SGDM (Sphere Grid Data Model) is an efficient method to deal with the global data because of the advantages of multi-resolution and hierarchy. However, SGDM has no distinct descriptions and lack of round mathematical basis for various applications. What’s more, most of mathematical model about global application have been based on the continuous methods. Although several researchers have consid...

In this paper, the profile of surfaces machined using end mills with flat and ball end tools in modeled. The real kinematics of the tool motion, the static deflection and the run out of the tool are included in the model. The cutting forces are calculated using a semi-empirical method based on orthogonal to oblique conversion of cutting coefficients. The thickness of the uncut chip is used as t...

A spherical polyhedron surface is a triangulated surface obtained by isometric gluing of spherical triangles. For instance, the boundary of a generic convex polytope in the 3sphere is a spherical polyhedron surface. This paper investigates these surfaces from the point of view of inner angles. A rigidity result is obtained. A characterization of spherical polyhedron surfaces in terms of the tri...

A spherical map of a cortical surface is often used for improved brain registration, for advanced morphometric analysis (eg, of brain shape), and for surface-based analysis of functional signals recorded from the cortex. Furthermore, for intersubject analysis, it is usually necessary to reparameterize the surface mesh into a common coordinate system. An isometric map conserves all angle and are...

Gear’s normal contact stiffness played an important role in the mechanical equipment. In this paper, the M-B fractal model is modified and the contact surface coefficient is put forward to set up the fractal model, considering the influence of friction, which could be used to calculate accurately the involute arc cylindrical gears’ normal contact stiffness based on the fractal theory and Hertz ...

Abstract The manufacturing precision of involute worms constitutes a major requirement. On the one hand, worm input element drive; secondly, helical surface is basic an worm-hob. This paper presents analytic comparison between surfaces obtained using theoretical equations, kinematic simulation cutting and charged with errors. error considered distance along normal direction to surface, measured...