This document discusses how to drill a square hole using a Reuleaux triangle-shaped drill bit. It explains that a Reuleaux triangle is a shape formed by the intersection of three circles where each circle passes through the center of the other two. When rotated, a Reuleaux triangle can closely approximate the path of a square. The document then describes how an actual drill bit shaped like a concave Reuleaux triangle can cut square holes by allowing unobstructed cutting at the corners. It concludes by mentioning other applications of the Reuleaux triangle shape in engines and manhole covers.

2. How to drill a square hole??
By
O L K ARAHVINTH

3. HOW??

4. Transportation in Early age??

5. Is CIRCLE unique??
ARE THEY
THE ONLY
SHAPE
HAVING
CONSTANT
WIDTH???

6. REULEAUX
The term ‘Reuleaux
triangle’ was derived
from the name Franz
Reuleaux, a 19th-
century German
engineer who did
pioneering work on
ways that machines
translate one type of
motion into another.

7. REULEAUX TRIANGLE
Shape formed by
the intersection of
three circles of
equal radii, each
of which
intersects the
centres of the
other two.

8. How it traces a square??

9. ANIMATION 1

10.  This shape created by the rotating
Reuleaux is about 99% the size of the
theoretical square it is trying to reproduce.
 The difficulty lies in reproducing the path
that the centroid of the Reuleaux triangle
travels. It can be closely approximated by
a super-ellipse |X|^r+|Y|^r= a^r.

11. Reuleaux’s position in a
square
The triangle is
normally tangent to
two sides of the
square with two
vertices touching the
square directly
opposite the points of
tangency (why?), as
in Figure 4a.
The exception is
Figure 4b, where the
Reuleaux triangle has
one point of tangency
and all three vertices
on the square (one

13. Floating Chuck
Fully floating chuck
designed by Harry Watts in
1914.

14. Actual drill for cutting square
holes
The actual drill bit
for the square is a
Reuleaux triangle
made concave in
three spots to allow
for unobstructed
corner-cutting and
the discharge of
shavings

15. Other Applications

17. VIDEO 1

18. Wankel Engine’s Animation

19. Solids of constant width

20. VIDEO 2

21. Other aspects
 Because all diameters are the same length, the Reuleaux
triangle, with all other curves of constant width, is an answer
to the question "Other than a circle, what shape can you
make a manhole cover so that it cannot fall down through
the hole?“
 Several pencils are manufactured in this shape, rather than
the more traditional round or hexagonal barrels. They are
usually promoted as being more comfortable or
encouraging proper grip, as well as being less likely to roll
off tables.
 A Reuleaux triangle can roll but makes a poor wheel
because it does not roll about a fixed center of rotation. An
object on top of rollers with cross-sections that were
Reuleaux triangles would roll smoothly and flatly, but an
axle attached to Reuleaux triangle wheels would bounce up

22. Questions??
THANK YOU
Done by
O L K ARAHVINTH
20082606