data presentation system in mechatronics

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Explain the significance of the following terms taken from the specifications of display systems. (a) Recorder: dead band $\pm 0.2 \%$ of span. (b) The hard disk has two disks with four read/write heads, one for each surface of the disks. Each surface has 614 tracks and each track 32 sectors. (c) Data logger: number of inputs 100 , cross-talk on any one input $0.01 \%$ of full-scale input. (d) Double-beam oscilloscope: vertical deflection with two identical channels, bandwidth d.c. to $15 \mathrm{MHz}$, deflection factor of $10 \mathrm{mV} / \mathrm{div}$ to $20 \mathrm{~V} / \mathrm{div}$ in 11 calibrated steps, time base of $0.5 \mu \mathrm{s} /$ div to $0.5 \mathrm{~s} /$ div in 19 calibrated steps.

Explain the problems of loading when a measurement system is being assembled from a sensor, signal conditioner and display.

Suggest a display unit that could be used to give: (a) a permanent record of the output from a thermocouple; (b) a display which enables the oil pressure in a system to be observed; (c) a record to be kept of the digital output from a microprocessor; (d) the transient voltages resulting from monitoring of the loads on an aircraft during simulated wind turbulence.

A cylindrical load cell, of the form shown in Figure 2.32, has four strain gauges attached to its surface. Two of the gauges are in the circumferential direction and two in the longitudinal axis direction. When the cylinder is subject to a compressive load, the axial gauges will be in compression while the circumferential ones will be in tension. If the material of the cylinder has a cross-sectional area $A$ and an elastic modulus $E$, then a force $F$ acting on the cylinder will give a strain acting on the axial gauges of $-F / A E$ and on the circumferential gauges of $+\nu F / A E$, where $\nu$ is Poisson's ratio for the material. Design a complete measurement system, using load cells, which could be used to monitor the mass of water in a tank. The tank itself has a mass of $20 \mathrm{~kg}$ and the water when at the required level $40 \mathrm{~kg}$. The mass is to be monitored to an accuracy of $\pm 0.5 \mathrm{~kg}$. The strain gauges have a gauge factor of 2.1 and are all of the same resistance of $120.0 \Omega$. For all other items, specify what your design requires. If you use mild steel for the load cell material, then the tensile modulus may be taken as $210 \mathrm{GPa}$ and Poisson's ratio 0.30.

Design a complete measurement system involving the use of a thermocouple to determine the temperature of the water in a boiler and give a visual indication on a meter. The temperature will be in the range 0 to $100^{\circ} \mathrm{C}$ and is required to an accuracy of $\pm 1 \%$ of full-scale reading. Specify the materials to be used for the thermocouple and all other items necessary. In advocating your design you must consider the problems of cold junction and non-linearity. You will probably need to consult thermocouple tables. The following data is taken from such tables, the cold junction being at $0^{\circ} \mathrm{C}$, and may be used as a guide: TABLE CAN'T COPY.

Design a measurement system which could be used to monitor the temperatures, of the order of $100^{\circ} \mathrm{C}$, in positions scattered over a number of points in a plant and present the results on a control panel.

A suggested design for the measurement of liquid level in a vessel involves a float which in its vertical motion bends a cantilever. The degree of bending of the cantilever is then taken as a measure of the liquid level. When a force $F$ is applied to the free end of a cantilever of length $L$, the strain on its surface a distance $x$ from the clamped end is given by $$ \text { strain }=\frac{6(L-x)}{w t^2 E} $$ where $w$ is the width of the cantilever, $t$ its thickness and $E$ the elastic modulus of the material. Strain gauges are to be used to monitor the bending of the cantilever with two strain gauges being attached longitudinally to the upper surface and two longitudinally to the lower surface. The gauges are then to be incorporated into a four-gauge Wheatstone bridge and the output voltage, after possible amplification, then taken as a measure of the liquid level. Determine the specifications required for the components of this system if there is to be an output of $10 \mathrm{mV}$ per $10 \mathrm{~cm}$ change in level.

Design a static pressure measurement system based on a sensor involving a $40 \mathrm{~mm}$ diameter diaphragm across which there is to be a maximum pressure difference of $500 \mathrm{MPa}$. For a diaphragm where the central deflection $y$ is much smaller than the thickness $t$ of the diaphragm, $$ y \approx \frac{3 r^2 P\left(1-\nu^2\right)}{16 E t^3} $$ where $r$ is the radius of the diaphragm, $P$ the pressure difference, $E$ the modulus of elasticity and $\nu$ Poisson's ratio. Explain how the deflection $y$ will be converted into a signal that can be displayed on a meter.

Suggest the elements that might be considered for the measurement systems to be used to: (a) Monitor the pressure in an air pressure line and present the result on a dial, no great accuracy being required. (b) Monitor continuously and record the temperature of a room with an accuracy of $\pm 1^{\circ} \mathrm{C}$. (c) Monitor the weight of lorries passing over a weighing platform. (d) Monitor the angular speed of rotation of a shaft.

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Part of the book series: Synthesis Lectures on Engineering, Science, and Technology ((SLEST))

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The chapter presents the interdisciplinary principles of mechatronics. It highlights the key role of sensors and actuators and illustrates mechatronics engineering with prominent examples, including automobile and smartphone mechatronics, CD-players and printers, robots and wind energy turbines. The miniaturization of mechatronic systems is described with micro electro-mechanical systems (MEMS), nanoscale mechatronics is exemplified with atomic force microscopy.

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Alciatore, D.G., Histand, M.B.: Introduction to Mechatronics and Measurement Systems. McGraw-Hill, International Edition of Higher Education, Boston (2003)

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Czichos, H.: Mechatronik—Grundlagen und Anwendungen technischer Systeme. Textbook on Mechatronics. Springer, Heidelberg, Berlin (2019) (in German)

Czichos, H.: Measurement, Testing ads Sensor Technology. Springer, Berlin (2018)

Daum, W.: Embedded sensors. In: Czichos, H. (ed.) Handbook of Technical Diagnostics. Springer, Berlin (2011)

Isermann, R.: Mechatronic Systems—Fundamentals. Springer, Berlin (2003)

Siciliano, B., Khatib, O. (eds.): Springer Handbook of Robotics. Springer, Berlin (2016)

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Czichos, H. (2022). Mechatronic Systems. In: Introduction to Systems Thinking and Interdisciplinary Engineering . Synthesis Lectures on Engineering, Science, and Technology. Springer, Cham. https://doi.org/10.1007/978-3-031-18239-6_4

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• Intro Video
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Medical Mechatronics for Healthcare

Yi-hung liu.

1 Department of Mechanical Engineering, National Taipei University of Technology, Taipei, Taiwan

David Moratal

2 Department of Electronics Engineering, Universitat Politècnica de València, Valencia, Spain

Javier Escudero

3 School of Engineering, Institute for Digital Communications, University of Edinburgh, Edinburgh, UK

Han-Pang Huang

4 Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan

1. Introduction

Advances in the healthcare technology have positioned biomedical technology as a major driver in global knowledge-based economies. A successful healthcare intervention depends on not only the capability or experience of clinicians but also the adequacy of medical instruments and assistive devices. In addition, the technical aids and assistive devices for elderly or people with severe motor disability are getting more attention due to our aging society all over the world, and they are widely used in daily life. As a result, medical mechatronics becomes an important emerging technology to improve healthcare. Medical mechatronics is the integration of technologies and knowledge from various domains [ 1 ], including biosignal sensing fusion, real-time clinical data analysis, electric and mechanical system design, assistive/rehabilitation robot development, and machine/deep learning algorithms. Although medical mechatronics has proven to be successful in healthcare applications, there still remain difficulties and challenges to overcome. For example, most previous assistive devices/robots were developed to provide patients with rehabilitation training in hospitals. With the rapid growth of aging population, these assistive devices are required to have smaller size and cheaper production cost and be safer in order to meet the requirement of in-house rehabilitation [ 2 ]. As a result, the medical mechatronic components in these assistive devices/robots need to be redesigned.

