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Angular measurements
This document discusses various instruments used to measure angles: - Protractors, bevel protractors, vernier bevel protractors, and optical bevel protractors are used to measure angles between two faces. Vernier bevel protractors provide more precise readings through a vernier scale. - Sine bars and sine centers are used with slip gauges to measure angles through trigonometric functions. Sine bars become inaccurate for angles over 45 degrees. - Angle gauges precisely measure angles through calibrated blocks that can be added or subtracted. - Spirit levels and clinometers measure angles of incline relative to horizontal, with clinometers providing a scale to measure the exact
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Overview of angles, measurement units, degrees, minutes, and radians.
Introduction to various angular measuring devices like protractors and bevel protractors.
Detailed discussion on the Vernier bevel protractor, its markings, and measurement techniques.
Sine bars as precision instruments for angle measurement, their advantages, and limitations.
Description and utility of sine centers for testing conical workpieces.
Construction of angle gauges, their features, and how they can be combined for precise measurement.
Introduction to spirit levels and clinometers, their applications, construction, and measurement capabilities.Summary of all angular measurement instruments introduced in the chapter.
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Angular measurements
- 1. CHAPTER Angular Measurement Presentation Preparedby Prof. Naman M. Dave Assistant Prof. (Mechanical Dept.) Gandhinagar Institute of Technology
- 2. Please refer thisfile just as reference material. More concentration should on class room work and text book methodology.
- 3. Introduction • The angleis defined as the opening between two lines which meet at a point. • Circle is divided into 360 parts, each part is called a degree ( º). • Each degree is divided in 60 minutes ( ') and each minute into 60 Seconds ( “) • Unit of angle derived from theoretical considerations is the radian, defined as the angle subtended at the centre of a circle by an are length equal to radius of circle. The general formula for converting from degrees to radians is to simply multiply the number of degree by Π /180°. The general formula for converting from radians to degrees to simply multiply the number of degree by 180°/(Π)
- 4. Angle Measurement Instrument Line Standard Angular Measuring Devices • Protractors • Universal Bevel Protractors Face Standard Angular Measuring Devices • Sine bar • Sine Center Measurement of Inclines • Spirit Level • Clinometer Angle Comparators • Autocollimators
- 5. Vernier Bevel protractor •The simplest instrument for measuring the angle between two faces of component. • Main scale on the protractor is divided into degrees from 0 to 90 each way.
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- 10. Measuring Acute Angles MeasuringObtuse Angles
- 11. Vernier Bevel protractor •These are marked 0-60 minutes of arc, so that each division equals 1/12 of 60, that is 5 minutes of arc. • These 12 divisions occupy the same space as 23 degrees on the main scale. Therefore, each division of the Vernier is equal to • As shown in the main scale is graduated in degrees of arc. • The Vernier scale has 12 Divisions each side of the centre zero.
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- 16. Optical bevel protractor •A circle divided at 1.0 minutes intervals throughout the circle is fitted inside the body. • Small microscope is fitted through which the circle graduations can be viewed. • Adjustable blade is clamped to a rotating member which carries its microscope.
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- 20. Sine bars • Aprecision angle measuring instrument used along with slip gauges
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- 22. Sine bars The sinebars inherently become increasingly impractical and inaccurate as the angle exceeds 45° because of following reasons : — The sine bar is physically clumsy to hold in position. — The body of the sine bar obstructs the gauge block stack, even if relieved. — Slight errors of the sine bar cause large angular errors. — Long gauge stacks are not nearly as accurate as shorter gauge blocks. — A difference in deformation occurs at the point of roller contact to the support surface and to the gauge blocks, because at higher angles, the weight load is shifted more toward the fulcrum roller. — The size of gauges, instruments or parts that a sine bar can inspect is limited, since it is not designed to support large or heavy objects.
- 23. Sine bars • Heightover the rollers can be measured by a vernier height gauge; using a dial test gauge mounted on the anvil of height gauge to ensure constant measuring pressure. • This is achieved by adjusting the height gauge until the dial gauge shows the same zero reading each time Sine bars
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- 25. Sine bars • Advantagesof sine bar 1. It is precise and accurate angle measuring device. 2. It is simple in design and construction. 3. It is easily available • Disadvantages 1. It is fairly reliable at angles less than 15 but become increasingly inaccurate as the angle increases. It is impractical to use sine bar for angle above 45 . 2. It is difficult to handle and position the slip gauges. 3. The sine bar is physically clumsy to hold in position. 4. The application is limited for a fixed center distance between two rollers. 5. Slight errors of the sine bar cause larger angular errors.
- 26. Sine Centre • Sinecenter is basically a sine bar with block holding centers which can be adjusted and rigidly clamped in any position. used for the testing of conical work, centered at each end as shown. • Extremely useful since the alignment accuracy of the centers ensures that the correct line of measurement is made along the workpiece. • The centers can also be adjusted depending on the length of the conical work piece, to be hold between centers.
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- 28. Angle Gauge • Anglegauges are made of hardened steel and seasoned carefully to ensure permanence of angular accuracy, and the measuring faces are lapped and polished to a high degree of accuracy and flatness like slip gauges.
- 29. Angle Gauge • Likelinear gauge blocks, angle gauge blocks can also be wrung together to build up a desired angle. • In addition, they can also be subtracted to form a smaller angle as a difference of two larger angles as shown in Figure. • The plus and minus ends of each block are marked.
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- 32. Spirit Level low viscosityfluids the vial is graduated in linear units
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- 35. Clinometers The clinometersis a special case of the application of the spirit level. It is an instrument used for measuring angle relative to the horizontal plane. • A circular scale is provided on the housing. A circular scale is used to measure the angle of inclination of the rotary member relative to the base. • The scale may cover the whole circle or only part of it. • The base of the instrument is placed on the surface and rotary member is adjusted till zero reading of the bubble is obtained as shown in Fig. • The angle of rotation is then noted on the circular scale against an index. • It consists of a spirit level mounted on a rotary member carried in a housing. • One face of the housing forms the base of the instrument.
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- 38. Clinometers • Micrometerclinometers is shown in Fig. In this type, one end of spirit level is attached at end of the barrel of a micrometer • The other end of the spirit level is hinged on the base. The base is placed on the surface whose inclination is to be measured. • The micrometer is adjusted till the level is horizontal. This type of clinometers is suitable for measuring small angles. • The most commonly used clinometers is of the Hilger and Walts type in which circular, scale is totally enclosed and is divided from 0 to 360 at l0' interval. For observation of 10‘-subdivision optical micrometer is provided..
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- 41. Protractor Bevelprotractor Vernier bevel protractor Optical bevel protractor Combination set…. Sine bar Sine centre Angle gauge Spirit level Clinometers CHAPTER Angular Measurement
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