 I welcome you all for module 8 lecture 3. In this lecture we will be discussing about angle measurement and radius measurement. The topics covered in this lecture 3 are like this angle measurement under this we will be studying about tilt measurement by autocollimator and then contact angle measurement, angle gauges, spirit level and doltile measurement. And then we will move to the radius measurement. Under radius measurement we will be studying about radius gauges, spirometers, cylindrometers, adjustable outside inside radius gauges, cutting tool radius measurement by optical system, digital radius gauge and then profile projector. Now let us start the discussion on angle measurement or tilt measurement by using autocollimator. You can see in this photograph we have a autocollimator setup. We can adjust the height of this tube depending upon the workpiece height and there is a stabilized voltage supply to light the light source and then where the various optical lenses are provided and then where there is a viewing eyepiece is there through which we have to take the readings. Now let us see how we can measure use this autocollimator for tilt measurement. So we have surface plate on which we have kept a mirror reflecting mirror. Now you can see here let us assume that we have kept this mirror on a surface workpiece surface like this and light ray will fall on the mirror and it will get reflected. Now let us assume that there is small tilt of the surface like this. So the angle theta is the tilt angle. So in this case light will fall on the mirror and because of this tilt it gets reflected in this path. So this is the reflected light. This reflected light will fall on the glass scale provided inside the autocollimator. So which we can read through the eyepiece. Now the constructional details are shown here. This is the reflector M. Now you can see there is a small tilt of theta which we wish to measure. We can see the objective lens and then eyepiece lens and there is a light source. Okay light will fall on the mirror and then it will fall on the reflecting surface. If there is a tilt the light gets reflected and then it will fall at point R2. If there is no tilt the light will fall on R1. If there is a tilt of theta then it will fall on the point R2. So this distance D between R1 and R2 we can measure using the eyepiece. Now inside the view field diagram you can see here. So the cross lines you can see this is the reference point and you can measure what is the tilt angle. So the least count is 1 division is equal to 1 minute. So by how many minutes the surface has tilted that we can read. Now let us learn about the contact angle and measurement of contact angle. This is the angle conventionally measured through the liquid where a liquid vapor interface meets a solid surface. You can see here we have a drop of liquid and the vapor this is the vapor and the drop of liquid and this is the solid surface. This contact angle quantifies the wettability of a solid surface by a liquid via the Young equation. Young equation is written here. We have the solid surface tension, liquid surface tension, solid and liquid boundary. All these factors are considered in this Young equation. Now you can see this angle theta. Angle theta formed by the solid surface and tangent of the droplet tangent of the droplet is called the contact angle. Now this contact angle is used as an indicator of wettability and has been adopted widely in industrial fields as an evaluation method of surface. By measuring this contact angle we can say what is the wettability between a liquid and a solid surface. You can see here in this case this is the tangent theta angle theta is greater than 90 degree. This is angle theta so which is greater than 90 degree. If there is large angle then it is difficult to wet that means the wettability is very poor. If the angle is less than 90 degree it indicates that wettability is very easy. Now the low contact angle values indicate that the liquid spreads on the surface while high contact angle values show poor spreading. If the contact angle is less than 90 degree the liquid wets the surface. Zero contact angle represents complete wetting. If the angle is greater than 90 degree the surface is set to be non wetting with that liquid. Now we can see here some images wherein we have a fabric cloth treated with hydrophobic agent. So on this a drop of liquid is placed. Now you can see a very large contact angle which indicates that wettability is very poor. And we have a lotus leaf on which a water drop is placed. Again you can see very large contact angle of about 147 degrees. So this image shows the image taken from a video contact angle device. So water drop on glass plate with the reflection below. So the contact angle is less so wettability is good. Now how do we measure this contact angle? So a contact angle goniometer is used to measure the contact angles. A few setups are shown here and a schematic diagram is shown here. High resolution CCD camera is used and there is a light source and there is a stage on which the dosing a drop of liquid is placed by using this dosing system. And then the image is taken and then the software is used to get the contact angle. So this contact angle is very important in the case of making of composite material wherein the liquid phase for example polymer matrix is used with the fibers of different maybe glass fibers