The elliptical trammel is a mechanism that uses two shuttles moving along perpendicular channels to trace an exact elliptical path. It works by inverting a double crank chain mechanism and fixing one link, so that when the two sliders move, any point on the central link traces out an ellipse. The semi-major and semi-minor axes of the ellipse are determined by the distances to the pivot points. This mechanism is used to precisely draw or cut ellipses.

2. Introduction
 The Elliptical Trammel (also known as the Elliptic
Trammel, or the Trammel of Archimedes) is a simple
mechanism which can trace an exact elliptical path.
 It consists of two shuttles which are confined
('trammelled') to perpendicular channels or rails, and a rod
which is attached to the shuttles by pivots at fixed positions
along the rod.

3. Introduction
 As the shuttles move back and forth, each along its
channel, the end of the rod moves in an elliptical path.
The semi-axes a and b of the ellipse are the distances
between the end of the rod and the two pivots.
 An ellipsograph is a trammel of Archimedes intended
to draw, cut, or machine ellipses, e.g. in wood or other
sheet materials.
 Usually the distances a and b are adjustable, so that
the size and shape of the ellipse can be varied.

4. Inversion
 Elliptical Trammel is an inversion of double crank
chain mechanism.
 A double slider crank chain consists of four links
forming two sliding pairs and two turning pairs.
 Link 1 Frame
 Link 2 Slider –I
 Link 3 Coupler
 Link 4 Slider - II

5. Inversion
 Pair A- Sliding pair, Link 1 and
Link 4.
 Pair B- Turning pair, Link 1 and
Link 2.
 Pair C-Turning pair, Link 2 and
Link 3.
 Pair D-Sliding pair, Link 3 and
Link 4.

6. Mechanism
 This inversion is obtained by fixing link 4. The
mechanism so obtained is called elliptical trammel
which is shown in Figure . This mechanism is used to
draw ellipse.
 The link 1, which is slider,
moves in a horizontal slot
of fixed link 4. The link 3
is also a slider moves in
vertical slot.

7. Mechanism
 When the links 1 and 3 slide along their respective
grooves, any point on the link 2 such as P traces out an
ellipse on the surface of link 4, as shown in Fig.
 A little consideration will show
that AP and BP are the semi-major
axis and semi-minor axis of the
ellipse respectively.
 This can be proved as follows :

8.  Let us take OX and OY as horizontal and
vertical axes and let the link BA is inclined at
an angle with the horizontal, as shown in Fig.
 Now the co-ordinates of the point P on the
link BA will be
x = PQ = AP cos t and y = PR = BP sin t
 x/AP = cos t
 Similarly, y/BP = sin t

9.  On Squaring and Adding , we get,
 This is the equation of an ellipse. Hence the
path traced by point P is an ellipse whose semi-
major axis is AP and semi-minor axis is BP.

10. Applications
 It is used in automatic tool changer in a machining.
 Elliptical Trammels are used for drawing large ellipses.
 They can be used to draw smaller ellipses but only
draw one half at a time, having to be reversed to draw
the complete ellipse.