Numerical Method on Intersecting Line of Biased Sphere and Cone

In mechanical dynamics, three-dimensional modeling of machines is essential. Among them, the drawing of the intersecting line of biased sphere and cone in 3D drawing software is still unsatisfactory. The spherical center is taken as the coordinate origin. The cone bottom is parallel to the × 1– × 2 plane. Then the coordinate system is established. A new algorithm corresponding to the auxiliary line method of the graphical method is proposed. The straight line equation of conic contour, which passes the cone top, and the spherical equation are combined to form a set of equations for solving the coordinates of points on the intersecting line. According to the actual situation, the solution of the equation set is divided into a set of points on the intersecting line of two parts. Based on the set of points mentioned above, the intersecting line is drawn. For the general positions of biased sphere and cone, the intersecting line can be obtained by conversion from a coordinate conversion matrix. The intersecting lines obtained by both methods are the same. The auxiliary surface method divides the intersecting line into two parts: front and rear. The auxiliary line method proposed in this article divides the intersecting line into two parts: upper and lower. The above research belongs to the teaching content of “Engineering Drawing”. The knowledge points worth mentioning in this course include: (1) The overlapping combination method of combinations should be the intersecting combination method. (2) A closed dimension chain can be defined as a dimension that can be calculated from other dimensions. (3) The partial view, the oblique view and the coincident section view should be called the partial basic view, the partial oblique view and the overlapping section view respectively. (4) The major diameter and minor diameter of the screw thread should be drawn according to the principle of “treating as contour as long as little solid objects”; The gear meshing area should be drawn according to the principle of “wide gear blocking narrow gear”. (5) The shaft shoulder groove includes grinding wheel overtravel groove, thread undercut groove, transverse anti blocking groove, and longitudinal anti blocking groove.