An epicycloid or hypocycloid mechanism is capable of drawing an exact epicycloid or hypocycloid curve. Similar mechanism designs can be found abundantly in industrial machines or educational equipments. Currently, the major type of epicycloid or hypocycloid configurations is planetary gear trains, which contain a binary link that has one fixed and one moving pivot, and a singular link adjacent ...

Several problems of trigonometric approximation on a hexagon and a triangle are studied using the discrete Fourier transform and orthogonal polynomials of two variables. A discrete Fourier analysis on the regular hexagon is developed in detail, from which the analysis on the triangle is deduced. The results include cubature formulas and interpolation on these domains. In particular, a trigonome...

Kinematics and simulation study on a two-joint linear hypocycloid tail driving system composed of a special planetary gear system and a linkage mechanism are conducted in this paper. First, the composition and working principle of the linear hypocycloid tail transmission system are introduced and analyzed. Second, the kinematics study on the transmission mechanism is conducted with graphical me...

This paper explores methods of generating fractals from the mapping z→z −n +c and discusses the structure of the resulting images. Lyapunov exponents and cycle periodicity show details of these fractals that are obscured by prior escape-time techniques. The resulting fractals are shown to have a hypocycloid shape. The associated Julia sets can be classified into a variety of types.

We present the first detailed investigation of modal properties in hypocycloid Kagomé fibers; even with an optimized input launch, higher order modes propagate over long fiber lengths, indicative that these modes have low attenuation. OCIS codes: (060.4005) Microstructured fibers; (060.2270) Fiber characterization

The problem of biped locomotion at steady speeds is discussed through a Lagrangian formulation developed for velocity-dependent, body driving forces. Human walking on a level surface is analyzed in terms of the data on the resultant ground-reaction force and the external work. It is shown that the trajectory of the center of mass is due to a superposition of its rectilinear motion with a given ...