MECHATRONICS A Foundation Course MECHATRONICS A Foundation Course Clarence W de Silva Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business MATLAB® is a trademark of The MathWorks, Inc and is used with permission The MathWorks does not warrant the accuracy of the text or exercises in this book This book’s use or discussion of MATLAB® software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB® software CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2010 by Taylor and Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S Government works Printed in the United States of America on acid-free paper 10 International Standard Book Number-13: 978-1-4200-8212-8 (Ebook-PDF) This book contains information obtained from authentic and 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please access www.copyright.com (http:// www.copyright.com/) or contact the Copyright Clearance Center, Inc (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400 CCC is a not-for-profit organization that provides licenses and registration for a variety of users For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com To Professor Jim A.N Poo for his friendship and continuous support “We live in a society exquisitely dependent on science and technology, in which hardly anyone knows anything about science and technology.” Carl Sagan Contents Preface xxiii Acknowledgments xxvii Author xxix Mechatronic Engineering .1 Study Objectives .1 1.1 Introduction 1.2 Mechatronic Systems 1.3 Modeling and Design 1.4 Mechatronic Design Concept 1.4.1 Coupled Design 1.4.2 Mechatronic Design Quotient 1.4.3 Design Evolution 1.5 Evolution of Mechatronics 1.6 Application Areas 10 1.7 Study of Mechatronics 11 1.8 Organization of the Book 12 Problems 14 Further Reading 15 Basic Elements and Components 17 Study Objectives 17 2.1 Introduction 17 2.2 Mechanical Elements 18 2.2.1 Mass (Inertia) Element 18 2.2.2 Spring (Stiffness) Element 20 2.2.3 Damping (Dissipation) Element 21 2.3 Fluid Elements 21 2.3.1 Fluid Capacitor or Accumulator (A-Type Element) 22 2.3.2 Fluid Inertor (T-Type Element) .22 2.3.3 Fluid Resistor (D-Type Element) 22 2.3.4 Derivation of Constitutive Equations 22 2.3.4.1 Fluid Capacitor 23 2.3.4.2 Fluid Inertor 26 2.3.4.3 Fluid Resistor 27 2.4 Thermal Elements 27 2.4.1 Thermal Capacitor 28 2.4.2 Thermal Resistor 28 2.4.2.1 Conduction 29 2.4.2.2 Convection .30 2.4.2.3 Radiation 30 vii viii Contents 2.5 2.6 2.7 2.8 2.4.3 Three-Dimensional Conduction 31 2.4.4 Biot Number 32 Mechanical Components 32 2.5.1 Transmission Components 33 2.5.2 Lead Screw and Nut 35 2.5.3 Harmonic Drives 38 Passive Electrical Elements and Materials 43 2.6.1 Resistor (Dissipation) Element .43 2.6.1.1 Conductance and Resistance 44 2.6.1.2 Resistivity 44 2.6.1.3 Effect of Temperature on Resistance 45 2.6.1.4 Effect of Strain on Resistance .46 2.6.1.5 Superconductivity 47 2.6.1.6 Color Code for Fixed Resistors .48 2.6.2 Dielectric Material and Capacitor Element 49 2.6.2.1 Permittivity 51 2.6.2.2 Capacitor Types 52 2.6.2.3 Color Code for Fixed Capacitors 52 2.6.2.4 Piezoelectricity 52 2.6.3 Magnetic Material and Inductor Element 55 2.6.3.1 Magnetism and Permeability 55 2.6.3.2 Hysteresis Loop 55 2.6.3.3 Magnetic Materials 55 2.6.3.4 Piezomagnetism 57 2.6.3.5 Hall-Effect Sensors 57 2.6.3.6 Magnetic Bubble Memories 58 2.6.3.7 Reluctance 58 2.6.3.8 Inductance 59 Active Electronic Components 60 2.7.1 Diodes 60 2.7.1.1 PN Junctions 60 2.7.1.2 Semiconductors 60 2.7.1.3 Depletion Region 61 2.7.1.4 Biasing 61 2.7.1.5 Zener Diodes 63 2.7.1.6 VVC Diodes .64 2.7.1.7 Tunnel Diodes 64 2.7.1.8 PIN Diodes 65 2.7.1.9 Schottky Barrier Diodes 65 2.7.1.10 Thyristors 65 2.7.2 Transistors 67 2.7.2.1 Bipolar Junction Transistors 67 2.7.2.2 Field-Effect Transistors 69 2.7.2.3 The MOSFET 70 2.7.2.4 The Junction Field Effect Transistor 71 Light Emitters and Displays 74 2.8.1 Light-Emitting Diodes 75 2.8.2 Lasers 76 Contents ix 2.8.3 Liquid Crystal Displays 78 2.8.4 Plasma Displays 79 2.9 Light Sensors 79 2.9.1 Photoresistors 80 2.9.2 Photodiodes 80 2.9.3 Phototransistor 81 2.9.4 Photo-Field Effect Transistor 81 2.9.5 Photocells 82 2.9.6 Charge-Coupled Device 82 2.9.7 Applications of Optically Coupled Devices 83 Problems 84 Modeling of Mechatronic Systems 91 Study Objectives 91 3.1 Introduction 91 3.2 Dynamic Systems and Models 92 3.2.1 Terminology 92 3.2.2 Dynamic Models 93 3.2.2.1 Model Complexity 93 3.2.2.2 Model Types 93 3.2.2.3 Types of Analytical Models 94 3.2.2.4 Principle of Superposition 95 3.2.3 Lumped Model of a Distributed System 95 3.2.3.1 Heavy Spring 96 3.3 Lumped Elements and Analogies 98 3.3.1 Across Variables and through Variables 99 3.3.2 Natural Oscillations 100 3.4 Analytical Model Development 100 3.4.1 Steps of Model Development 101 3.4.2 Input–Output Models 102 3.4.3 State-Space Models 102 3.4.3.1 Linear State Equations 102 3.5 Model Linearization 111 3.5.1 Linearization about an Operating Point 111 3.5.2 Function of Two Variables 113 3.5.3 Reduction of System Nonlinearities 114 3.5.4 