 Welcome you all for the series of lecture on metrology. Now, we will start module gate. In this module, we will learn about taper measurement, tilt measurement, angle measurement and radius measurement. In the first lecture, we will be covering about the introduction to taper, tilt and angle, what is the meaning of these terminologies and then what are the various instruments used for the measurement of taper, tilt and angle. We will study about the instruments like combination set, vurnier bevel protractor, optical bevel protractor, line bar, sign center and sign table. In between, we will also conduct some experiments to understand the measurement of these taper, tilt and angle. Now, let us start the introduction to taper, tilt and angle. In our daily life, we come across with these terminologies. Taper, it means to become narrower towards one end. So, you can see here, there is a component here. The length of this particular portion of the component is 40 millimeter and from here to here, the diameter is 40 millimeter and now it is towards one end, towards other end, the diameter is reducing. At this particular location, the diameter is 30 millimeter. That means the size is getting narrowed towards one end. Such components are called tapered components. You can see one example here, a tapered roller bearing and then we will tilt a sloping position or movement. So, one simple example is shown here. We have a solar panel. Its inclination is changed. The tilt or the orientation of the solar panel is changed. That means this sloping position or sloping movement is known as tilt and then we have the term angle. It is the space between two intersecting lines or surfaces at or close to the point where they meet. That means, if you take the two lines 0A and 0B, these two lines are getting intersected at this point O. Now, this space is known as angle. Similarly, we can have two surfaces. So, we have one surface like this and another surface. So, this space between these two surfaces is called angle. You can see some examples here. We have machine tool guideway. This is slide and this is guideway. We have sloping surfaces here. The inclination between these two surfaces is the angle. Similarly, we have a sloping surface here and we have a flat surface. So, the inclination between these two surfaces is there is some angle and this angle tilt and taper they are normally measured in terms of degrees or radiance. That means, there are two commonly used units of measurement for angle or taper or tilt. The more familiar unit is degrees. A circle is divided into 360 equal degrees so that a right angle is 90 degrees. Degrees may further be divided into minutes and seconds. Each degree is divided into 60 equal parts. Each part is called a minute. So, 7 and a half degree can be called 7 degrees 30 minutes written as 7 degree 30 minute. Each minute is further divided into 60 equal parts. Each small part is called one second. So, for instance, 2 degrees, 5 minutes and 30 seconds is written as shown here. Now, parts of a degree are now usually referred to decimally. For instance, 7 and a half degree is now usually written as 7.5 degree. So, this indicates that it is 7 degree 30 minutes. Now, the other common measurement of angle is radiance. For this measurement, consider a unit circle, a circle of radius 1 unit whose center is the vertex of the angle in question. If you see this diagram, this is the vertex and this is the circle with 1 unit radius, then the angle cuts off an arc of the circle and the length of that arc is the radiant measure of the angle. Now, you can see here we have a line here. We have another line here. These two lines, they cut the circle. So, this length of arc is the radiant. It is easy to convert between degree measurement and radiant measurement. The circumference of the entire circle is 2 pi. The circumference of the entire circle is 2 pi so that 360 degree equals 2 pi radiance. Hence, 1 degree equals pi by 180 radiance. Now, there is another term cone angle which is frequently used. It is an included angle between generatrix as measured in the axial plane section. Now, you can see here we have a conical part here. We have multiple generators. We can have multiple generators like this. Now, the included angle between two generators is called cone angle which is measured in the axial plane section. The method of dimensioning and tolerancing conical surfaces and drawings is covered in ISO 3040-1990 standard. Now, various instruments are used for measurement of angle or tilt or taper. Now, we have a combination set. We can see here we have a steel rule and then we have a center head and then we have a square head and then this is the protractor part. We have a body. So, this is the body. This is the blade which can be rotated and we have the scale here, rotary scale here. This is a simple protractor wherein there is no varnier. You can see the details of the simple protractor. We have a rotary scale. You can see the markings 0 to 90, 100, 110 up to 180 and similarly in the other direction 0 to 180 degree. The least count of this simple protractor is 1 degree. We have a reference mark here. You can see 0 is marked here. This is the reference and there is a clamp to clamp the blade on the steel rule at any orientation. Now, what we have to do is we have to insert the workpiece whose angle is to be measured. For example, this is the workpiece. This angle between this particular surface and this particular surface we want to measure. Now, the workpiece is placed between the steel rule and the blade and then there should be intimate contact between the workpiece surfaces and the blade surfaces and then what is the reading of the protractor? So, this 0 is a reference with respect to this. What is the angle indicated or shown by the