Mathematics
Linear Measure and Precision
Linear measure refers to the measurement of length, typically using units such as meters or centimeters. Precision in linear measure refers to the degree of exactness or accuracy in the measurement. It is important to consider precision when making measurements, as it can impact the reliability and usefulness of the data collected.
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7 Key excerpts on "Linear Measure and Precision"
eBook - PDF- John Peterson, Robert Smith(Authors)
- 2019(Publication Date)
- Cengage Learning EMEA(Publisher)
178 SECTION 3 LINEAR MEASUREMENT: CUSTOMARY (ENGLISH) AND METRIC OBJECTIVES After studying this unit you should be able to ● ● Determine the degree of precision of any given number. ● ● Compute the greatest possible error of customary and metric length units. ● ● Compute absolute error and relative error. Degree of Precision, Greatest Possible Error, Absolute Error, and Relative Error DEGREE OF PRECISION The cost of producing a part increases with the degree of precision called for; therefore, no greater degree of precision than is actually required should be specified on a drawing. The degree of precision specified for a particular machining operation dictates the type of machine, the machine setup, and the measuring instrument used for that operation. The exact length of an object cannot be measured. All measurements are approxima-tions. By increasing the number of graduations on a measuring instrument, the degree of precision is increased. Increasing the number of graduations enables the user to get closer to the exact length. The precision of a measurement depends on the measuring instrument used. The degree of precision of a measuring instrument depends on the smallest graduated unit of the instrument. No measurement is truly correct, but some are more precise than others. Depending on the need for precision in a measurement, you might measure one object with a tape mea-sure and something else with a micrometer, a caliper, or a dial bore gage. As a general rule, a measuring instrument should measure to a degree 10 times finer than the smallest unit it will be used to measure. Machinists often work to 0.001-inch or 0.02-millimeter precision. In the manufacture of certain products, very precise measurements to 0.00001 inch or 0.0003 millimeter and 0.000001 inch or 0.00003 millimeter are sometimes required. Various measuring instruments have different limitations on the degree of precision possible. There is always some “rounding” involved in measuring.
eBook - ePub- Roger Timings(Author)
- 2007(Publication Date)
- CRC Press(Publisher)
6 Measuring When you have read this chapter you should understand: • What is meant by linear measurement. • How to make linear measurements. • What is meant by angular measurement. • How to make angular measurements. • The factors affecting accuracy of measurement. • The terminology of measurement. • The general rules for accurate measurement. • How to measure workpieces having square, rectangular, circular and irregular-shaped sections. 6.1 Introduction Measuring can be considered to be the most important process in engineering. Without the ability to measure accurately, we cannot: • Mark out components as described in Chapter 7. • Set up machines correctly to produce components to the required size and shape. • Check components whilst we are making them to ensure that they finally end up the correct size and shape. • Inspect finished components to make sure that they have been correctly manufactured. 6.2 Linear measurement When you measure length, you measure the shortest distance in a straight line between two points, lines or faces. It doesn't matter what you call this distance (width, thickness, height, breadth, depth or diameter) it is still a measurement of length. There are two systems for the measurement of length, the end system of measurement and the line system of measurement. The end system of measurement refers to the measurement of distance between two faces of a component, whilst the line system of measurement refers to the measurement of the distance between two lines or marks on a surface. No matter what system is used, measurement of length is the comparison of the size of a component or a feature of a component and a known standard of length. In a workshop this may be a steel rule or a micrometer caliper, for example
eBook - PDF- Karl Smith(Author)
- 2016(Publication Date)
- Cengage Learning EMEA(Publisher)
For example, the measurement might be to the nearest inch, nearest foot, or nearest mile. The precision of a measurement depends not only on the instrument used but also on the purpose of your measurement. For example, if you are measuring the size of a 7 ft by 12 ft room to lay carpet, the precision of your measurement might be different than if you are measuring the size of an airport hangar. The accuracy refers to your answer. Suppose that you measure with an instrument that measures to the nearest tenth of a unit. You find one measurement to be 4.6 and another measurement to be 2.1. If, in the process of your work, you need to multiply these numbers, the result you obtain is 4.6 3 2.1 5 9.66 This product is calculated to two decimal places, but it does not seem quite right that you obtain an answer that is more accurate (two decimal places) than the instrument you are using to make your measurements (one decimal place). Figure 8.1 compares and con-trasts the ideas of precision and accuracy. Accurate Inaccurate Precise Imprecise FIGURE 8.1 Precision and accuracy In this text, we will require that the accuracy of your answers not exceed the preci-sion of the measurement. This means that after the calculations are completed, the final answer should be rounded. The principle we will use is stated in the following box. All measurements are as precise as given in the text. If you are asked to make a measurement, the precision will be specified. Step 1 Carry out all calculations without rounding. Step 2 After you obtain a final answer, round this answer to be as accurate as the least precise measurement. Step 3 If you are working with money, round your final answer to the nearest cent. Accuracy Procedure Used in This Text Spend a few moments thinking about the ideas of precision and accuracy. The answers we give will conform to this procedure. Copyright 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.