Linearization Using Experimental Operating Curves 120 3.5.4.1 Torque–Speed Curves of Motors 120 3.5.4.2 Linear Models for Motor Control 120 3.6 Linear Graphs 122 3.6.1 Variables and Sign Convention 123 3.6.1.1 Sign Convention 123 3.6.2 Linear Graph Elements 125 3.6.2.1 Single-Port Elements 125 3.6.2.2 Two-Port Elements 127 3.6.3 Linear Graph Equations 131 3.6.3.1 Compatibility (Loop) Equations 131 3.6.3.2 Continuity (Node) Equations 132 451 Sensors and Transducers 6.16 An active suspension system is proposed for a highspeed ground transit vehicle in order to achieve improved ride quality The system senses jerk (rate of change of acceleration) due to road disturbances and adjusts system parameters accordingly (a) Draw a suitable schematic diagram for the proposed control system and describe the appropriate measuring devices + C q Cp Piezoelectric sensor R Cc Insulation Cable Output vo − FIGURE P6.17 Equivalent circuit for a quartz crystal (piezoelectric) accelerometer (b) Suggest a way to specify the “desired” ride quality for a given type of vehicle (Would you specify one value of jerk, a jerk range, or a jerk curve with respect to time or frequency?) (c) Discuss the drawbacks and limitations of the proposed control system with respect to such factors as reliability, cost, feasibility, and accuracy 6.17 A design objective in most mechatronic applications is to achieve small time constants An exception is the time constant requirements for a piezoelectric sensor Explain why a large time constant, on the order of 10 s, is desirable for a piezoelectric sensor in combination with its signal conditioning system An equivalent circuit for a piezoelectric accelerometer, which uses a quartz crystal as the sensing element, is shown in Figure P6.17 The charge generated is denoted by q, and the voltage output at the end of the accelerometer cable is vo The piezoelectric sensor capacitance is modeled by Cp, and the overall capacitance experienced at the sensor output, whose primary contribution is due to cable capacitance, is denoted by Cc The resistance of the electric insulation in the accelerometer is denoted by R Write a differential equation relating vo to q What is the corresponding transfer function? Using this result, show that the accuracy of the accelerometer improves when the sensor time constant is large and when the frequency of the measured acceleration is high For a quartz crystal sensor with R = × 1011 Ω and C5 = 300 pF and a circuit with Cc = 700 pF, compute the time constant 6.18 Applications of accelerometers are found in the following areas: (a) Transit vehicles (automobiles—microsensors for airbag sensing in particular, aircraft, ships, etc.), (b) power cable monitoring, (c) robotic manipulator control, (d) building structures, (e) shock and vibration testing, and (f) position and velocity sensing Describe one direct use of acceleration measurement in each application area 6.19 A strain gage accelerometer uses a semiconductor strain gage mounted at the root of a cantilever element with the seismic mass mounted at the free end of the cantilever Suppose that the cantilever element has a square cross section with a dimension of 1.5 × 1.5 mm The equivalent length of the cantilever element is 25 mm, and the equivalent seismic mass is 0.2 gm If the cantilever is made of an aluminum alloy with Young’s modulus E = 69 × 109 N/m2, estimate the useful frequency range of the accelerometer in hertz Hint: When force F is applied to the free end of a cantilever, the de ection y at that location may be approximated by the formula y= Fl 3EI 452 Mechatronics: A Foundation Course where l is the cantilever length I is the second moment area of the cantilever cross section about the bending axis = bh3/12 b is the cross section width h is the cross section height 6.20 Applications of piezoelectric sensors are numerous; push-button devices and switches, airbag MEMS sensors in vehicles, pressure and force sensing, robotic tactile sensing, accelerometers, glide testing of computer disk-drive heads, excitation sensing in dynamic testing, respiration sensing in medical diagnostics, and graphics input devices for computers Discuss the advantages and disadvantages of piezoelectric sensors What is the cross sensitivity of a sensor? Indicate how the anisotropy of piezoelectric crystals (i.e., charge sensitivity quite large along one particular crystal axis) is useful in reducing cross-sensitivity problems in a piezoelectric sensor 6.21 As a result of advances in microelectronics, piezoelectric sensors (such as accelerometers and impedance heads) are now available in miniature form with built-in charge ampli ers in a single integral package When such units are employed, additional signal conditioning is usually not necessary An external power supply unit is needed, however, to provide power for the ampli er circuitry Discuss the advantages and disadvantages of a piezoelectric sensor with built-in microelectronics for signal conditioning A piezoelectric accelerometer