protractor that we have to see that indicates the inclination. In this particular case, it is showing 40, 45 degree. That means, the angle between this particular surface and this particular surface is 45 degrees. Now, we shall conduct a simple experiment to show how to use a combination set for the measurement of angle. Now, we can see I am trying to measure this. This is the guide way, the slide of the ram of a shaper. I am trying to measure the inclination and the angle between this particular surface and this particular surface. So, I am using a simple protractor for measurement of the angle between these two surfaces. The steel rule should intimately contact this particular surface and the blade of the protractor should contact intimately with this particular surface and then we can read the scale with reference to this particular reference mark. Now, you can see the reading. It is showing 0 degree, 10 degree, 20, 30, 40, 50 and 55 degree. So, inclination between the two surfaces of the slide is 55 degree. You can see the reading 55 degrees. So, a clamp is provided here. We can clamp the steel rule with the protractor and we can remove and then we can read the protractor. So, another normally used instrument for measurement of angle is Vernier Bible Protractor. In the previous case, we saw a simple protractor wherein there was no Vernier, but here we have a Vernier. This is the rotary scale which reads 0 to 360 degree. So, least count of this particular rotary scale is 1 degree and then we have a Vernier. So, this is the 0 reference towards one side. It shows 60 minutes and the other side it shows 60 minutes. Now, least count for this particular Vernier is 5 minutes. That means, 5 minutes, 10 minutes, 15 minutes, 20, 25, 30 minutes. Like this, each degree is divided into 12 parts. So, each part representing the 5 minutes. Now, this is the body which contains rotary scale as well as the Vernier and then there is a clamp to clamp the blades at any desired angle. Now, this shows the full view of the Bible Protractor. Now, it measures angle between two phases of a component. There will be one blade which is fixed to the body. You can see here, this is the body to which the circular scale is fixed and as well as Vernier is also fixed. There is another blade which is slidable, which moves. So, sliding blade length, it varies from 150 to 300 millimeter. Least count of this Vernier Bible Protractor is normally 5 minutes. Here it is the mechanical display is there, scale is there. There are Bible Protractors with digital display also. Now, you can see there are some attachments to the basic Bible Protractor. There is an acute angle measurement. This is 90 degree and this angle is 30 degree and we have a sliding blade. So, this is again beveled at 45 degree and this shows this angle is 60 degree. We can use these ends of the blade to check 45 degrees and 60 degrees. There is a magnifying lens for easy reading and there is a fine adjustment now for proper adjustment of the blades and this is the clamp to clamp the blade to the body. So, with these additional attachments, the simple Bible Protractor is called universal Bible Protractor. Now, another important thing when we use Protractor is there should be intimate contact between blade with the beveled surfaces. You can see here, this is the sliding blade and this is the blade which is fixed to the body. The surface of the fixed blade and the sliding blade should contact the surface of the workpiece intimately. Then only the proper reading can be taken. You can see here in picture B, we have intimate contact here, but there is no proper contact at this place. So, the reading shown is greater than the actual angle. Here it is showing 55 degree which is the correct angle. Here it is showing more than 55 degree because of this error. So, sometimes the one blade, sliding blade is in contact with the workpiece, but here fixed blade is not in contact. It is actually the Protractor is climbing on the workpiece. So, there is no contact here. So, the angle shown is 54 degree which is smaller than the actual angle. So, again see when we one blade should come in contact with one surface of the workpiece and then we should slide the Protractor like this till the other blade comes in contact with the beveled surface and then further we should push the instrument so that there is proper contact at this place. Then we should take the reading, we should clamp the blades and then we should take out and then we can read the instrument. If we further push the instrument, you can see here when we push there will be proper contact like this and if we try to push further again the sliding blade further rotates and then there will be error in the reading. Such things should not be there. So, while using this bevel Protractor, the surfaces of the workpiece should be properly cleaned and surface of the blades of the Protractor, bevel Protractor should be properly cleaned and then we should carefully use the instrument. Now, we will conduct a simple experiment to learn how to use a Protractor. Now, you can see here I am using a bevel Protractor with vernier and this is the workpiece, B block is the workpiece and I want to measure the inclination angle between this particular surface and this surface. You can see how to keep the blades, we should see that one blade is in contact with this particular surface and the other blade should properly contact the other surface. Now, you can see the proper contact. So, if necessary we can take a piece of paper or a filler gauge and we should try to insert here to see whether there is proper contact or not between the work surface and the blade. Now, you can see the contact at this particular place. Now, we can read the instrument. This is the circular scale and then we have the