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在机械加工和测量中,常常遇到空间角度计算。解这类问题,通常用解析几何法、投影分析法或球面三角法。这些方法公式繁杂,空间关系不易想象,实际生产工作者常感不便。为此,我们用矢量法推导出一个定理,并举例说明它的应用,它能简便、容易地解决一些空间角度计算问题。一、锥斜切角正弦定理设锥角为2α的圆锥面与二面角为2θ的两平面M和N相切。圆锥顶点O在棱L上(见图1)。若圆锥轴线OO′与二面角棱L的夹角为β(该角为圆锥面和两平面斜切后的倾斜角,简称斜切角),则下式成立:
In machining and measurement, often encountered spatial angle calculation. Solve this problem, usually using analytic geometry, projection analysis or spherical trigonometry. These methods are complex formulas, spatial relationships are not easy to imagine, real production workers often feel inconvenience. For this reason, we derive a theorem by the vector method and give an example of its application. It can easily and easily solve some spatial angle calculation problems. First, the bevel chamfering sine Theorem Set the conical angle 2α conical surface and dihedral angle 2θ of the two planes M and N tangent. The cone vertex O is on the edge L (see Figure 1). If the angle between the cone axis OO ’and the dihedral angle L is β (the angle is the bevel angle of the conical plane and the two planes after beveling, referred to as the bevel angle for short), then the following formula holds: