 First, I am Dr. Prakash Samke from Mechanical Engineering Department of Walshian Institute of Technology. Today, we are going to discuss the topic of study of mechanical comparators. So, this is from the meteorology series on the topic of comparator. At the end of this session, it is expected that students will be able to explain the principle and working of mechanical comparators. Basically, what is mechanical comparator? Mechanical comparators employ mechanical means for magnification. Now, what are the different mechanical means that are used for magnification? Can you tell? Magnification which is done mechanically. Yes, yes. So, mechanical magnification can be done with different elements which includes levers basically, as you know. Then gear trains, rack and pinion, combination of all this, etc. So, these are the different mechanical means that are used for magnification. And the comparators which use, say these means for magnification, they are known as mechanical comparators. Now, these mechanical comparators, they have normally a sensing element in the form of spindle or plunger, which senses the deviation and gets displaced. The usual magnification obtained is in the range of 250 to 1000. In some cases nowadays, of course, the range of magnification is more than 1000 also. But sir, this is the general range. There are several types of mechanical comparators. However, we shall study following types which are used widely generally. So, one is Johansson's microkator, another is Dialgate, third is Sigma comparator. So, let us study one by one. First, Johansson microkator. This instrument was first devised by CF Johansson and hence the name. It uses a twisted strip to convert small linear movement of a plunger into a large circular movement of a pointer. It is a simple device. It is therefore also called as a twisted strip comparator. The magnification method was designed based on the principle which was devised by H. Abram, which is also known as Abransson movement. It is the name of the scientist Abransson. Say that is Abransson movement. A twisted thin metal strip carries every light pointer normally of glass fitted at its center as shown in the figure. So, let us see the figure. Yes, can you see? Yes, in this figure you can see that the twisted strip is there. Yes, so this is the twisted strip. So that is fitted centrally. On one end, say there is a cantilever strip. You can see this. So this is the cantilever strip. On the other end, so this is a lever. So this is a bell crank lever. So this is a bell crank lever and say one arm of this lever. So that carries it. At the center you can see. So this is the pointer. So normally it will be of some light material. Earlier it was glass. Nowadays even plastics are being used. Say in everywhere metals, materials are being changed. And say this is the plunger. This is the plunger. So that is the sensing element, sensing element. And say there is slit washer, slit washer. Say which acts as a guide and supports to the cement plunger. So to keep it centrally and say guide it. So this is, say I mean this figure is taken from a source. That textbook by metrology by M. Mahajan. Now let us see the construction and working. As we have seen one end of the strip is fixed to the adjustable cantilever strip. So that cantilever strip is adjustable. The other end is joined to the spring elbow. Which is one arm of a bell crank lever. A bell crank lever is there so that arm, so that is a spring elbow. Because it can act as a spring. So that elbow, that arm, so that is known as spring arm. Other arm of the bell crank lever is placed on the measuring plunger. That we have seen in the figure. Say if you want to see, yes. So this other arm is set on the measuring plunger. Other arm of the bell crank lever is placed on the measuring plunger. Upward movement of the plunger will rotate the arm of the cantilever. So that plunger will be sensing the displacement from the standard. The working of the comparator that initially that plunger will be set to the standard. Then the standard will be replaced by the number of components that are to be measured. If the component is having same size, there will not be any displacement. If the component is of higher size than the standard, then the plunger will move upward. And that will rotate the arm of the cantilever which in turn will apply tension on the twisted strip. So if we see the figure again. So this upward movement of the plunger, so that will rotate. I mean say this particular bell crank lever around this particular particular fulcrum or pin. And say this end, so that will move in this direction and that will apply tension to the twisted strip. So that is the working. So as a result the strip gets untwisted as it moves here. So it has to expand and say for that untwisting, say that will take place. Which will cause a rotation of pointer. The pointer will rotate. So this happens when the plunger is moving upwards. If the component is smaller, then the plunger will move downwards. The spring elbow will restore and will cause twisting of the strip and pointer will rotate in opposite direction. Again if we see the figure, say if the plunger moves downwards, the elbow is spring, so the other arm. So this will move inside and so that will cause shortening of the length. So that will cause the twisting of the strip in opposite direction. And pointer will rotate in the opposite direction. So this is the working. This is the working that how that movement of the plunger is converted into rotation of the say pointer. So the strip is perforated to reduce the weight and consequently stress. So the magnification is in the ratio of rate of change of pointer movement to the rate of change of length of the strip. We have seen the length of the strip will change. So that m is equal to dq by dl, where it can be shown that dq by dl is proportional to l by w square into n. Where q is twist, so dq is the change in twist with respect to change in length. So dq by dl, the q is twist of midpoint of strip with respect to the end. So that is measured with respect to the end, how much twist so that is there. l is length of twisted strip measured along its neutral axis. So length of twisted strip since it is having width. So where to measure the length again, so it is measured at the neutral axis. Because say above neutral axis and below neutral axis there are chances of slight bending. Okay neutral axis is one where there will not be any bending. So length will remain constant. W is width of the twisted strip. So width is the dimension measured in perpendicular to the length. And n is number of turns of twist. So how many twisted turns are there, so depending on length. So if we see, so this movement depends on, it is proportional to l. l is more than dq by dl, so that response, so that will be proportional to it. If w is small, then as w becomes smaller, response will be greater. So rather it is square, I mean proportional to w square. And as the number of twists, say I mean increase, say then there will be decrease in the movement or this thing. If the number of turns are smaller, then there will be more, I mean magnification. So if we see, so this is the outer construction, so this is the dial. I mean inner mechanism we have seen, say this is the plunger and this can be fitted on particular stack. Okay, so this is showing the maximum and minimum limits which can be shown. If we see the strip, so this is the strip, so this is the w and this is the l, this is the l. So this is taken from the Wikipedia from the website, say that is mentioned here. So the Johansson. Now from the expression of magnification, it is clear that magnification will increase with length of the strip. Magnification will decrease with shorter width of the strip. Magnification will increase with number of turns of twist and thickness of the strip should be small as small as possible. So it should be thin. The instrument is initially set with the standard specimen and then the reading is set to zero for this value. For the pointer, the pointer will be set to zero. Then standard is replaced by other component whose dimension is to be measured. Any difference in the measured dimension and that of the standard, so that will cause the lowering or rising of the plunger. And consequently, so that will cause the movement of the pointer. So this is the working of the Johansson microgator. The reference for this particular topic was taken from the textbook of metrology by M. Mahajan, Dhanpatra and Company Private Limited.