Unit-IV; Professional Sales Representative (PSR).pptx
Elliptical trammel
1.
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.