or carbon fibers. In that case we should know whether wettability is good or not. So in such cases the contact angles are measured. Now other important devices used or angle gauges this photograph shows a set of 16 angle gauge blocks. This set forms all angles between 0 degree to 99 degree in one second step. A total of 356400 combinations. So in a step of one second we can build the angles between this range 0 to 99 degrees. Different grades of angle gauges are available. Laboratory master grade to an accuracy of 1 fourth second is available. The inspection grade angle gauges are available with an accuracy of half second and then tool room grade angle gauges are available with one second accuracy. So whenever we want to calibrate other device angle measurement devices we use these laboratory master grades for calibration of angle measuring devices. Now we can see here this table shows a set of 14 piece set. We have a set of 5 pieces of 1 degree, 3 degree, 9 degree, 27 degree and 41 degree and under minutes category we have 1 minute gauge, 3 minute gauge, 9 minute gauge and 27 minute gauge and then under seconds we have 3 seconds gauge, 6 seconds gauge, 18 seconds gauge and 30 seconds gauge. In addition to these pieces we have another square block. Now how do we build the angles using these angle gauges? You can see here in the previous picture we saw we have this mark which indicates that this side is having smaller width and the other side is having larger width. When we keep the angle gauges in this fashion wherein the mark is like this then the angle between this surface and this surface is totally it is 27 degree plus 41 degree so we get 68 degrees. When they are placed in the opposite sides like this then we have to subtract 27 degree from 41 degree. So total angle between this surface and this surface is 14 degrees. So like this we can build the angles. So we have a workpiece with an angle of 120 degree. So how do we check this workpiece, this V gauge? So you can see here we can use angle gauges we have used a 90 square plate and then a 27 degree gauge and then 3 degree gauge. So totally it becomes 120 degree. So this is this combination is used to check whether the angle on the workpiece is proper is okay or not. Now let us take a simple numerical example. Build an angle of 40 degrees 13 minutes and 15 seconds using a set of 13 pieces. These are the angle gauges provided. So we have to build 40 degrees. You can see here we have to take this 41 degree gauge block and then 1 degree gauge block and then we have to arrange like this. So this is 41 degree and then we have to subtract 1 degree from this. So this is 1 degree. So totally this angle becomes 40 degrees. So this is a combination A. So next we have to build an angle of 13 minutes. So to build 13 minutes we can select this 9 minute gauge block, 3 minute gauge block and 1 minute gauge block. So totally if we assemble them it becomes 13 minutes. So this is 9 minute and then we have to take 3 minutes, 3 minutes and then 1 minute. So totally this angle is 13 minutes, 13 minutes. So this is a combination B and then we have to build 15 seconds. For that we can select 18 seconds gauge and 3 seconds gauge and we have to assemble them. So this is 18 seconds and then we have to subtract 3 seconds from this. So this angle becomes 15 seconds. So this is combination. Then finally we have to add all these combinations A, B, C. So this is a combination A with 2 gauges, gauge blocks and then we have combination B with 3 gauge blocks and we have another combination C with 2 gauge blocks. So totally this angle is 40 degrees, 40 degrees, 13 minutes, 15 seconds, 15 seconds. So like this we can build the angles. Now let us move to the another instrument spirit level which is mostly used for measurement of tilt of surfaces. This is a device consisting of a sealed glass tube partially filled with alcohol or other liquid containing an air bubble whose position reveals whether a surface is perfectly leveled. It is used to check the level of plane table by placing it on the board in two positions at right angles to each other. When the bubble remains in the center at any point on the table then table is considered to be properly leveled. So different configurations of spirit level are available. This is a flat base level. This is the glass tube which is partially filled with alcohol. There will be a bubble here. You can see the base is flat and we have a weak groove in the base. So you can see the side view. We have a 120 degree weak groove and the inside there is a glass tube and there is sometimes a cross level is also provided and this is a square block level again with 120 degree v on the base. Now the glass tube has a slight upward curve. We can see in this photograph the slight upward curve so that the bubble naturally rests in the center. When the base is properly placed on a properly leveled surface the bubble will be at the center which is the highest point. At slight inclinations the bubble travels away from the marked center, marked center position to indicate what is the level. Now this is the glass tube with markings and at the center we have a bubble and this is a cross sectional view of the spirit level. This is the glass tube filled with spirit and there is a bubble which is this tube is placed in a frame and this is the base and this curvature is r. Now what is the relationship between the