球面渐开线研究

寂静回声

问





答


The spherical involute is the 3D counterpart of the planar involute of a circle. Similar to the definition of the planar involute, the spherical involute is defined as a 3D curve traced by a point P on a taut chord  unwrapping from base circle of radius rb that lies on sphere S with origin at Os and radius r0 (see Figure 2). Point P in Figure 2 is a point of an involute curve traced while it unwraps from base circle of radius rb, obtained as the intersection between the base cone and the sphere of radius r0. The spherical involute is traced on the surface of the sphere S while point P unwraps over it from the base circle. Therefore, the arc length of the great circle  is equal to the arc length of base circle, which is , and according to this

《Generation principle of concave tooth surface of spherical involute spiral bevel gear》
https://www.zhygear.com/generati ... -spiral-bevel-gear/

《The computerized generation of straight bevel gears with spherical involute profiles is developed and the advantages of its application investigated. Possible microgeometry modifications of the gear tooth surfaces are proposed to provide stable contact patterns when errors of alignment occur.》
https://thermalprocessing.com/co ... ing-or-3d-printing/