Since the mode of Pythagorean-Hodograph curve’s derivate is a polynomial, its involute should be a rational polynomial. We study the expression form of PH cubic’s involute, discovering that its control points and weights are all constructed by corresponding PH cubic’s geometry property. Moreover, we prove that cubic PH curves have neither cusp nor inflection; there are two points coincidence in...

We study three dimensional parametric agile design of gears and related software platforms in terms of: parameterization, modularization, and the software being easy to use, expand and maintain. We base our study on SolidWorks platform, aiming to generate 3-D solid models of gears automatically in terms of: i) inputting parameters to improve the modeling speed, ii) build up foundations for stru...

In this work, we deal with a classical differential geometry topic in Minkowski space-time. First, we prove that there are no timelike involutes of a time-like evolute. In the light of this result, we observed that involute curve transforms to a time-like curve when evolute is a space-like helix with a time-like principal normal. Then, we investigated relationships among Frenet-Serret apparatus...

In this thesis we build the parametric mathematical model of machine tool and solid models of traction gears using in subway locomotive by analyzing the machining process of involute gears and meshing principle of involute gears. The optimization design is done through deduce the relations between basic parameters of gear and loading capacity of transmission. On the base of analyzing optimizati...

This is a geometric approach to spatial involute gearing which has recently been developed by Jack Phillips [4]. Due to Phillips' fundamental theorems helical involute gears for parallel axes (Fig. 2) serve also as tooth flanks for a uniform transmission between skew axes, and the transmission ratio is even independent of the relative position of the axes.

in this study, a generalization of the theory of involute-evolute curves is presented for ruledsurfaces based on line geometry. using lines instead of points, two ruled surfaces which are offset in the senseof involute-evolute are defined. moreover, the found results are clarified using computer-aided examples

In this study, a kind of generalized involute and evolute curve pair is considered in 4 dimensional semi Euclidean space with 2 index. The curvatures the associated Frenet Frame generalized
 involute-evolute are presented.

This paper focuses on the geometric theory of scroll compressor, which includes the determination of the discharge angle, the calculation of the volume in different compression stages, the axial gas force under the condition that the number of scroll turns equals an arbitrary real number. NOMENCLATURE . (J :expanding angle of the involute (rad) a :initial angle of the involute (rad) 6 : orbitin...

BACKGROUND Vascular malformations and hemangiomas, which are endothelial lesions of childhood, may result in considerable morbidity because they can cause discomfort and functional impairment and have a negative affect on the patient's appearance. Although vascular malformations may initially appear very similar to hemangiomas, they have distinct clinical courses. Infantile hemangiomas progress...