tilt angle theta? You can see here we have a tilt angle theta bubble movement. So this is when the surface is perfectly leveled bubble will be at the center A. When there is a slight inclination tilt of theta then bubble moves from A to A1 and we have radius r the radius of curvature r height h of one end of the base above the other end. Now you can see here B end it has raised by h with respect to the other end O and base length L. Now what is the relationship? If the length is one L is one meter and if the one end rises by an amount of say 0.02 millimeter then bubble will move by one graduation. That means if bubble moves from A to A1 it indicates that the end B has raised by an amount of 0.02 millimeter. Now this photo shows a commercially available spirit level and there is a this is the pivot and there is a provision for adjustment and this is the glass tube and we can also see the bubble and then the graduations are also visible. Now let us study about do-tile check. In most of the machine tools do-tiles are used the do-tiles they look like this. Now this we have rollers or balls of same diameter kept in position like this and we can take the measurement over rollers or balls. So this will be m. So this is m. So m is measurement over balls or rollers and then this is B width of top surface and this is h that is depth. H is the depth and this is angle alpha. This angle is alpha and D is diameter of the ball. D is diameter of the ball. Now by knowing any four out of these five parameters B, M, D, H, alpha if you know any four parameters the other unknown can be calculated using this relationship. Now let us conduct an experiment to check do-tile. Now you can see here we have a do-tile here of milling machine. We have kept a ball of known diameter. On the other side also we have kept another ball of same diameter. Now we are measuring the m measurement over balls using the Vernier caliper. Now you can see here we have kept another ball here and we are measuring the distance over the two balls. You can see the measurement it is 242 millimeter and then we have to see the coinciding division that is the 630 into 0.0. 242 plus we have to add the Vernier scale reading. Now we can take the reading 242 millimeter and then 6th division it is coinciding with the main scale reading. Now we are taking the measurement over the top surface that is B. You can see the reading so it is 195 plus we have to see the coinciding division that is 25th division is coinciding with the main scale marking. Now I can see we are measuring the depth h we are measuring the depth h it is 22 millimeter. Now we are measuring the diameter of steel ball. Now the measured values can be fed into these this equation and unknown value can be determined. Now we have completed the first part of module 8 that is angle measurement tilt measurement and taper measurement. Now we will move to the next part that is radius measurement. So for measuring the radius of a component the most commonly used instrument is radius gauge. This is also known as fillet gauge which is used to measure the radius of an object. Radius gauges require a bright light behind the object to be measured. The gauge is placed against the edge to be checked and any light leakage between the gauge and edge indicates a mismatch that requires correction. A good set of gauges will offer both convex and concave gauges and allow for their application in acquired locations. Every leaf has different radius the material of the leaf is stainless steel it is of two types internal measurement leaf and external measure that is concave measurement and convex measurement is possible. It is used to check the radius of inner and outer surfaces. You can see here a set of radius gauges and here we have radius of different values this is 10 millimeter radius 10.25 10.5 10.75 like this the different leaves are commercially available and available ranges are like this 0.5 to 13 millimeter 26 leaves that is 0.5 to 13 mm in steps of 0.5 mm and from 1 to 7 millimeter 34 leaves 1 to 3 millimeter in steps of 0.25 millimeter 3.5 to 7 millimeter in steps of 0.5 millimeter and from 7.5 to 15 millimeter 32 leaves are available 7.5 to 15 mm in steps of 0.5 mm and then 15.5 to 25 mm totally 30 leaves will be available 15.5 mm to 20 mm in steps of 0.5 mm measurement is possible 21 to 25 mm in steps of 1 mm measurement is possible. Now let us conduct an experiment to learn how we can use radius gauge for measuring the radius. Now I can see radius gauge set I can see different leaves 1 mm 1.5 mm 2 mm 3 mm and here it is 6 mm that means the radius is 6 mm so the diameter will be 12 mm. So this is to check the concave radius and this portion can be used to check the convex radius 6.5 millimeter radius 6 millimeter 5.5 millimeter radius 4.5 millimeter radius 4 millimeter 3.5 7.5 8 so like this different leaves are available 11 millimeter 10.5 10 millimeter so leaves are available in steps of 0.5 11.5 12 12.5 and here holder is provided along with the set to hold the leaf. Now we have to keep the gauge radius gauge into the holder I can see how to use this radius gauge we have a threaded screw we want to measure the shank dia. Now I can see there is proper match between the surface of the screw thread and the gauge so the diameter is 12 millimeter. Now let us learn how to check the concave radius I can see there is a slot we want to check we want to measure