The goal of this special issue is to bring together the researchers in these fields and present high-quality research on recent developments on medical mechatronics and novel applications of medical mechatronics in healthcare, as well as the relevant prospect on opportunities and challenges. The selected eleven papers underwent a rigorous refereeing and revision process. Most of the studies were carried out on clinical data, which provides the results reported in this special issue a high confidence level. Moreover, most of the papers in this special issue include mechatronics and healthcare experts as coauthors, which is beneficial to open new methods and issues to medical experts in this multidisciplinary field.

2. The Special Issue

Stroke is a leading cause of long-term disability, and virtual reality- (VR-) based stroke rehabilitation is effective in increasing motivation and the functional performance in people with stroke. Although much of the functional reach and grasp capabilities of the upper extremities is regained, the pinch movement remains impaired following stroke. In the study by S.-C. Yeh et al., a haptic-enhanced VR system is proposed to simulate haptic pinch tasks in order to assist in long-term poststroke recovery of upper extremity fine motor function. Their results also suggest that this system is also effective under certain challenging conditions such as being in the chronic stroke phase or a coside of lesion and dominant hand (nondominant hand impaired).

In addition to VR-assisted rehabilitation, rehabilitation/mobile robot plays also a critical role in healthcare. This special issue collects a set of papers involving rehabilitation/healthcare robots. Ankle rehabilitation exercises act an important role in recovering walking ability of patients after stroke. Currently, patients mainly perform ankle exercise to reobtain range of motion (ROM) and strength of ankle joint under therapist assistance by manual operation. However, most of the rehabilitation devices focus on ankle functional training and ignore the importance of neurological rehabilitation in the early hemiplegic stage. Q. Liu et al. developed a novel robotic ankle rehabilitation platform to assist patients in executing ankle exercise. This robotic platform consists of two three-DOF symmetric layer-stacking mechanisms, which can execute ankle internal/external rotation, dorsiflexion/plantarflexion, and inversion/eversion exercises while the rotation center of the distal end of the robotic platform always coincides with patient's ankle pivot center. Y. Feng et al. proposed a new applicable and effective sitting/lying lower limb rehabilitation robot (LLR-Ro), which has a mechanical limit protection, an electrical limit protection, and a software protection to prevent the patient from being secondary damaged. As a new type of the rehabilitation robots, its hip joint rotation ranges are different in the patient sitting training posture and lying training posture. The mechanical leg of the robot has a variable workspace to work in both training postures. In addition, to eliminate accident interaction force between patients and LLR-Ro in the process of the passive training, an amendment impedance control strategy based on position control is also proposed to improve the compliance of the LLR-Ro. On the other hand, mobile robotics is a potential solution to home behavior monitoring for the elderly. For a mobile robot, there are several types of uncertainties for its perceptions, such as the ambiguity between a target object and the surrounding objects. The problem could be more serious for a home behavior monitoring system, which aims to accurately recognize the activity of a target person, in spite of these uncertainties. W. Yu et al. proposed a new strategy of active sensing, called active sensing with categorized further explorations. It detects irregularities and categorizes situations requiring further explorations, which strategically maximizes the information needed for activity recognition while minimizing the costs. Two schemes of active sensing, based on two irregularity detections, namely, heuristic-based and template-matching-based irregularity detection, were implemented and examined for body contour-based activity recognition. Their proposed approach can guide the robot system to sense the target person actively and achieve high accuracy of activity recognition.

Biceps brachii muscle illness is one of the common physical disabilities that requires rehabilitation exercises in order to build up the strength of the biceps brachii muscle after surgery. It is also important to monitor the condition of that muscle during the treatment or rehabilitation exercise. Electromyography (EMG) is one of the preferred methods for measuring and recording the activity of the biceps brachii muscle, and wavelet transform (WT) has been widely used as a temporal-spectral analysis method for monitoring EMG signals. However, WT parameter selection remains a challenging task. N. Burhan et al. analyzed and investigated the selection of the best mother wavelet (MWT) function and depth of the decomposition level in the wavelet denoising EMG signals of the biceps brachii muscle. The efficacy of the wavelet denoising signal was determined through an analysis of the activity of the biceps brachii muscle for vicenarians during the rehabilitation exercise.