vernier here. You can see we should read from one end. So, the reading is 20 degree, 30 degree, 40 degree, 40 degree and then we should see which mark is coinciding with the main scale. Main scale reading is 40, 41 degree, 42 degree, 43 degree, 44 degree. Main scale reading is 44 degree and then we should see the coinciding division in the same direction that is you can see here this particular mark on the vernier is coinciding with this 50 degree line. So, the vernier reading is 5 minutes, 10 minutes, 15 minutes. So, the angle is 44 degrees and 15 minutes. So, that is the angle. So, another variation of bevel protractor instrument is optical bevel protractor. Here we can see there is a body which houses a circular glass scale which reads from 0 to 360 degrees. Again least count in this particular case is 5 minutes. You can see the peeping hole here. So, we have to keep the workpiece between these two blades. Say this is the workpiece and we want to measure this angle between these two surfaces. So, this surface should contact with this blade and the other surface should contact the other blade and then we should establish intimate contact between the surfaces and then by operating this lever we can clamp it. We can clamp the blades and then we can remove the protractor from the workpiece and then by peeping through this peeping hole we can read the scale. Inside there is a glass circular scale. So, like this. So, which reads 0 degree, 10 degree, 20 degree like this and then with the 1 degree marks. So, it is 5 degree again 6, 7, 8, 9, 10 like this and then there will be a vernier. So, with 5 minutes least count. So, with reference to this 0 on the vernier which we should take the main scale reading as well as the vernier reading and then we can note down the inclination, the angle. So, this is the backside view of the bevel protractor. You can see a groove here. So, which will move inside the body there is a projection and over that this movable slideable blade slides. So, at any desired position we can clamp the blade. Now, this picture shows the full set. We have the body clamp peeping hole and then sliding blade with 60 degree bevel on one side and 45 degree bevel on other side and this is the blade which is fixed to the body and this is the blade which is slideable. There is a spare longer blade is provided. So, wherever necessary we can remove this smaller removable blade and we can insert this blade and we can use it. Now, we will see we will conduct an experiment to show how to use optical protractor. Now, you can see this is the milling machine table. I am trying to measure the inclination. So, this is the guideway. We have the top surface of the guideway and then we have inclined surface of the guideway. I am trying to measure the inclination between these two surfaces using this optical bevel protractor. So, we have this slideable blade and this is the fixed blade. This is the body clamp for clamping the blades and peeping hole through which we can take the readings, the backside view of the optical protractor. Now, you can see the one blade. One blade should come in contact with the top surface of the guideway and other blade should contact this sloping surface. Intimate contact is very essential to get the proper readings. Now, we can see the contact, intimate contact between the surfaces and the blade surfaces. So, another very common instrument used for measurement of angles and tapers is a sign bar. This photograph shows a sign bar. This is the body of the sign bar and we have two rollers, very precise, precisely machined rollers fixed to the two ends of the sign bar and we have circular holes here to reduce the weight of the sign bar. So, this is a very high precision and most accurate angle measuring instrument. We can measure the angles even to an accuracy of few seconds. So, these sign bars are made of high carbon, high chromium steel, they are hardened, stabilized and ground and lapped. They are available in various sizes of 100 millimeter length, 200 millimeter length and 300 millimeter length. This length means the distance between center of this roller and this center, the distance between the centers of the rollers is the size of the sign bar. So, these relief holes are provided to make it light and for easy handling. The diameters of these two cylinders or rollers attached at the two ends diameters are equal, equal diameter rollers. The axis of these two cylinders or rollers are mutually parallel to each other and also parallel to and at equal distance from the upper and lower surface of the sign bar. That means the axis of this roller and axis of this roller should be parallel to each other, should be parallel to the top surface of the sign bar and parallel to the bottom surface of the sign bar. Now, sign bar it is used in combination with slip gauges for precise angular measurement. It is used either to measure angle very accurately or to locate any workpiece to a given angle. Accuracy up to 0.01 millimeter per meter length of sign bar can be obtained. These sign bars they are made as per Indian standard 53-59 of 1969. Now, accuracy requirement and tolerance specified in Indian standard 53-59 of 1969 for a 100 millimeter sign bar are as follows. Flatness of upper and lower surfaces should be 0.001 millimeter and the flatness of side faces should be 0.005 millimeter. Squareness of side faces to upper surface. That means if this is the sign bar squareness of the side surfaces to the upper surface should be within this 0.003 per 25 millimeter. Similarly, squareness of end faces to upper surface should be within this value 0.003 per 25 mm and straightness and circularity of rollers should be less than 0.002 millimeter. Variation in distance between roller axis should be less than plus or minus 0.003 millimeter. Now, these