eBook - PDF- Connie Dotson(Author)
- 2015(Publication Date)
- Cengage Learning EMEA(Publisher)
Accuracy, precision, and reliability exist in dif-ferent time frames. If a steel cylinder is a precise part or an accurate part, we know that historically it measures within a range of permissible sizes. If it is reliable, we expect it to perform a certain way in the future. Reliability can refer to the manufacturing or in-spection process or to the part’s expected future per-formance. As we have seen in other areas, it is vital that all parties involved understand exactly what was measured when reporting on reliability. For example, we might speak of an accurately inspected cylinder, a reliably designed cylinder, a cylinder with a precision tolerance, and so forth. Precision answers the question how much? It pro-vides fineness for the range of sizes allowable for one part or many parts, or it defines the fineness to which an instrument can read. Precision may be vague— high FIGURE 2–11 A change in one variable, such as wind, alters the results as shown. Does this show which shooting was most reliable? Shooter: Score: A 3 B 0 C Target Analogy Change of One Variable 8 D 4 E 10 Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 22 Fundamentals of Dimensional Metrology length standards, for example, to answer this vital question. As we created cities and governments, we needed better refined standards for manufacturing and bartering with other cultures. After all, not ev-eryone’s forearm, for example, is the same length. The ruler of a certain city or state would usually eliminate conflict by choosing his own body parts as the standards.
eBook - PDF- John Peterson, Robert Smith(Authors)
- 2018(Publication Date)
- Cengage Learning EMEA(Publisher)
Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 312 OBJECTIVES After studying this unit you should be able to ■ express lengths as smaller or larger metric linear numbers. ■ perform arithmetic operations with metric linear units. ■ select appropriate linear metric units in various applications. ■ express given metric length, area, and volume measures in larger and smaller units. ■ express given metric capacity and weight units as larger and smaller units. ■ solve practical applied metric length, area, volume, capacity, and weight problems. ■ express metric compound unit measures as equivalent compound unit measures. ■ solve practical applied compound unit measures. ■ convert between customary measures and metric measures. The International System of Units, called the SI metric system, is the primary mea-surement system used by all countries except the United States, Liberia, and Myanmar (Burma). In the United States, the customary units tend to be used in areas such as construction, real estate transactions, and retail trade. Other areas, such as automotive maintenance, nursing, other health care areas, and biotechnology, use the metric system. Linear Measure A linear measurement is a means of expressing the distance between two points; it is the measurement of lengths. Most occupations require the ability to compute linear mea-surements and to make direct length measurements. A drafter computes length measurements when drawing a machined part or an ar-chitectural floor plan, an electrician determines the amount of cable required for a job, a welder calculates the length of material needed for a weldment, a printer “figures” the number of pieces that can be cut from a sheet of stock, a carpenter calculates the total length of baseboard required for a building, and an automobile technician computes the amount of metal to be removed for a cylinder re-bore.
eBook - PDFMechanotechnics N4 Student's Book
TVET FIRST
- R Cameron(Author)
- 2021(Publication Date)
- Macmillan(Publisher)
4 Module 71 Precision measurement TVET FIRST Precision measurement Overview of Module 4 In mass production, large numbers of components are produced every day by different kinds of machines. Each component must be produced to precise specifications. Some components are manufactured in different countries and must then be assembled together. If they are not made to specification, they will not fit. Metrology (the science of measurement) plays an important role in making sure that machinery is properly set up and aligned. Metrology is also an important part of the inspection of completed components. Measurements of length, squareness (also known as angularity), surface finish, concentricity, straightness and flatness are important aspects of manufacturing. In this module, you will learn about precision measuring instruments and do calculations on precision measuring. Starter activity Discuss the following in class: 1. How are internal angles measured? 2. How big is a micron? 3. Is a precise metal ruler an accurate measuring instrument? Explain your answer. Figure 4.1: Using a probe to measure the dimensions of a component Precision measurement Precision measuring instruments ● Vernier caliper ● Vernier protractor ● Micrometer ● Clock gauge ● Optical projector ● Coordinate measuring machine ● Slip gauge Trigonometric ratios used to determine dimensions of machined parts 1. Basic principles of precision measurement 2. Determining tapers using balls and rollers Dimensions of tapers Using balls and rollers to measure tapers Principles that apply when solving problems using balls or rollers Using balls to determine (through calculation) the included angle of a taper Using rollers to determine the angle of the dovetail Construction of a sine bar General application of a sine bar Testing a taper plug gauge with a sine bar Sine centres Sine bar calculations 5.
eBook - ePub- Douglas K. Brumbaugh, Peggy L. Moch, MaryE Wilkinson(Authors)
- 2004(Publication Date)
- Routledge(Publisher)
5 Measurement Focal Points- Terminology
- Attributes
- Systems
- Units, Tools (instruments), and Precision Linear Measure Area Volume Capacity Weight Time Money Temperature Angle Measure Dimensional Analysis
What is the first thing that comes to your mind when you hear the word “measurement”? Do you think about how many gallons of gasoline you had to buy yesterday, how many miles you must travel to get to class, how many minutes you will be in class, how many dollars will be in your next paycheck, how many ounces of potato chips are in a bag, how warm it will be today, or even how many square yards of carpet you had to buy to cover your bedroom floor? Perhaps you considered one or more of these without thinking of the word “measurement.”Measures are important in our world and we are so comfortable with the concepts that we often accept and understand the information without much thought. Have you ever considered how much the gasoline in your tank weighs, how many times your left front tire revolves as you drive to class, how many seconds you spend in class, what your net salary per hour is, or how temperature is related to humidity? These are all valid measures, you just don’t think of them as relevant to your daily life.The measurement concepts that are so familiar to us have developed over many years. Primitive people used rudimentary methods to measure distances for their foraging or hunting boundaries, but there were no standard units. Figure 5.1 represents ancient Egyptians, who lived along the Nile River and used standard linear measures and elaborate survey methods to mark and remark their crop boundaries as the river flooded and receded, taking and restoring cropland. The Babylonians looked to the stars to measure the length of a year; their calculations were surprisingly accurate and their methods of astronomical observations are the basis for calculations today.TerminologyFig. 5.1Many early measurement techniques were based on human anatomy, as shown in Fig. 5.2
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