is connected to a charge ampli er An equivalent circuit for this arrangement is shown in Figure 6.21 (a) Obtain a differential equation for the output vo of the charge ampli er with acceleration a as the input, in terms of the following parameters: Sa = the charge sensitivity of the accelerometer (charge/acceleration); Rf = the feedback resistance of the charge ampli er; τc = the time constant of the system (charge ampli er) (b) If an acceleration pulse of magnitude ao and duration T is applied to the accelerometer, sketch the time response of the ampli er output vo Show how this response varies with τc Using this result, show that the larger the τc the more accurate the measurement 6.22 Give the typical values for the output impedance and the time constant of the following measuring devices: (a) (b) (c) (d) Potentiometer Differential transformer Resolver Piezoelectric accelerometer A RTD has an output impedance of 500 Ω If the loading error has to be maintained near 5%, estimate a suitable value for the load impedance 6.23 A signature veri cation pen has been developed by IBM Corporation The purpose of the pen is to authenticate the person who provides the signature by detecting whether the user is forging someone else’s signature The instrumented pen has analog sensors Sensor signals are conditioned using microcircuitry built into the 453 Sensors and Transducers = Torque-sensing locations pen and sampled into a digital computer at the rate of 80 samples/s using an ADC Typically, about 1000 data samples are collected per signature Prior to the pen’s Link (assume use, authentic signatures are collected off-line and Stator fixed) stored in a reference database When a signature and the corresponding identi cation code are supplied to the computer for veri cation, a program in the procesTm sor retrieves the authentic signature from the database, B A Tm by referring to the identi cation code, and then com2 pares the two sets of data for authenticity This process Jm takes about s Discuss the types of sensors that could θm θl be used in the pen Estimate the total time required Jl for a signal veri cation What are the advantages and Link disadvantages of this method in comparison to having the user punch in an identi cation code alone or proRotor Stiffness vide the signature without the identi cation code? K 6.24 Consider the joint of a robotic manipulator, shown schematically in Figure P6.24 Torque sensors are FIGURE P6.24 mounted at locations 1, 2, and If the electromag- Torque sensing locations for a manipulator joint netic torque generated at the motor rotor is Tm, write equations for the torque transmitted to link 2, the frictional torque at bearing A, the frictional torque at bearing B, and the reaction torque on link in terms of the measured torques, the inertia torque of the rotor, and Tm 6.25 A strain gage sensor to measure the torque Tm generated by a motor is shown schematically in Figure P6.25 The motor is oated on frictionless bearings A uniform rectangular lever arm is rigidly attached to the motor housing and its projected end is restrained by a pin joint Four identical strain gages are mounted on the lever arm, as shown Three of the strain gages are at point A, which is located at a distance a from the motor shaft and the fourth strain gage is at point B, which is located at a distance 3a from the motor shaft The pin joint is at a distance l from the motor shaft Strain Motor housing Frictionless bearings Motor torque Tm A Load B Reaction R ω = Strain gage a 3a l FIGURE P6.25 A strain gage sensor for measuring motor torque 454 Mechatronics: A Foundation Course gages 2, 3, and are on the top surface of the lever arm and gage is on the bottom surface Obtain an expression for Tm in terms of the bridge output δvo and the following additional parameters: Ss is the gage factor (strain gage sensitivity) vref is the supply voltage to the bridge b is the width of the lever arm cross section h is the height of the lever arm cross section E is the Young's modulus of the lever arm Verify that the bridge sensitivity does not depend on a and l Describe the means to improve the bridge sensitivity Explain why the sensor reading is only an approximation to the torque transmitted to the load Give a relation to determine the net normal reaction force at the bearings, using the bridge output 6.26 Discuss the advantages and disadvantages of the following techniques in the context of measuring transient signals (a) (b) (c) (d) (e) DC bridge circuits versus ac bridge circuits Slip ring and brush commutators versus ac transformer commutators Strain gage torque sensors versus variable-inductance torque sensors Piezoelectric accelerometers versus strain gage accelerometers Tachometer velocity transducers versus piezoelectric velocity transducers 6.27 Brie y describe how strain gages may be used to measure (a) Force (d) Pressure (b) Displacement (e) Temperature (c) Acceleration Show that if a compensating resistance Rc is connected in series with the supply voltage vref to a strain gage bridge that has four identical members, each with resistance R, the output equation is given by δvo R kSs = ε vref (R + Rc ) in the usual rotation A foil-gage load cell uses a simple (one-dimensional) tensile member to measure force Suppose that k and Ss are insensitive to temperature change If the temperature coef cient of R is α1, that of the series compensating resistance Rc is α2, and that of the Young’s modulus of the tensile member is (−β), determine an expression for Rc that would result in automatic (self) compensation for temperature effects Under what conditions is this arrangement realizable? 