Overnight polysomnography (PSG) is a standard diagnostic procedure for obstructive sleep apnea (OSA). However, there are no sensor systems to hook up with PSG for accurate head position monitoring available clinically. W.-Y. Lin et al. presented a CORDIC- (COordinate Rotation DIgital Computer-) based tilting sensing algorithm to quickly and accurately convert accelerometer raw data into the desired head position tilting angles. Their system can hook up with PSG devices for diagnosis to have head position information integrated with other PSG-monitored signals. It has been applied in an IRB test in Taipei Veterans General Hospital and been proved that it can meet the medical needs of accurate head position monitoring for PSG diagnosis. In addition to the head-posture monitoring during sleep, vibration condition monitoring is also a crucial factor in sleep study. H. Kimura et al. developed a new mechanical bed for inducing sleep to investigate the effects of different vibration conditions. The new bed has two active DOFs, vertical and horizontal directions, to examine the anisotropy of sensation. The bed includes three main parts: a vertical driver unit, horizontal driver unit, and unique 2-DOF counterweight system. Due to the new counterweight system, the required torque is extremely small and the driving sound is suppressed to less than 40 dB. Their results have suggested the ability of appropriate vibration to induce sleep.

C.-H. Kuo et al. proposed an oscillometric blood pressure (BP) measurement approach based on the active control schemes of cuff pressure. Compared with conventional electronic BP instruments, their proposed BP measurement approach is based on the utilization of a variable-volume chamber which can better actively and stably alter the cuff pressure during inflating or deflating cycles, because the variable-volume chamber could significantly eliminate the air turbulence disturbance during the air injection stage when compared to an air pump mechanism. C.-Y. Lin and P.-J. Hsieh developed an automatic dispensing system for Chinese herbal decoctions with the aim of reducing manpower costs and the risk of mistakes. They employed machine vision in conjunction with a robot manipulator to facilitate the grasping of ingredients. An offline least square curve fitting method was used to calculate the amount of material grasped by the claws and thereby improve system efficiency as well as the accuracy of individual dosages. Their experiments on the dispensing of actual ingredients have demonstrated the feasibility of their proposed system.

In the study of A. Chromy and O. Klima, a 3D scan model and thermal image data fusion algorithms are presented. At present, medical thermal imaging is still considered a mere qualitative tool enabling us to distinguish between but lacking the ability to quantify the physiological and nonphysiological states of the body. Such a capability would, however, facilitate solving the problem of medical quantification. Accordingly, they proposed a generally applicable method to enhance captured 3D spatial data carrying temperature-related information. Their method can be utilized for high-density point clouds or detailed meshes at a high resolution but is conveniently usable in large objects with sparse points. Also, the technique offers a wide application potential in medicine and multiple technological domains, including electrical and mechanical engineering.

Acknowledgments

The guest editors of this special issue would like to thank all authors of the submitted papers, as well as all reviewers for their hard work and detailed reviews that led to eleven accepted papers.

Yi-Hung Liu David Moratal Javier Escudero Han-Pang Huang

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Mechatronics Engineering

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Introduction till mechatronic product, sensors and converters, signal conditioning, data presentation systems, Actuation systems, Basic system models, signal systems and navigation, real time interfacing, software and rechtssache studies. Mechatronis system construction

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Introduction to Mechatronics and Measurement Systems

Jan 05, 2020

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SMJP 3333 ( Mechatronics). Introduction to Mechatronics and Measurement Systems. by Dr.Aung Lwin Moe REF: Prof. I. Charles Ume. Mechatronics. The synergistic combination of mechanical, electrical, and computer engineering Emphasis on integrated design for products

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SMJP 3333 (Mechatronics) Introduction to Mechatronics and Measurement Systems by Dr.Aung Lwin Moe REF:Prof. I. Charles Ume

