Scales

It is difficult to draw the components to their actual size, because they may be too large to be accommodated on the drawing sheet or too small to draw and cannot be effectively used in the shop floor. For example, think of making the drawing of motor car. It is too long and wide to be drawn on the drawing sheet to its original size. Similarly small component like a wheel of a wrist watch or its needle, if it is drawn to its original size will not be legible enough for use in the shop floor.

So depending upon the situation, drawings are drawn smaller or larger than the actual sizes. When we say that the drawings are smaller or larger, we mean that the given length in the drawing will be smaller or larger than the corresponding length in the object.

The ratio of the length in the drawing to its corresponding length of an object, when both the lengths are in the same unit, it is called the Representative fraction

R F =size of component in drawing /actual size of component c

Depending on the situation the term scale implies either RF or a measuring device itself made for a particular RF.

RF has two elements of which one of the elements is always ‘1’.

Example of RF: 1 : 5, 1 : 10, 150 : 1 etc.

First element in the RF always represents the size in the drawing while the second element represents the corresponding size of the object.

Archimedes spiral

Archimedes spiral:

It is a plane curve generated by a point which moves uniformly around and towards or away from a fixed point called the “ pole “ or it is a locus of a point which moves away or towards from another fixed point at a uniform linear velocity and uniform angular velocity

When the point on the spiral moves through 360 degree, it is called on “convolution”

Practical application Scroll plate of lathe chucks, spring of clocks, watches, tooth profile of helical gears and cams etc.

Helix

Helix :

When a point moves at a constant speed along a line which revolve at a constant rate around a fixed axis. The point traces a curve similar to the coil of a spring, such a curve is called helix.

The fixed distance through which the point moves parallel to the axis for each revolution of the line is called the “pitch “of the helix. (or lead).

The helix is called as cylindrical helix when the revolving line is parallel to the axis of the revolution.

If the revolving line is inclined to the axis of revolution the resulting helix is called conical helix.

The helix may be either right handed or left handed. The right handed helix climbs from the base towards right side as it rises along the axis.

Practical application Threads on bolts, screws, nuts, springs, spiral staircase etc. have helical curves in them.

Involutes

Involutes :

It is the curve traced out by a point on a cord as it unwinds (but remains taut) around a circle or polygon

Alternatively an involute may be defined as the curve traced out by a point on a straight line which rolls around a circle or polygon without slip. Depending upon plane shape around which the line rolls, the involutes are named as involute of a triangle, involute of a square, involute of a polygon, involute of a circle etc.

The most common application of involute is seen in the manufacture of gears. The profile of a gear tooth is the shape of involute.

Hypocycloid

Hypocycloid:

When the generating circle rolls on the inside (concave side) of a larger circle, the path of the point is hypocycloid.

 

Practical application:  The cycloidal curve has its application in the design of gears and used to form gear teeth outline

Epicycloid

Epicycloid :

When the generating circle rolls on the outside (convex side) of a larger circle, the path of the point is epicycloid.

Cycloid

Cycloid:

When the generating circle rolls on a straight line, the path of the point is a Cycloid.