6.28 The read–write head in a disk drive of a digital computer should oat at a constant but small height (say, a fraction of a μm) above the disk surface Because of the aerodynamics resulting from the surface roughness and the surface deformations of the disk, the head can be excited into vibrations that could cause head–disk contacts These contacts, which are called head–disk interferences (HDIs), are clearly undesirable They can occur at very high frequencies (say, MHz) The purpose of a glide Sensors and Transducers 455 test is to detect HDIs and to determine the nature of these interferences Glide testing can be used to determine the effect of parameters such as the ying height of the head and the speed of the disk and to qualify (certify the quality of) disk drive units Indicate the basic instrumentation needed in glide testing In particular, suggest the types of sensors that could be used and their advantages and disadvantages 6.29 What are the typical requirements for an industrial tactile sensor? Explain how a tactile sensor differs from a simple touch sensor De ne the spatial resolution and force resolution (or sensitivity) of a tactile sensor The spatial resolution of your ngertip can be determined by a simple experiment using two pins and a helper Close your eyes Instruct the helper to apply one pin or both pins randomly to your ngertip so that you will feel the pressure of the tip of the pins You should respond by telling the helper whether you feel both pins or just one pin If you feel both pins, the helper should decrease the spacing of the two pins in the next round of tests The test should be repeated in this manner by successively decreasing the spacing between the pins until you feel only one pin when both pins are actually applied Then measure the distance between the two pins in millimeters The largest spacing between the two pins that will result in this incorrect sensation corresponds to the spatial resolution of your ngertip Repeat this experiment for all your ngers, repeating the test several times on each nger Compute the average and the standard deviation Then perform the test on other subjects Discuss your results Do you notice large variations in the results? 6.30 The motion dexterity of a device is de ned as the ratio (the number of degrees of freedom in the device)/(the motion resolution of the device) The force dexterity may be de ned as (the number of degrees of freedom in the device)/(the force resolution of the device) Given a situation where both types of dexterity mean the same thing and a situation where the two terms mean different things, outline how force dexterity of a device (say, an end effector) can be improved by using tactile sensors Provide the dexterity requirements for the following tasks by indicating whether motion dexterity or force dexterity is preferred in each case: (a) (b) (c) (d) Gripping a hammer and driving a nail with it Threading a needle Seam tracking of a complex part in robotic arc welding Finishing the surface of a complex metal part using robotic grinding 6.31 Using the usual equation for a dc strain-gage bridge, show that if the resistance elements R1 and R have the same temperature coef cient of resistance and if R3 and R4 have the same temperature coef cient of resistance, the temperature effects are compensated for up to the rst order A microminiature (MEMS) strain-gage accelerometer uses two semiconductor strain gages, one integral with the cantilever element near the xed end (root) and the other mounted at an unstrained location of the accelerometer The entire unit including the cantilever and the strain gages has a silicon IC construction and measures smaller than mm in size Outline the operation of the accelerometer What is the purpose of the second strain gage? 6.32 A simple rate gyro, which may be used to measure angular speeds, is shown in Figure P6.32 The angular speed of spin is ω and is kept constant at a known value The angle of the rotation of the gyro about the gimbal axis (or the angle of twist of the torsional spring) is θ and is measured using a displacement sensor The angular 456 Mechatronics: A Foundation Course speed of the gyro about the axis that is orthogonal to both gimbal axis and spin axis is Ω This is the angular speed of the supporting structure (vehicle), which needs to be measured Obtain a relationship between Ω and θ in terms of parameters such as the following: J is the moment of inertia of the spinning wheel k is the torsional stiffness of the spring restraint at the gimbal bearings b is the damping constant of rotational motion about the gimbal axis and the spinning speed θ Ω ω J k b How would you improve the sensitivity of this device? 