Third Inversion:
This inversion is attained by fixing link 4. The mechanism so obtained is called elliptical trammel that is illustrated in given figure. This mechanism is utilized to draw ellipse. The link 1 that is slider moves in a horizontal slot of fixed link 4. The link 3 is also a slider moves in vertical slot. The point D on the extended part of link 2 traces ellipse along the system of axes illustrated in the figure, the position coordinates of point D are as follows
xD = AD sin θ or sin θ = xD/ AD
yD = CD sin θ or cos θ = yD / CD
As,
sin 2 θ+ cos2 θ= 1
Putting for sin θ & cos θ in this equation, the following equation of ellipse is attained.
The semi-major axis of the ellipse is AD & semi-minor axis is CD.
