Descriptive Geometry/Axonometric Projection/Axonometric Scales/Directions

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It is possible to find the axial directions in order to obtain the axonometric axial directions if the numbers for the scales are given.

Given: Length Ratios( 1:X:Y)

  1. Draw an arbitrarily sized semi-circle on the line B’C’.
  2. Draw a line O’C’ such that it is at an angle arcCos(X) with the horizontal and intersects the semi-circle at point O’.
  3. Draw a line (O’B’1) at angle arcCos(Y) to the horizontal.
  4. Transfer points B’1, O’, and C’ down to the bottom view.
  5. Draw a circle centered at O through B.
  6. Transfer point B’ down such that it lies on the constructed circle, creating point B. Then use point O and point B to construct a line.
  7. Construct a perpendicular line OB through point C until it intersects vertically with point B at a new point: A. Connect A to point O.
  8. The line segments BO, AO, and CO form the angles of the graphic scale.

Axonometric Projection Scale given scale factors

An example problem is given below.

Construction of a graphic directional scale using given scale factors.