6.33 Level sensors are used in a wide variety of applications, including soft drink bottling, food packaging, FIGURE P6.32 monitoring of storage vessels, mixing tanks, and pipe- A rate gyro speed sensor lines Consider the following types of level sensors, and brie y explain the principle of operation of each type in level sensing Also, what are the limitations of each type? (a) (b) (c) (d) Capacitive sensors Inductive sensors Ultrasonic sensors Vibration sensors 6.34 Consider the following types of position sensors: inductive, capacitive, eddy current, ber-optic, and ultrasonic For the following conditions, indicate which of these types are not suitable and explain why: (a) (b) (c) (d) (e) (f) (g) Environment with variable humidity Target object made of aluminum Target object made of steel Target object made of plastic Target object several feet away from the sensor location Environment with signi cant temperature uctuations Smoke- lled environment 6.35 Discuss advantages and disadvantages of ber-optic sensors Consider the beroptic position sensor In the curve of light intensity received versus x, in which region would you prefer to operate the sensor, and what are the corresponding limitations? 6.36 The manufacturer of an ultrasonic gage states that the device has applications in measuring cold roll steel thickness, determining parts positions in robotic assembly, lumber sorting, measurement of particle board and plywood thickness, ceramic tile dimensional inspection, sensing the ll level of food in a jar, pipe diameter gaging, rubber tire positioning during fabrication, gaging of fabricated automotive components, edge detection, location of aws in products, and parts identi cation Discuss whether the following types of sensors are also equally suitable for some or all of the foregoing applications In each case where you think that a particular sensor is not suitable for a given application, give reasons to support your claim 457 Sensors and Transducers Motion command Motion controller Amplifier Motor DC tachometer Gearbox Coupling Load Response Motion sensor Optical encoder FIGURE P6.37 Block diagram of a motion control system (a) (b) (c) (d) (e) (f) Fiber-optic position sensors Self-induction proximity sensors Eddy current proximity sensors Capacitive gages Potentiometers Differential transformers 6.37 (a) Consider the motion control system that is shown by the block diagram in Figure P6.37 (i) Giving examples of typical situations, explain the meaning of the block represented as “Load” in this system (ii) Indicate the advantages and shortcomings of moving the motion sensors from the motor shaft to the load response point, as indicated by the broken lines in the gure (b) Indicate, giving reasons, what type of sensors you will recommend for the following applications: (i) In a soft drink bottling line, for online detection of improperly tted metal caps on glass bottles (ii) In a paper processing plant, to simultaneously measure both the diameter and eccentricity of rolls of newsprint (iii) To measure the dynamic force transmitted from a robot to its support structure, during operation (iv) In a plywood manufacturing machine, for online measurement of the thickness of plywood (v) In a food canning plant, to detect defective cans (with damage to ange, side seam, etc.) (vi) To read codes on food packages 6.38 Consider the two quadrature pulse signals (say, A and B) from an incremental encoder Using sketches of these signals, show that in one direction of rotation, signal B is at a high level during the up-transition of signal A and in the opposite direction 458 Mechatronics: A Foundation Course of rotation, signal B is at a low level during the up-transition of signal A Note that the direction of motion can be determined in this manner, by using level detection of one signal during the up-transition of the other signal 6.39 Explain why the speed resolution of a shaft encoder depends on the speed itself What are some of the other factors that affect speed resolution? The speed of a dc motor was increased from 50 to 500 rpm How would the speed resolution change if the speed were measured using an incremental encoder by the (a) Pulse-counting method? (b) Pulse-timing method? 