Mechatronics The synergistic combination of mechanical, electrical, and computer engineering • Emphasis on integrated design for products • Optimal combination of appropriate technologies

Mechatronics Systems Computers Cars Tools Stealth Bomber Consumer Electronics High Speed Trains MEMS Micro to Macro Applications

Mechatronics Systems -Manufacturing Applications- Micro Factory Micro Factory Drilling Unit • Desktop sized Factory • Build small parts with a small factory • Greatly reduces space, energy, and materials

Mechatronics Systems CNC Bending • Fully automated bending: load sheet metal and the finished bent parts come out • Can bend complex shapes

Mechatronics Systems CNC Machining Advantages • Deliver the highest accuracies • Can create very complex shapes

Mechatronics Systems -Transportation Applications- Automobiles Typical Applications • Brake-By-Wire system • Steer-By-Wire • Integrated vehicle dynamics • Cam-less engines • Integrated starter alternator OEM Driven • Reliability • Reduced weight • Fuel economy • Manufacturing flexibility • Design freedom • Advanced safety features • Cost

Mechatronics Systems - Door System/Module- “Smart” Mirror motor-unit pin-header “Smart” Doorlock CAM Bus Switchboard with CAN Bus Gateway “Smart” Window Lift-unit

Mechatronics Systems -Seat System/Module- Seat Harness Architecture showing various smart connector interconnections solutions

Mechatronics Systems High Speed Trains • Train Position and Velocity constantly monitored from main command center. • Error margin in scheduling no more than 30 seconds • Fastest trains use magnetic levitation JR-MaglevTop Speed: 574 km/h (357 mph)Country: Japan Magnetic Levitation TransrapidTop Speed: 550 km/h (340 mph) Country: German

Mechatronics Systems Segway Systems Uses • Tilt and pressure sensors • Microcontroller • Motors • Onboard power source Advantages • Simple and intuitive personal transportation device

Mechatronics Systems -Smart Robotics Application- BigDog System Can • Carry 340 lb • Run 4 mph • Climb, run, and walk • Move over rough terrain Advantages • Robot with rough-terrain mobility that could carry equipment to remote location.

Mechatronics Systems Vacuum Floors • Robots can vacuum floors and clean gutters so you don't have to. Cleans Gutter

Mechatronics Systems -Space Exploration Application- Phoenix Mars Lander's System Can • Collect specimens • Has automated onboard lab for testing specimens Advantages • Robot that can travel to other planets and take measurements automatically.

Mechatronics Systems -Medical Applications- Prosthetics • Arms, Legs, and other body parts can be replaced with electromechanical ones.

Mechatronics Systems Pace Maker -Medical Applications- Used by patients with slow or erratic heart rates. The pacemaker will set a normal heart rate when it sees an irregular heart rhythm. Implantable Defibrillation Monitors the heart. If heart fibrillates or stops completely it will shock the heart at high voltage to restore a normal heart rhythm.

Mechatronics Systems -Defense Applications- • Advanced technology is making our soldiers safer. • Some planes can now be flown remotely. Stealth Bomber Unmanned Aerial Vehicle

Mechatronics Systems -Sanitation Applications- System Uses • Proximity sensors • Control circuitry • Electromechanical valves • Independent power source Advantages • Reduces spread of germs by making device hands free • Reduces wasted water by automatically turning off when not in use

Mechatronics Systems Systems Uses • Motion sensors • Control circuitry • Electromechanical actuators • Independent power source Paper Towel Dispenser Soap Dispenser Advantages • Reduces spread of germs by making device hands free • Reduces wasted materials by controlling how much is dispensed

Mechatronics Systems -Sports Applications- Running Shoes Advantages Automatically changes cushioning in shoe for different running styles and conditions for improved comfort

Mechatronics Systems -Smart Home Applications- Washing Machine Solution Power Supply Rectifiers/Regulator Pressure Sensor MPX5006/MPX2010

Mechatronics Systems -Smart Home Applications- Smoke Detector System

Copy Machine • It includes analog and digital circuits, sensors, actuators, and microprocessors. • A high intensity light source scans the original and transfers the corresponding image as a charge distribution to a drum. • The image is transferred onto the paper with an electrostatic deposition of ink toner powder that is heated to bond to the paper. • Analog circuits control the lamp, heater, and other power circuits in the machine. • Digital circuits control the digital displays, indicator lights, buttons, and switches forming the user interface. Other digital circuits include logic circuits and microprocessors that coordinate all of the functions in the machine.

