# Sine Bar – Working Principle, Construction, Working, Errors and types of Sine Bar

Sine Bar is a precise angle measuring instrument. It is used to measure angles very accurately or to align the workpiece at a given angle. Sine Bar is the most accurate instrument for measuring angles.

Sine bar is made up of high carbon high chromium corrosion resistance steel. Sine bar is made with this material so that it can avoid wear and tear of sine bar when handling. As the tear and wear are avoided, the errors are eliminated and the accuracy of the sine bar is maintained.

### Working Principle of Sine Bar:

The principle of operation of the sine bar is based on the law of trigonometry.
If one roller of sine bar is placed on the surface plate and the other roller is placed on the height of slip gauges, then the structure formed by the sine bar, surface plate, and slip gauges forms a triangle. The hypotenuse of this triangle is the sine bar, perpendicular is formed by combination of slip gauges and the surface plate is the base.
Suppose the height of slip gauges is H and the length of the sine bar is L, then sine ratio the angle theta will be H divided by L.
Now the angle θ can be calculated as sin inverse of H divided by L.

### Construction Of Sine Bar:

A sine bar consists of a ground body made with hardened material like steel. Two rollers are attached at the end of the steel bar. The rollers are of equal diameters and axes of these rollers are parallel to each other.
The top of the steel bar is parallel to the line through the centres of two rollers.
The length of the sine bar is equal to distance between centre of two rollers.
This length of the sine bar is either 100mm, 200mm or 300 mm.This length is very precise and accurate. Relief holes are provided just to minimize the weight of sine bar.

Only a sine bar alone can’t be used for measurement of angles of a component. The sine bar is always used in association with slip gauges and height gauge for measurement of the angles.

Surface Plate:
A surface plate is used as the base for the arrangement of sine bar and other components like slip gauges and height gauge.
It can be assumed that the surface plate provides an exact horizontal surface to the sidebar. If we have a sine bar on the surface plate then the upper surface of the sine bar should be parallel to the horizontal surface of surface plate.

Dial Gauge:
A dial gauge is used to check the parallelism of a surface. If a dial gauge shows zero deflection while traveling on the surface, then we can say that the surface is parallel to its base. In the sine bar arrangement, the dial gauge is used to check whether the upper surface of the workpiece is parallel to the surface plate or not to measure the angle of tapered side of the workpiece.

Block Gauges or Slip Gauges:
Block Gauges or Slip Gauges are the standards for measuring the height or length of an object in a very precise manner.

Vernier height gauge:
A vernier height gauge is used to measure the height of the roller of the sine bar when the angle of a large component is to be measured.

### Working of Sine Bar:

Sine Bar is used in different ways for measuring angle of workpieces of different types.

Working when angle of small component is to be measured:

To measure the angle of a small component, the sine bar is set up at an approximate angle on the surface plate by placing one roller of sine bar over the suitable number of slip gauges combination.
The component whose angle is to be measured is placed over the sine bar.
A dial gauge is used to check whether the upper surface of the component is parallel to the surface plate. This dial gauge is moved over the component throughout its length.

The variation in parallelism of the upper surface of the component and the surface plate can be detected by the deflection of pointer of dial gauge.
After that the height of the slip gauges are adjusted by adding or removing block of slip gauges. It is adjusted until the reading of the dial gauge becomes zero throughout the length of the component.
When this condition is reached, the angle of component becomes equal to the angle of sine bar over the surface plate.

Now the angle of sine bar over surface plate can be easily measured by taking sine inverse of H divided by L, where H is the height of slip gauges and L is the length of sine bar.

where,
θ = angle of the component to be measured
H = height of the slip gauges
L = length of the sine bar

Working when angle of large component is to be measured:
In case of large component, the sine bar is placed over the component as the component cannot be placed over the sine bar.
When the sine bar is placed over large component, the lower surface of the large component is parallel to the datum surface.
The sine bar is placed on the upper surface of the component. The upper surface of the component is inclined and its angle is to be measured.
The sine bar over the upper surface is also in an inclined position and there is difference in heights of two rollers of the sine bar.

The height of the two rollers is measured using vernier height gauge and the height of two rollers is written as H1 and H2. Here the height H1 is more than H2.
The difference in heights H1 and H2 is the rise of the sine-bar.
The measuring pressure is also measured using a dial gauge. The height gauges are until the dial gauge reading becomes zero each time.

The angle of this large component is evaluated using the formula below:

where,
θ = angle of the component to be measured
H1 = height of the upper roller
H2 = height of lower roller
L = length of the sine bar

### Conditions required for accurate reading of sine bar:-

1) The axes of the two rollers of the sine bar must be parallel to each other.
2) The upper surface of the sine bar must be parallel and absolutely flat.
3) The rollers in the sine bar must be of equal diameters.
4) The distance between the centres i.e L must be accurately measured.

### Types of errors in sine bar:

1) Progressive Angle Error:
This error occurs duw to error in the distance of centres of two rollers.

2) Contant Angle Error:
This error occurs when the surface of the component and the roller axes are not parallel to each other.

### Types Of Sine Bar:

Different Sine bars are available according to the purpose of its use and method of application. Some types of sine bar are:

1) Sine centre:
This type of os sine bar is used to measure angles of conical objects that have male and female parts. Sine centre cannot measure an angle of more than 45 degrees.

2) Sine Table:
Sine Table is a special type of sine bar which is large and wide. This sine bar has a mechanism for locking it in place after positioning which is used to hold the workpiece during operations.

3) Compound Sine Table:
A compound sine table is used to measure the angles of large workpieces which cannot be measured using a simple sine bar. In the compound sine table, two sine tables are placed one over the other at right angles. These tables can be twisted to get the required alignment.