sign bars should not be used for angles greater than 60 degrees. For smaller angles these can be used to get the precise angular values. To measure unknown angles or tapers or small workpieces these are preferred these sign bars are preferred and you can see the arrangement how we can use a sign bar for measurement of taper angle you can see here. This is the workpiece and we need to measure the taper or the angle between this surface and this surface. This is the angle that is to be measured. We have to keep the workpiece on we have to clean the surface of the workpiece and we should keep the workpiece on this cleaned surface plate and then over that we have to mount the sign bar as shown in this picture. We can take the help of maybe the angle plate or magnetic stand to mount the sign bar over the workpiece. Now, you can see here one roller is in contact with the surface plate and then the gap between the roller and the surface plate is filled with slip gauge which indicates an height of H and the distance between the centres of rollers is L this is the length of sign bar. Now, by knowing the value of H and knowing the value of L we can find out the angle theta using this relationship. Sign theta is equal to H1 – H2 divided by L where in this case H2 is 0 and this is H1. If we have the arrangement like this, so this is the surface plate and then this is the component the taper of which is to be measured and then we have to mount the sign bar like this and now this is the roller and we have another roller here. So, in this case we have to fill this gap between rollers and surface plate using these slip gauges. So, in this case this is H1 and here it is H2 and this is L. So, now this theta this theta can be calculated using this relationship. So, theta is equal to sign inverse H1 – H2 divided by L. Now, we will conduct a simple experiment to learn how to measure the angles using sign bars. Now, you can see the arrangement for measurement of taper angle of this particular tapered component. Now, we have the surface plate. We have to clean the surface of the surface plate and then we have to keep the cleaned workpiece on the surface plate. We can take the help of an angle plate for proper mounting of the sign bar. This is the sign bar. These are the relief holes and we have two rollers of equal diameter, two cylinders of equal diameter fixed to the sign bar and then this is the magnetic stand and then we have the slip gauge box to fill the gap between roller and the surface of the surface plate. You can see the close view of the tapered component is dead center of the lathe. This taper or cone angle we want to measure angle plate. This is the top surface of the sign bar and this is the side surface of the sign bar. You can see the relief holes. We have the slip gauge box. Now, we have to mount the sign bar on the workpiece that is tapered component and then we have to keep the magnetic stand in front of the sign bar so that it would not fall. So, back side on the other side we have the angle plate and from the front side we have magnetic stand to support the sign bar and then magnetic stand is switched on. Now, we can see the component, taper component below the sign bar and then this gap between the cylinder and the surface plate should be filled using slip gauges. So, that will give h1, height h1. On the other side also we should fill the gap between this cylinder and the surface plate using slip gauges. So, that will give h2. Knowing the values of h1, h2 and l, we can find out the taper angle theta that is theta is equal to sign inverse h1 minus h2 divided by l. Sometimes the workpiece will be very heavy. So, checking of unknown angles of heavy component in that case how do we use the sign bar. So, we can place the sign bar as shown here. You can see the top surface of the sign bar is in contact with the component, heavy component, cylinders are on the other side. Now, we can use vernier height gauges to check the h1 and h2. So, we can always use the vernier height gauge to check this height, this is the height h1 and here this height is h2 and then l is the length of the sign bar. So, knowing h1, h2 and l, we can find out the angle theta, this angle theta using the relationship, sign theta is equal to, so the difference between h2 and h1, h2 minus h1 h2 minus h1 divided by l. So, using this relationship we can find the taper angle of the component. Now, you can see the another application of sign bar, this is a setting of lathe for taper turning. You can see the workpiece in which we have to cut the taper, we want to maintain some, we want to cut some taper and now the tile stock can be, tile stock quill can be moved. You can see the sign bar and this is the reference bar, sign bar and between the cylinder, cylinder of the sign bar and this reference surface we have filled with the slip gauge. So, like this knowing the value of h1 difference h2, h1 minus h2 and length of the sign bar, we can find out theta or if we know what is the angle that is required, we can find out what is the height of slip gauge and then we can arrange the lathe for taper turning in this fashion. Now, another variation of sign bar is sign center. You can see here we have the body of the sign center, these are the relief holes and then we have cylinders fixed to the body of the sign center and then here we have two centers. These centers they are slideable, you can see the slot here, we can loosen the clamp and then we can move the centers axially like this. To accommodate the workpiece of a different lens, so this sliding arrangement is provided. So, these sign centers they are used in situations where it is difficult to mount the sign bar on the component. So, what we can do is we can mount the workpiece between centers like this and then using a