Inkjet printer components

Elements of a measurement system It is important for designers and users of measurement systems to develop confidence in their use, to know their important characteristics and limitations, and to be able to select the best elements for the measurement task at hand. The following figure shows an example of a measurement system. The thermocouple is a transducer that converts temperature to a small voltage; the amplifier increases the magnitude of the voltage; the A/D (analog-to-digital) converter is a device that changes the analog signal to a coded digital signal; and the LEDs (light emitting diodes) display the value of the temperature.

DC motor power-op-amp speed controller • The light-emitting diode (LED) provides a visual cue to the user that the microcontroller is running properly. • The speed input device is a potentiometer (or pot), which is a variable resistor. • The resistance changes as the user turns the knob on top of the pot. The pot can be wired to produce a voltage input. • The voltage signal is applied to a microcontroller to control a DC motor to rotate at a speed proportional to the voltage. • Voltage signals are “analog” but microcontrollers are “digital,” so we need analog-to digital (A/D) and digital-to-analog (D/A) converters Finally, we need a power amplifier to boost the voltage and source the necessary current

The power-amp speed controller

Functional diagram of the stepper motor position and speed controller • The input devices include a pot to control the speed manually, four buttons to select predefined positions, and a mode button to toggle between speed and position control. • In position control mode, each of the four position buttons indexes the motor to specific angular positions relative to the starting point (0 , 45 , 90 , 180 ). In speed control mode, turning the pot clockwise (counterclockwise) increases (decreases) the speed. • The LED provides a visual cue to the user to indicate that the PIC is cycling properly. • A/D converter is used to convert the pot’s voltage to a digital value. • A microcontroller uses that value to generate signals for a stepper motor driver circuit to make the motor rotate

Photograph of the stepper motor position and speed controller

Functional diagram for the DC motor position and speed controller

A numerical keypad enables user input, and a liquid crystal display (LCD) is used to display messages and a menu-driven user interface. • The motor is driven by an H-bridge, which allows the voltage applied to the motor (and therefore the direction of rotation) to be reversed. The H-bridge also allows the speed of the motor to be easily controlled by pulse-width modulation (PWM), where the power to the motor is quickly switched on and off at different duty cycles to change the average effective voltage applied. • A digital encoder attached to the motor shaft provides a position feedback signal. This signal is used to adjust the voltage signal to the motor to control its position or speed. • This is called a servomotor system because we use feedback from a sensor to control the motor. Servomotors are different from stepper motors in that they move smoothly instead of in small incremental steps. • Two PIC microcontrollers are used in this design because there are a limited number of input/output pins available on a single chip. The main (master) PIC gets input from the user, drives the LCD, and sends the PWM signal to the motor. • The secondary (slave) PIC monitors the digital encoder and transmits the position signal back to the master PIC upon command via a serial interface.

Photograph of the DC motor position and speed controller

■CLASS DISCUSSION ITEM • Household Mechatronic Systems • What typical household items can be characterized as mechatronic systems? • What components do they contain that help you identify them as mechatronic systems? • If an item contains a microprocessor, describe the functions performed by the microprocessor. • ??????????????

Measurement Fundamentals 1. Be able to define SI units and use them in calculations 2. Know how to use statistics fundamentals to characterize measured data 3. Be able to compute the error associated with a measurement

SYSTEMS OF UNITS • Fundamental to the design, analysis, and use of any measurement system is a complete understanding of a consistent system of units used to quantify the physical parameters being measured. • To define a system of units, we must select units of measure for fundamental quantities to serve as a basis for the definition of other physical parameters. • Units for mass, length, time, temperature, electric current, amount of • substance, and luminous intensity form one possible combination that • serves this purpose. • Other units used to measure physical quantities in mechatronic systems can be defined in terms of these seven base units. • The seven base units we use to define mass, length, time, temperature, electric current, amount of substance, and luminous intensity are the kilogram, meter, second, Kelvin, ampere, mole, and candela.

