Cabinet Axonometry Projections (斜二轴测图)

Construction of cabinet axonometry projection(斜二轴测图的形成)

When the axonometric projection plane is parallel to a coordinate plane,and the coefficient of axial deformation of two axes that parallel to the coordinate plane are equal, the cabinet axonometry is produced,as shown in Fig. 5-10.

它是将轴测投影面平行于一个坐标面,且平行于坐标平面的那两个轴的轴向伸缩系数相等的斜轴测投影,如图5-10所示。

 Angle between oblique axes and coefficient of axial deformation 斜二轴测图的轴间角和轴向伸缩系数

Since the frontal view (XOZ-plane) is parallel to the axonometric projection plane, axonometric projections appear in true size and shape. The angle between axonometric axes is ∠X1O1Z1=90°. Coefficients of axial deformation for O1X1-axis and O1Z1-axis are the same with p=r=1.The angle between O1Y1-axis and horizontal line is 45°.Coefficient of axial deformation for O1Y1-axisis q=0.5. See Fig. 5-11 for anillustration.

由于坐标面(XOZ)平行于轴测投影面,这个坐标面的轴测投影反映实形,其轴间角∠X1O1Z1 =90°,这两根轴(O1 X1及O1Z1)的轴向伸缩系数p=r=1。O1Y1与水平线成45°角,其轴向伸缩系数为q=0.5,如图5-11所示。

Based on the above, we know that the oblique projections of circles on planes that are parallel to the XOZ projection plane appear in true sizes and shapes. For example, in Fig. 5-12, all circular faces of the wheel are parallel to the frontal plane and therefore, they appear as perfect circles on the oblique drawing. For circular faces that are parallel to other planes (XOY、YOZ), the circles become ellipse. One should note the following: In oblique drawing, always ensure that the faces containing circles are parallel to the XOZ projection plane, so that the projections of the circles appear in real sizes and shapes, which makes the drawing task more simple and convenient.

由此可得斜二轴测图的特点:平行于XOZ坐标面的圆,其斜二轴测投影反映实形。如图5-12所示。轮子上面的圆形在斜二测投影中仍为正圆形,而平行于另外两个坐标平面(XOY、YOZ)上圆形的斜二测投影则为椭圆。注意:在作带有圆弧的斜二轴测图时,应尽量使圆弧所在的面平行于XOZ面,这样可反映其真实尺寸和形状,从而使作图简单方便。