what is the diameter now it is 7.5 it is properly matching with the contour. Now another most commonly used instrument for measurement of curvature of lens surface is a sparrow meter it is used for precise measurement of radius of a spear these instruments are used by opticians to measure the curvature of surface of lens the usual form consists of a fine screw moving in a nut carried on the center of a small three-legged table the feet forming the vertices of an equilateral triangle the lower end of the screw and those of the table legs are finely tapered that means the ends are conical so that each end rests on a point if the screw has 1 mm pitch and head scale that is dial is divided into 100 parts then the least count of the instrument is 0.01 millimeter a vertical scale phasen to the table indicates the number of old turns of the screw and serves as an index for reading the divisions on the head an electric contact arrangement may be attached to the sparrow meter in order to indicate the moment of touching that is when the screw just touches the surface of the lens or workpiece it indicates that there is a contact so otherwise we can simple method is we can always take a filler gauge or a piece of thin paper we should try to insert between the screw and the workpiece surface if it enters it indicates that there is a gap if it does not enter indicates that the screw is in contact with the workpiece surface now the construction of sparrow meter is like this this photograph shows that this is the central screw and three legs are there the screw is screw end is conical similarly all the three legs they have conical end this is the dial on which the markings are there and then there is a vertical scale to indicate how many rotations the screw has rotated the the three ends of the three legs form the vertices of an equilateral triangle the outer legs that means these legs outer legs of some sparrow meters can be moved to a set of inner holes in order to accommodate smaller surfaces as we can see here there is a central leg that is screw and there is a reading device for measuring the distance the central leg that is moved by what distance the central leg has moved the vertical scale is marked off in units of one millimeter this is the vertical scale one complete term of the dial corresponds to one millimeter and each small graduation on this dial that means this rotary scale represents 0.01 millimeter this parameter directly measures h using the mean length between the outer legs l the spherical radius r can be calculated by the formula r is equal to h by 2 plus l into l divided by 6 h so h is given by the sparrow meter so using this relationship we can find the radius radius of curvature now let us conduct an experiment to study how we can use a sparrow meter for measurement of radius of curvature you can see we have a lens the sparrow meter is placed on the lens whose radius of curvature is to be determined now we are measuring the concave portion of the lens I can see the screw end is in contact with the lens so that is so we can check whether the this point screw point is in contact with the workpiece surface whether it is making proper contact or not that we can check by insert by we have to try to insert a piece of paper if it enters it indicates that there is gap if it does not enter it indicates that there is no gap now we have to take the reading on the vertical scale as well as on the dial rotary scale so this gives the h I can see the dial is reading the 81 81 or 82 now we have to keep the sparrow meter on a plane paper and we have to press it to get the location of the legs three legs of the sparrow meter now we have to mark those three points and then we have to join all these three points and then we should get the lens of length l 1 length l 2 and length l 3 and finally we should calculate the average length l so again we are trying to find the length l where to measure l 1 l 2 l 3 and find the average now we can see we are measuring the radius of curvature of convex lens the screw should be withdrawn slightly and then the sparrow meter should be kept at the center screw end should be at the center three legs are in contact with the lens now we have to rotate the dial or screw so that it just touches the topmost point on the lens now we are rotating the screw screw is moving down now it is making contact with the surface of the lens now we have to note down the reading the dial reading as well as vertical scale reading yeah dial reading and then vertical scale reading we should note down by knowing h and l we can calculate the radius of curvature now the calculation of radius of curvature or calculation of radius of curvature for convex lens so we have observed that h that is vertical scale reading plus dial reading into least count is equal to vertical scale reading is one unit and then dial reading was 92 into least count is 0.01 mm so h is 1.92 millimeter and length average length that is distance between the tips of legs average distance is 45 millimeter then we have to feed these values in the equation and finally we get radius of curvature of 176.74 millimeter similarly for concave lens h was 2.83 millimeter and l was 45 millimeter so radius of curvature was 120.67 millimeter like this using the sparrow meter we can find radius of curvature now what are the other uses of sparrow meter so apart from measuring the radius of curvature