The kilogram is the only unit defined in terms of a material standard. It is • established by a platinum-iridium prototype in the laboratory of the Bureau des • Poids et Mesures in Paris. • The meter is defined as 1,650,763.73 wavelengths of the emission resulting from the transition between the 2p10 and 5d5 electron energy levels of the krypton 86 atom. This atomic standard for the meter was proposed long ago by Maxwell (1873) but not implemented until 1960. • The second is defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom. • The unit of absolute thermodynamic temperature is the Kelvin. The Kelvin scale has an absolute zero of 0 K, and no temperatures exist below this level. • The ampere is defined as the constant current that, if maintained in two straight parallel conductors of infinite length and negligible circular cross section and placed 1 meter apart in a vacuum • The mole is defined as the amount of substance that contains as many elementary entities as there are atoms in 0.012 kg of carbon 12 ( 12C). • The candela is defined as the luminous intensity, in the perpendicular direction, of a surface area of 1/600,000 m 2 of a black body at the freezing point of platinum under a pressure of 101,325 N/m 2 • .

Three Classes of SI Units SI units are divided into three classes: base units, derived units, and supplementary units. The complete set of SI base units and their symbols are listed in Table A.1 .

Derived units are expressed as algebraic combinations of the base units. Any known physical parameter can be quantified using a derived unit. Some examples of derived units are listed in Table A.2 .

Several derived units have been given special names and symbols, which may be used themselves to express other derived units in a simpler way than in terms of base units. Some examples of these supplemental units are listed in Table A.3 Often the base, derived, and supplemental units are modified with prefixes to enable convenient representation of large numerical ranges.

Often the base, derived, and supplemental units are modified with prefixes to enable convenient representation of large numerical ranges. The prefixes express orders of magnitude (powers of 10) of the unit, providing an alternative to scientific notation. The prefix names, symbols, and values are listed in Table A.4 .

Conversion Factors English units are still common in engineering practice in the United States. Table A.5 lists several factors that help when converting between English and SI units.

SIGNIFICANT FIGURES Whenever we deal with numerical data, we need to be aware of precision, accuracy, and different ways to present the data. Also, in establishing a rational approach to making numerical calculations with measured values, we must present decimal numbers with the appropriate number of digits. The significant digits or significant figures in a number are those known with certainty. A measured value represented by N digits consists of N -1 significant digits that are certain and 1 digit that is estimated.

STATISTICS When we process sets of data obtained from experimental measurements, we must handle the data in a rational, systematic, and organized fashion. The field of statistics provides models and rules for doing this properly

ERROR ANALYSIS • The process of making measurements is imperfect, and uncertainty will always be associated with measured values. It is important to recognize sources of error and estimate the magnitude of error when one makes a measurement. Usually a manufacturer defines the accuracy of an instrument in published specifications, but other factors come into play. • A systematic error is one that reoccurs in the same way each time a measurement is made. The method used to minimize the magnitude of systematic error is calibration, where the measurement instrument is used to record values from a standard input and is adjusted to compensate for any discrepancy. • Random errors occur due to the stochastic variations in a measurement process. Some of the statistical tools presented in the previous section enable us to reduce the effects of these errors. • Blunders occur when the engineer or scientist makes a mistake. Blunders can be avoided by careful design and review and through the use of methodical procedures.

Figure A.3 illustrates systematic and random errors. The center of the target represents the desired value, and the shot pattern represents measured data. The systematic error, called inaccuracy, is associated with the shift of the shot pattern from the center of the target and could be corrected by improved sighting, known as calibration .The random error, called imprecision, is the size of the shot pattern and cannot be improved by adjusting the sighting. Accuracy is the closeness to the true value, and precision is the repeatability or consistency of the measurements.

Rules for Estimating Errors

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