Essay On Reuleaux Triangles

CH.1:- INTRODUCTION
1.1 INTRODUCTION:-
 A square hole drilling machine is a special purpose machine. In this machine we are used Reuleaux Triangle method. It is developed by German mechanical engineer Franz Reuleaux
 Reuleaux is first which demonstrate constant width properties.
 When the distinguished German mechanical engineer Franz Reuleaux discussed the famous curvy triangle, which it started being used in numerous mechanisms.

In this machine to making a square hole different type of component is used which is given below:
1. BASE PLATE
2. UNIVARSAL JOINT
3. SPINDLE SHAFT
4. REULEAUX TRIANGLE
5. SLIDING ARRANGEMENT
6. CUTTING TOOL
7. WORK PIECE HOLDER 1.2 PROBLEM SUMMARY:-
In our project generally use for square hole drill

The width of a closed convex curve in a given direction is the distance between two parallel supporting lines perpendicular to that direction.
A set of constant width B has the same with in all direction . Besides the circle, the best known closed convex curve of constant width b is the Reuleaux triangle of width b. i.e., a set in R2 whose boundary consist of three congruent circular arcs of radius b.
The Blaschke Lebesgue Theorem states that the Reuleaux triangle has the least area of all plane convex sets of the same constant width b. The minimum area is
((π-√3)/2)b2.
This theorem was first proved independently by Blaschke. He was the first to demonstrate its constant width properties and the first to use the triangle in numerous real world mechanisms.

5.2 MATHEMATICAL CALCULATION:-
5.2.1 Determination of distance of centre from sides:-
AC= s
AR=

It provides the base for the longitudinal placement of tool with accuracy as its axis would be the defining axis of the tool whose placement will confine the overall tool movement. It will take the rpm as given by the machine and drives the tool.

6.2 Universal Coupling:-
This is the base of the revolution movement necessary for the tool to follow square path and generate the required dimension.
The primary function of this coupling is to provide the rotational motion as output which it is getting as an input from the machinery.
The secondary but equally important function is to provide a link which allows for the centric movement of the Reuleaux guiding triangle which in turn will guide the square cutting tool.

6.3 Cutting Tool–
It is that part which has to actually trace the square and cut the material while following the traced path. The profile is based for the maximum removal of chip without disturbing the geometry of the