Elliptical Trammel
First Inversion (Elliptical Trammel)
It is a device to draw an ellipse. Fig. shows an elliptical trammel in which two grooves are cut at right angles in a plate that is fixed. The plate forms the fixed link 4. Two sliding blocks are fitted into the grooves. The slides form two sliding links 1 and 3. The link joining slides form the link 2. Any point on link 2 or on its extension traces out an ellipse on the fixed plate, when relative motion occurs.
x = BC cos θ
or, x/BC = cos θ
y = AC sin θ
or, y/AC = sin θ
Squaring and adding, we get
x²/BC² + y²/AC² = 1 …..(1.11)
Eq. 1.11 is called the equation of an ellipse.
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