What is Sigma Comparator and How does it works?

This article is about sigma comparator along with their construction, working principle, applications, advantages, and disadvantages.

Basically, comparators are classified into  categories as follows,

  • Mechanical comparators
  • Pneumatic comparators
  • Electrical comparators
  • Optical comparators
  • Mechanical optical comparators

Based on these categories sigma comparator comes under the category of mechanical comparators.

Before going to the topic we shall see the definition of a comparator and how the mechanical comparator works?

Comparator definition

Comparators are the measuring device which is used to measure the dimensional difference between the absorbed value and the standard value. Based on this we can measure the roughness of a surface. Based on the working principle they are classified into categories as  I mentioned above.

Now let us see how a mechanical comparator works?

Working principle of mechanical comparators

Every mechanical comparator comes with a plunger set up. The movement of the plunger is enhanced by some gears such as rack and pinion, levers, and other components. This plunger movement is used to find the dimensional differences.

Now let us see about sigma comparator along with their definition, construction, working principle, application, advantages, and disadvantages.

What is a sigma comparator?

Sigma comparator is a mechanical comparator introduced by a USA instruments manufacturing company. They are mainly used to measure the roughness of the surface by calculating the dimensional difference between the measured value and the standard value of the surface material. The magnification range of about 300 to 500 is obtained while this comparator.

sigma comparator
Sigma Comparator

Let us see the parts of the sigma comparator.

Construction (or) Parts of sigma comparator

sigma comparator
(Parts of sigma comparator)
Sigma comparator is constructed using the following parts and they are discussed below.


The plunger is a sensing element. It is used to sense the roughness of the given surface and it is mounted on the slit diaphragm. The plunger is always in contact with the surface to measure the roughness.

Slit diaphragm (or)slit washer

It helps in mounting the plunger and results in a frictionless linear displacement. They are placed on both sides of the plunger at the bottom. Actually, they are manufactured using a polymer-based material.


The knife-edge is an external additional attachment to the plunger, which transfers the linear displacement of the plunger to the movable block. The knife-edge is positioned to be contacted with both the plunger and the movable block. In the plunger, there is a small groove, where the knife edge is kept in contact.

Adjustable screws

Adjustable screws are used to hold the knife edge along with the plunger. The height of the plunger is adjusted by using these adjustable screws.


There are three blocks namely bearing block, movable block, and fixed block. The bearing block is made to have contact with the knife-edge in the setup and the movable block is positioned in between the bearing block and fixed block. The fixed block is permanently fixed and the movable block tends to move. Both the fixed and movable blocks are attached to each other with an elastic cross-strip.

Cross strip hinge

They are made by flexible flat steel springs which are alternatively arranged at right angles to each other. They are used to interconnect the movable and fixed blocks. It can also be used as a pivot of small angular movement which can be more efficient. When the force is applied the strip can be deformed and comes to its original position at rest.

Forked arms

The above movable block has an attachment with two forked arms. It exactly looks like a ‘Y’ shaped. Forked arms are made of lightweight metal.

Flexible driving band

This flexible driving band is a thin phosphor bronze ribbon that is fastened at the ends of the forked arms.

Driving drum

The driving drum is a small radiused drum which is wrapped around the flexible driving band fastened to the ‘Y’ shaped forked arms. It is mounted on the spindle.


The pointer (or) needle is carried by a spindle in the driving drum. This spindle is always connected to the driving drum center.

Reading scale

The reading scale is circular in shape which helps the pointer to point to the value. This measured value is used for further calculations.

Now let us see how the entire setup works.

Working principle of sigma comparator

The entire setup is placed on the surface to measure the dimensional difference or their roughness. In the entire setup, the plunger is always in direct contact with the surface.

When the object or the surface moves forward, the plunger system tends to move up and down regularly due to roughness. If the surface is flat, then the plunger remains constant.

Hence the deflection of the surface is detected by the plunger.  The displacement in the plunger transferred to the knife-edge through grooves.

This results in the movement of the movable parameter in the cross strip hinge act as a pivot.

This causes the rotation of a ‘Y’ shaped arm or forked arm.

The driving drum also starts to rotate due to the rotation of the ‘Y’ shaped arms. The driving drum rotates due to the contact with the flexible driving band fastened at the ends of the forked arm.

Finally, the pointer or needle starts to deflect. This deflection is due to the pointer spindle in the driving drum which connects both pointer and the driving drum.

Therefore the deflection of the pointer indicates the roughness of the surface. In case there will be no deflection if there is a flat surface.

This animation video helps to understand the working principle of sigma comparator.

Magnification in sigma comparator

Lets us have some considerations in the sigma comparator.

The total length of the ‘Y’ shaped arm or forked arm is taken as the length (L), and also let us consider the distance between the knife edge and the cross strip hinge as X.

The ratio of total forked arm length to the distance between the knife edge and cross strip hinge is considered as the first stage of magnification.$$\displaystyle \text{First stage of magnification = }\frac{L}{X}$$

The flexible driving phosphor bronze band which is fastened at both ends of the forked arm is passed around the driving drum. And the radius of the driving drum is considered as ‘r’.The entire length of the needle is considered as ‘R’.

The second stage of magnification is obtained by taking the ratio of needle length to the radius of the driving drum.$$ \displaystyle \text{Second stage of magnification = }\frac{R}{r}$$

The total magnification is obtained by the product of both magnification stage.$$ \displaystyle \text{Total magnification(M) =}\frac{L}{X}\times \frac{R}{r}$$

The total magnification of the sigma comparator is directly proportional to the length of the forked arm and the total length of the needle. It is inversely proportional to driving drum radius and distance between the knife edge and hinge.

Thus the magnification can be increased by increasing the length of the forked arm and the needle length.

Significance of sigma comparator

The drastic movement of the plunger was not transmitted due to the placement of the knife-edge and the cross strip. This drastic movement mostly occurs when the load quickly jerks.

The pointer of this comparator gives a reading with little or no oscillation when the pointer spindle is placed with a non-ferrous disc and making it movable in a magnetic field.

Parallax error due to incorrect viewing position of the measurement object can be averted due to the presence of a reflective strip in the reading scale of the sigma comparator.

While using the magnetic plunger and a keeper bar on it, the total measuring pressure range of the comparator is obtained.

Applications of sigma comparator

  • It is widely used in assembly line production and automation.
  • It is used as an inspection tool.

Advantages of sigma comparator

  • Since it is a mechanical comparator, there is no need for any power supply.
  • No technicians are required since it is easy to operate.
  • It is compact in size and easy to carry from one place to another place.
  • By comparing other comparators, it is cheaper in cost.
  • It has the least count of up to 0.25 microns.
  • The readings displayed on the scale are easy to read and understand.

Disadvantages of sigma comparator

  • Sensitivity and accuracy are reduced due to friction between the moving internal components.
  • Unlike other comparators, it has more number of moving internal components.
  • Wear, tear, and vibration also occurs in the internal components.
  • Due to the absence of a reflective strip in the reading scale of some sigma comparator, parallax error can be noticed by the beginners who use this comparator for the first time.

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