6.40 Describe methods of improving the displacement resolution and the velocity resolution in an encoder An incremental encoder disk has 5000 windows The word size of the output data is 12 bits What is the angular (displacement) resolution of the device? Assume that quadrature signals are available but that no interpolation is used 6.41 An incremental optical encoder that has N windows per track is connected to a shaft through a gear system with gear ratio p Derive formulas for calculating the angular velocity of the shaft by the (a) Pulse-counting method (b) Pulse-timing method 6.42 6.43 6.44 6.45 What is the speed resolution in each case? What effect does step-up gearing have on the speed resolution? What is the main advantage of using a gray code instead of straight binary code in an encoder? Give a table corresponding to a gray code for a bit absolute encoder What is the corresponding code pattern on the encoder disk? Discuss the construction features and operation of an optical encoder for measuring rectilinear displacements and velocities A centrifuge is a device that is used to separate components in a mixture In an industrial centrifugation process, the mixture to be separated is placed in the centrifuge and rotated at high speed The centrifugal force on a particle depends on the mass, radial location, and the angular speed of the particle This force is responsible for separating the particles in the mixture The angular motion and temperature of the container are the two key variables that have to be controlled in a centrifuge In particular, a speci c centrifugation curve is used that consists of an acceleration segment, a constant-speed segment, and a braking (deceleration) segment and this corresponds to a trapezoidal speed pro le An optical encoder may be used as the sensor for microprocessor-based speed control in the centrifuge Discuss whether an absolute encoder is preferred for this purpose Give the advantages and possible drawbacks of using an optical encoder in this application Suppose that a feedback control system (Figure P6.45) is expected to provide an accuracy within ±Δy for a response variable y Explain why the sensor that measures y should have a resolution of ±(Δy/2) or better for this accuracy to be possible An x–y table has a travel of m The feedback control system is expected to provide an accuracy of ±1 mm An optical encoder is used to measure the position for feedback 459 Sensors and Transducers Reference input u = yd Error e – Response y System Sensory feedback FIGURE P6.45 A feedback control loop in each direction (x and y) What is the minimum bit size that is required for each encoder output buffer? If the motion sensor used is an absolute encoder, how many tracks and how many sectors should be present on the encoder disk? 6.46 The pulses generated by the coding disk of an incremental optical encoder are approximately triangular (actually, upward shifted sinusoidal) in shape Explain the reason for this Describe a method for converting these triangular (or shifted sinusoidal) pulses into sharp rectangular pulses 6.47 Explain how the resolution of a shaft encoder could be improved by pulse interpolation Speci cally, consider the arrangement shown in Figure P6.47 When the masking windows are completely covered by the opaque regions of the moving disk, no light is received by the photosensor The peak level of light is received when the windows of the moving disk coincide with the windows of the masking disk The variation of the light intensity from the minimum level to the peak level is approximately linear (generating a triangular pulse), but more accurately sinusoidal, and may be given by 2πθ v = vo − cos ∆θ where θ denotes the angular position of the encoder window with respect to the masking window, as shown, Δθ is the window pitch angle Note that, in the sense of rectangular pulses, the pulse corresponds to the motion in the interval Δθ/4 ≤ θ ≤ 3Δθ/4 By using this sinusoidal approximation for a pulse, as given above, show that one can improve the resolution of an encoder inde nitely simply by measuring the shape of each pulse at clock cycle intervals using a high-frequency clock signal LED ∆θ Moving disk θ Masking disk Photosensor FIGURE P6.47 An encoder with a masking disk Motion 460 Mechatronics: A Foundation Course Input (V) Output (V) 4.0 3.5 (a) 1.0 1.5 Input (V) 1.0 3.0 5.0 6.0 (b) 8.0 10.0 11.0 13.0 15.0 Time t (s) FIGURE P6.48 (a) The I/O characteristic of a Schmitt trigger; (b) a triangular input signal 6.48 A Schmitt trigger is a semiconductor device that can function as a level detector or a switching element with hysteresis The presence of hysteresis can be used, for example, to eliminate chattering during switching caused by noise in the switching signal In an optical encoder, a noisy signal detected by the photosensor may be converted into a clean signal of rectangular pulses by this means The I/O characteristic of a Schmitt trigger is shown in Figure P6.48a If the input signal is as shown in Figure P6.48b, determine the output signal 6.49 Compare and contrast an optical incremental encoder against a potentiometer by giving the advantages and disadvantages for an application involving the sensing of a rotatory motion A schematic diagram for the servo control loop of one joint of a robotic manipulator is given in Figure P6.49 The motion command for each joint of the robot is generated by the robot controller, in accordance with