Overview of process

Below are pictures showing how to create a large ellipse (half of one but can also be used to draw a full ellipse). I used this technique to make arc sections in a set of bookcases. No complicated jig to build; just a board, clamp and stick with slot for pencil and nail to set minor axis length.

Pictures illustrating setup and drawing
Initial Setup Starting position
Drawing the ellipse Final result

The Mathematics

The Y Axis represents a guide board perpendicular to board upon which you want to draw the ellipse.

  • Segment E1E3 is the stick used in the operation
  • Point E2 is where the nail is placed
  • Point E3 is the notch for the pencil.
  • See diagram below for an illustration.

x = \overline{E1 E3}*sin(\alpha)
and
y = \overline{E2 E3}*cos(\beta)
and from geometry
\alpha = \beta

Using these as parametric equations and eliminate the angle \alpha and \beta we get equation of an ellipse:

{\LARGE \frac{x^2}{\overline{E1 E3}^2} + \frac{y^2}{\overline{E2 E3}^2} = 1}

Illustration on coordinate system

ellipse_trace

Page where you can simulate the drawing of the ellipse with different parameters.

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