摘要
两圆柱相交时其表面交线一般情况下是空间四次曲线。当两圆柱的轴线垂直相交时,其表面交线在与两轴线平行的平面上的投影一般重影为双曲线,常用面上找点法作出。工程上有时为了简化作图,常用两圆柱中大圆柱的半径所作的圆弧来代替双曲线。这种代替有时两者的形状相差较大。本文通过正交两圆柱表面交线数学表达式及投影图、误差曲线图等多方面的考察分析,提出在投影图上使用圆弧代替双曲线的合适范围与条件。
generally speaking, when two cylinders intersect each other, the surface intersecting line might be space quad ric curve. When the axes of two cylinders meet at right angles, the surface intersecting line and its projection on the plane parallel to the axes might merged into a hyperbola. The habitual practice is to find spots from plane. In engineering, the arc drawn by the radius of the bigger one of the two cylinders is often used to replace the hyperbola in order to simplify drawing. This replacement sometimes leads a great difference in shape. So, on what circumstances is this replacement suitable? The author in this paper is to put forward the right ranges and conditions of the replacement of hyperbola by arc in projection figure through observation and analyses on mathematical expression of surface intersecting line of two vertical-intersecting cylinders, error hyperbola, projection figure, etc.
出处
《河北职业技术学院学报》
2004年第4期24-26,共3页
Journal of Hebei Polytechnic
关键词
双曲线
圆柱
圆弧
一般
作图
垂直
平面
交线
相交
近似
arc
hyperbola
cylinder
line of intersection
surface intersecting line
space quadric curve
mathematical expression
common symmetric plane
