The ovalturner should know at least the following about ellipses from his school books.
2101 Ellipse axes and linear
The simplest method of drawing an ellipse is the thread construction, e.g. for marking and cutting an elliptical blank from a board or a block. Draw the two axes AA and BB in the wanted lengths, with the intersection M, on the board, set a pencil compass to the half-axis length MA = a and draw an arc - as in Figure 2101b - around one of the end points B of the short axis. It cuts the large axis in the two foci F1 and F2. Fix nails into these points and also into one of the B points. Draw a thread loop around these 3 nails knotting at the extreme ends (Figure 2102a). Pull the nail from point B and draw the ellipse with a pencil. Keep the thread tight when drawing the ellipse (Figure 2102b).
Thread construction of the Ellipse:
Ellipsographs are mechanisms, which guide a pencil or pen for drawing an ellipse onto a fixed drawing board. Instead of the pen a glass cutter or a knife can be used for cutting paper or cardboard as frame inlays. The ellipse axes can be adjusted on the ellipsograph. The kinematic principle of the ellipsograph is achieved by using double slider linkage, the trammel (Figure 2103). The sliders 2 and 4 run in stationary cross slot 3. They are connected in their joints A and B by a coupler 1, the point C of which writes the ellipse kC into the stationary plane. The adjustment of the required half axes is calculated by the distances BC = a and AC = b. The distance AB = a - b = d is the half-axes difference. The midpoint M of the distance AB runs along the circle kM around the ellipse centre M0. The radius of this circle is r = d/2.
Figure 2103 Kinematic scheme of the Ellipsograph
Using the Ellipsographs shown in the following figures ellipses can be drawn and, if the pen/pencil is substituted by a knife, paper or card ellipses may be cut out. When cutting glass exchange the pen/pencil with a glass cutter.
Figure 2104 Ellipse- and Circle-Glas-Cutter (Firma J. Bohle, D 42755 Hann)
Figure 2105 Drawing-Ellipsograph
The ellipsograph in Figure 2106 draws and cuts ellipses to the side of the mechanism. This allows the smallest ellipses to be drawn. The mechanism corresponds with a patent by F. O. Kopp. Instructions for its use have been published [6.1].