the required trajectory An optical incremental encoder is used for both position and velocity feedback in each servo loop Note that for a six-degree-offreedom robot, there will be six such servo loops Describe the function of each hardware component shown in the gure and explain the operation of the servo loop 20 kHz signal (internal) Motion command Max ±2.5 V Control processor DAC PWM amplifier PWM signal 10 V dc 2A V dc Power supply Feedback pulse signals (¼ phase offset) FIGURE P6.49 A servo loop of a robot ±20 V Permanentmagnet dc motor Incremental encoder 461 Sensors and Transducers Photodiode Masking plate (stationary) Code plate (moving) Photodetector FIGURE P6.50 Photodiode–detector arrangement of a linear optical encoder After several months of operation, the motor of one joint of the robot was found to be faulty An enthusiastic engineer quickly replaced the motor with an identical one without realizing that the encoder of the new motor was different In particular, the original encoder generated 200 pulses/rev whereas the new encoder generated 720 pulses/rev When the robot was operated, the engineer noticed an erratic and unstable behavior at the repaired joint Discuss reasons for this malfunction and suggest a way to correct the situation 6.50 (a) A position sensor is used in a microprocessor-based feedback control system for accurately moving the cutter blades of an automated meat-cutting machine The machine is an integral part of the production line of a meat processing plant What are the primary considerations in selecting the position sensor for this application? Discuss the advantages and disadvantages of using an optical encoder in comparison with an LVDT in this context (b) Figure P6.50 illustrates one arrangement of the optical components in a linear incremental encoder The moving code plate has uniformly spaced windows as usual, and the xed masking plate has two groups of identical windows, one above each of the two photodetectors These two groups of xed windows are positioned in a half-pitch out of phase so that when one detector receives light from its source directly through the aligned windows of the two plates, the other detector has the light from its source virtually obstructed by the masking plate Explain the purpose of the two sets of photodiode–detector units, giving a schematic diagram of the necessary electronics Can the direction of motion be determined with the arrangement shown in Figure P6.50? If so, explain how this could be done If not, describe a suitable arrangement for detecting the direction of motion 6.51 (a) What features and advantages of a digital transducer will distinguish it from a purely analog sensor? (b) Consider a “linear incremental encoder,” which is used to measure rectilinear positions and speeds The moving element is a nonmagnetic plate containing a series of identically magnetized areas uniformly distributed along its length The pickoff transponder is a mutual-induction-type proximity sensor 462 Mechatronics: A Foundation Course Output vo Primary supply vref Magnetized areas Pitch p Nonmagnetic code plate Rectilinear motion x, v FIGURE P6.51 A linear incremental encoder of the magnetic induction type (i.e., a transformer) consisting of a toroidal core with a primary winding and a secondary winding A schematic diagram of the encoder is shown in Figure P6.51 The primary excitation vref is a high-frequency sine wave Explain the operation of this position encoder, clearly indicating what types of signal conditioning would be needed to obtain a pure pulse signal Also, sketch the output vo of the proximity sensor as the code plate moves very slowly Which position of the code plate does a high value of the pulse signal represent and which position does a low value represent? (c) Suppose that the “pulse period timing” method is used to measure speed (v) using this encoder The pitch distance of the magnetic spots on the plate is p, as shown in Figure P6.51 If the clock frequency of the pulse period timer is f, give an expression for the speed v in terms of the clock cycle count m Show that the speed resolution Δv for this method may be approximated by ∆v = v2 pf It follows that the dynamic range v/Δv = pf/v If the clock frequency is 20 MHz, the code pitch is 0.1 mm, and the required dynamic range is 100 (i.e., 40 dB), what is the maximum speed in m/s that can be measured by this method? 