dial indicator we have to keep the slip gauges here. So, this is the surface plate. So, this is H 1 and this is H 2. Now, we should find what should be the value of H 1 minus H 2 minus H 1, H 2 minus H 1 divided by L. We know what is the size of the sign bar and say we have a tapered component. So, we should place the tapered component here between centers and then we should adjust this height H 1 minus H 2 minus H 1 difference height we should adjust till the dial indicator reads 0. So, we can always change this theta by varying this height difference. So, that the dial indicator we have to move the dial indicator on the generator of the tapered component. When we move the dial indicator on the generator of the workpiece this should read 0 like that we should adjust this inclination. So, when it reads 0 then there will be a particular value of theta. So, that is the cone angle of the tapered component. So, like this we can use the sign center for measurement of angles taper angles. Now, we can see an advanced sign center this is the base and then this is the sign table. So, it is pivoted here. So, this sign table can be tilted in this fashion we can tilt the table and we can place here there is a roller and this is the surface of the sign table. So, here after lifting it after tilting it we have to fill this gap using the slip gauges you can see in this picture slip gauges are placed. So, we should calculate the we should adjust the slip gauge height till the dial indicator reads 0. We have to mount the tapered component between the centers you can see the centers. Now, the body which contains the center can be moved horizontally like this to accommodate this also can be slided. To accommodate the workpiece of different lengths these two can be slided you can see here the tapered component is mounted between centers and then there is an attachment here there is a arrangement for mounting the dial indicator you can see the dial indicator is mounted and this head can be moved up and down. You can see the guide ways here. So, this head can be moved up and down again to accommodate the the workpieces of different sizes then the dial indicator is moved horizontally till it reads 0 throughout. So, like that we should adjust the slip gauge height and then the angle can be calculated that will be the angle of taper angle of the workpiece. Now, another variation of sign table you can sign center a variation of sign center you can see here this is called sign table. So, this is the base of the sign table you can see the table sign table can be tilted. So, this table can be tilted you can see the pivot here a roller is fixed to the sign table and between the roller and the base surface stop surface the base we have to insert the slip gauge. So, and there is another this is a basically a compound sign table. So, this table can be tilted like this there is another table mounted over this table which can be tilted in this fashion. So, in two planes we can tilt the plates these two plates again you can see the pivot here and there is a roller fixed to the bottom surface of this top plate. So, here we have to keep the slip gauge for adjusting the required angle. You can see the holes are provided for mounting the component on this particular table. So, these sign tables are heavy duty tables they are very rugged to hold the parts for machining of for measurement of angles as well as for machining of angle workpieces can be mounted on this table and it can be machined. You can see the clamp for the two plates or two tables using these clamps the tables the angles can be rigidly clamped the tables can be clamped. Now these are schematic views of simple sign table here we have only one swiveling table pivot and roller which is fixed to the bottom of swiveling table and this is the reference surface on which slip gauge should be placed. So, between roller and the reference surface slip gauge can be placed and then required angle can be maintained and this is the schematic diagram of compound sign table we have two plates here this is one plate which can be tilted in this fashion and there is another table which can be tilted in this manner. So, we have one pivot for this swiveling table and this is a pivot for another table you can see the t-slots for mounting the workpieces on the top of swiveling table. So, we will see a simple sign table you can see the top surface of the sign table we can also see the t-slots you can see the pivot here pivot roller there is a provision to put a rod here using that rod we can tilt it so that required angle can be maintained. I can clearly see the t-slots here for mounting the workpieces and we can see the slots here for mounting this sign table on the table of machine tools where rod can be placed here and then this pivot can be rotated to change the angle slots for mounting this sign table machine table now this is the surface on which slip cases should be placed we should clean the surface and then we should keep the workpieces slip gauges and we can also see the roller fixed to the bottom surface the swiveling plate. So, between the roller and this surface we should keep the slip gauges and we can also see the pivot roller and now let me summarize the topics covered in this lecture we discussed about the meanings of taper tilt and angle we also learnt about the various instruments used for measurement of taper and angle we learnt about the combination set and then burnier bevel protractor optical bevel protractor we also studied about sign bar, sign center and sign table of different types that is simple sign table and compound sign table we also conducted some experiments to learn about how to use these instruments. So, we will stop the lecture at this point and we will continue this in the next lecture thank you.