this sparrow meter it can also be used to measure the thickness of thin plates thin metallic plates thin glass plates thickness can be measured the instrument is placed on a perfectly level plane surface and the screw turned until the point just touches the surface the dial and vertical scale are red and the screw is raised the thin plate is slipped under it and the process is repeated the difference between the two readings gives the required thickness the instrument can measure the depression in an otherwise flat plate the micrometer portion is placed over the depression and the measurement is taken below the surface instead of above to check the depression now let us move to another instrument cylinder meter see the sparrow meter is used to check the to measure the radius of curvature whereas the the cylinder meter is used to measure the radius of cylindrical surfaces it is a modified version of a sparrow meter the construction is shown here instead of three legs we have a totally four legs which are all the four legs are fixed to this base and this base has a vertical scale and at the center of the base we have a threaded screw and then circular dial on which markings are there so similar to the sparrow meter this instrument can be used to measure the radius of cylindrical surface that means we have to say this is the cylindrical surface we want to measure the cylindrical the radius in we have to keep this instrument on the surface and then the screw should be moved till it just touches the surface and then we have to take the readings vertical scale reading and then dial reading and then using the equation we can find the diameter of diameter radius of cylindrical surface now these are adjustable radius gauges this is outside gauge measure used to measure the convex workpieces radius of convex workpieces you can see here totally three points are there all the all these three points should be in contact with the workpiece and then we should move this slide when the central point just touches the workpiece the scale indicates what is the radius similarly this is the inside gauge the three points should be in contact with the concave surface and the scale directly gives what is the radius now how do we measure the radius of tool tip so this is a single point cutting tool and this is the principle cutting edge and axillary cutting edge and here there will be a small radius is provided so this radius we want to measure so for that we can use an optical tool radius measurement setup this is a microscope which has a table on which we have to keep the cutting tool and then throw the eyepiece we can get the image of the nose and using the scale provided we can get the reading or we can put a camera here and then amplified image we can have on the monitor and using the software we can measure the diameter or the radius of tool nose you can see here we have a carbide tip tool with some radius so using an optical microscope like this we can measure the radius and again radius on the tool insert so radius measurement range of such microscopes are 10 micrometer to 20 millimeter with an accuracy of plus or minus 200 nanometer so setting times quickly we can measure the radius setting time is about 3 to 5 seconds now the other instrument used to measure the radius is digital radius gauge you can see we have an indicator with a spindle and then with digital indicator and then we have a fixture with two points two legs so this fixture we have to insert on to the spindle and we should keep this digital radius gauge say this is the surface of the workpiece for the radius of this workpiece we want to measure this is the indicator digital indicator with the spindle and we have to mount this fixture the other two legs should be in contact now slowly we have to move this spindle or because the spring it moves down and it makes contact with the workpiece and then the indicator will indicate what is the radius so different fixtures are available different jaws are available so this tells outside or inside arc radius automatically no calculation is needed directly it gives what is the value this can also be used to check depth or thickness of objects range of such instrument is 5 to 1000 millimeter with the resolution of 0.005 millimeter so five measuring jaws are provided with the size 10 millimeter 20 millimeter 30 millimeter 60 millimeter and 100 millimeter this gap is 100 millimeter and then we can use profile projector for measuring the radius so we have to select appropriate function functional key the data processor say we want to measure this radius so we have to feed three data points and then the data processor will calculate and it will tell what is the radius is a very quick method of measuring the radius so for measuring the diameter we have to feed three points so it will give the diameter half of that will give the radius let us summarize this session so in this lecture we discussed about the contact angle measurement and use of spirit level for measurement of angles tilts also we learnt about how to use auto collimator for measurement of tilt and then we discussed about measurement of radius what are the various instruments used for the measurement of radius instruments like spirometers radius gauges distal radius indicator and how to use profile projector for measurement of radius so these things we discussed we will conclude this session thank you