A Kinematic Theory for Planar Hoberman and Other Novel Foldable Mechanisms

In this paper, we present a kinematic theory for Hoberman and other similar foldable linkages. By recognizing that the building blocks of such linkages can be modeled as planar linkages, different classes of possible solutions are systematically obtained including some novel arrangements. Criteria for foldability are arrived by analyzing the algebraic locus of the coupler curve of a PRRP linkage. They help explain generalized Hoberman and other mechanisms reported in the literature. New properties of such mechanisms including the extent of foldability, shape-preservation of the inner and outer profiles, multi-segmented assemblies and heterogeneous circumferential arrangements are derived. The design equations derived here make the conception of even complex planar radially foldable mechanisms systematic and easy. Representative examples are presented to illustrate the usage of the design equations and the kinematic theory.

Atomic layer deposition of ZrO2 thin films: Study of growth kinetics and dielectric behaviour

Thin films of ZrO2 have been deposited by ALD on Si(100) and SIMOX using two different metalorganic complexes of Zr as precursors. These films are characterized by X-ray diffraction, transmission and scanning electron microscopies, infrared spectroscopy, and electrical measurements. These show that amorphous ZrO2 films of high dielectric quality may be grown on Si(100) starting about 400degreesC. As the growth temperature is raised, the films become crystalline, the phase formed and the microstructure depending on precursor molecular structure. The phase of ZrO2 formed depends also on the relative duration of the precursor and oxygen pulses. XPS and IR spectroscopy show that films grown at low temperatures contain chemically unbound carbon, its extent depending on the precursor. C-V measurements show that films grown on Si(100) have low interface state density, low leakage current, a hysteresis width of only 10-250 mV and a dielectric constant of similar to16-25.

Rainbow Connection Number and Connectivity

The rainbow connection number, rc(G), of a connected graph G is the minimum number of colors needed to color its edges, so that every pair of vertices is connected by at least one path in which no two edges are colored the same. Our main result is that rc(G) <= inverted right perpendicularn/2inverted left perpendicular for any 2-connected graph with at least three vertices. We conjecture that rc(G) <= n/kappa + C for a kappa-connected graph G of order n, where C is a constant, and prove the conjecture for certain classes of graphs. We also prove that rc(G) < (2 + epsilon)n/kappa + 23/epsilon(2) for any epsilon > 0.