many applications such as simulating the motion of spinal column. However, kinematics of this type parallel manipulator has not been studied enough because of short history. The study of kinematics of the manipulators leads inevitably to the problem of singular configuration. Singularity of a 5-DoF 3R2T fully-symmetrical parallel manipulator, 5-RRR(RR), is illustrated in this study. According to the singularity classification by Fang and Tsai, both limb singularity and actuation singularity are illustrated by screw theory and Grassmann geometry. The result of this study will be helpful for singularity analysis of 5-DoF 3R2T fully-symmetrical parallel manipulators because of their similar constraint property

Silicon nitride metalenses for unpolarized high-NA visible imaging

As one of nanoscale planar structures, metasurface has shown excellent superiorities on manipulating light intensity, phase and/or polarization with specially designed nanoposts pattern. It allows to miniature a bulky optical lens into the chip-size metalens with wavelength-order thickness, playing an unprecedented role in visible imaging systems (e.g. ultrawide-angle lens and telephoto). However, a CMOS-compatible metalens has yet to be achieved in the visible region due to the limitation on material properties such as transmission and compatibility. Here, we experimentally demonstrate a divergent metalens based on silicon nitride platform with large numerical aperture (NA~0.98) and high transmission (~0.8) for unpolarized visible light, fabricated by a 695-nm-thick hexagonal silicon nitride array with a minimum space of 42 nm between adjacent nanoposts. Nearly diffraction-limit virtual focus spots are achieved within the visible region. Such metalens enables to shrink objects into a micro-scale size field of view as small as a single-mode fiber core. Furthermore, a macroscopic metalens with 1-cm-diameter is also realized including over half billion nanoposts, showing a potential application of wide viewing-angle functionality. Thanks to the high-transmission and CMOS-compatibility of silicon nitride, our findings may open a new door for the miniaturization of optical lenses in the fields of optical fibers, microendoscopes, smart phones, aerial cameras, beam shaping, and other integrated on-chip devices.Comment: 16 pages, 7 figure

Upper bound of a band complex

Band structure for a crystal generally consists of connected components in energy-momentum space, known as band complexes. Here, we explore a fundamental aspect regarding the maximal number of bands that can be accommodated in a single band complex. We show that in principle a band complex can have no finite upper bound for certain space groups. It means infinitely many bands can entangle together, forming a connected pattern stable against symmetry-preserving perturbations. This is demonstrated by our developed inductive construction procedure, through which a given band complex can always be grown into a larger one by gluing a basic building block to it. As a by-product, we demonstrate the existence of arbitrarily large accordion type band structures containing $N_C=4n$ bands, with $n\in\mathbb{N}$.Comment: 6 pages, 4 figure