This paper illustrates the use of the envelope theorem for the geometric design of a cycloidal speed reducer. Specifically, it proposes two designs for a mathematical model with tooth differences: a pin wheel epitrochoid meshing which is a cycloidal wheel (internal rotor) profile equidistant to an epitrochoid (or extended epicycloid) curve and a cycloida! wheel is generated by a pin wheel (exte...

A new type of compressors named “internal-meshing rotary compressor” is proposed in this paper. This compressor could be applied in carbon dioxide trans-critical refrigerating cycle perfectly due to it simple structure, self-balanced initial mass and endurance of high pressure. However, there are few basic geometric theories to guide the design including the generation of profiles, mesh relatio...

It is known that the popular effective medium approximation ~EMA! for the effective conductivity se of a composite is exactly realizable by certain multiscale hierarchical microstructures. We have found a class of periodic, single-scale dispersions that achieve the EMA function at a given phase conductivity ratio for a two-phase, two-dimensional composite over all volume fractions. Moreover, to...

We show that a class of exactly solvable quantum Ising models, including the transverse-field Ising model and anisotropic XY model, can be characterized as the loops in a two-dimensional auxiliary space. The transverse-field Ising model corresponds to a circle and the XY model corresponds to an ellipse, while other models yield cardioid, limacon, hypocycloid, and Lissajous curves etc. It is sho...