6.52 What is a Hall-effect tachometer? Discuss the advantages and disadvantages of a Hall effect motion sensor in comparison with an optical motion sensor (e.g., an optical encoder) 6.53 Discuss the advantages of solid-state limit switches over mechanical limit switches Solid-state limit switches are used in many applications, particularly in the aircraft and aerospace industries One such application is in landing gear control to detect the up, down, and locked conditions of the landing gear High reliability is of utmost importance in such applications The mean time between failure (MTBF) of over 100,000 h is possible with solid-state limit switches Using your engineering judgment, give an MTBF value for a mechanical limit switch 6.54 Mechanical force switches are used in applications where only a force limit, rather than a continuous force signal, has to be detected Examples include detecting closure force (torque) in valve closing, detecting t in parts assembly, automated clamping devices, robotic grippers and hands, overload protection devices Sensors and Transducers 463 in process/machine monitoring, and product lling in containers by weight Expensive and sophisticated force sensors are not needed in such applications because a continuous history of a force signal is not needed Furthermore, they are robust and reliable and can safely operate in hazardous environments Using a sketch, describe the construction of a simple spring-loaded force switch 6.55 Consider the following three types of photoelectric object counters (or object detectors or limit switches): Through (opposed) type Re ective (re ex) type Diffuse (proximity, interceptive) type Classify these devices into long-range (up to several meters), intermediate range (up to m), and short-range (up to a fraction of a meter) detection 6.56 A brand of autofocusing camera uses a microprocessor-based feedback control system consisting of a CCD imaging system, a microprocessor, a drive motor, and an optical encoder The purpose of the control system is to focus the camera automatically based on the image of the subject as sensed by a matrix of CCDs (a set of metaloxide-semiconductor eld-effect transistors, or MOSFETs) The light rays from the subject that pass through the lens will fall onto the CCD matrix This will generate a matrix (image frame) of charge signals, which are shifted one at a time, row by row, into an output buffer (or frame grabber) and passed on to the microprocessor after conditioning the resulting video signal The CCD image obtained by sampling the video signal is analyzed by the microprocessor to determine whether the camera is focused properly If not, the lens is moved by the motor so as to achieve focusing Draw a schematic diagram for the autofocusing control system and explain the function of each component in the control system, including the encoder 6.57 Today, image processing and machine vision are used in many industrial tasks including process control, monitoring, pattern classi cation, and object recognition In an industrial system based on image processing, an imaging device such as a CCD camera is used as the sensing element The camera provides an image (picture) to an image processor of a scene related to the industrial process (the measurement) The computed results from the image processor are used to determine the necessary information about the process (plant) A digital camera has an image plate consisting of a matrix of MOSFET elements The electrical charge that is held by each MOSFET element is proportional to the intensity of light falling on the element The output circuit of the camera has a chargeampli er-like device (capacitor-coupled), which is supplied by each MOSFET element The MOSFET element that is to be connected to the output circuit at a given instant is determined by the control logic, which systematically scans the matrix of MOSFET elements The capacitor circuit provides a voltage that is proportional to the charge in each MOSFET element (a) Draw a schematic diagram for a process monitoring system based on machine vision, which uses a CCD camera Indicate the necessary signal modi cation operations at various stages in the monitoring loop, showing whether analog lters, ampli ers, ADC, and DAC are needed and if so, at which locations An image may be divided into pixels (or picture elements) for representation and subsequent processing A pixel has a well-de ned coordinate location in the picture frame, relative to some reference coordinate frame In a CCD camera, the 464 Mechatronics: A Foundation Course number of pixels per image frame is equal to the number of CCD elements in the image plate The information carried by a pixel (in addition to its location) is the photointensity (or gray level) at the image location This number has to be expressed in the digital form (using a certain number of bits) for digital image processing The need for very large data-handling rates is a serious limitation on a real-time controller that uses machine vision (b) Consider a CCD image frame of the size 488 × 380 pixels The refresh rate of the picture frame is 30 frames/s If bits are needed to represent the gray level of each pixel, what is the associated data (baud) rate? (c) Discuss whether you prefer hardware processing or programmable softwarebased processing in a process monitoring system based on machine vision Actuators Study Objectives • The purpose of actuators in a mechatronic system • Types of actuators • • • • Stepper motors and dc motors (including brushless dc motors) AC motors (induction motors and synchronous motors) Linear actuators Hydraulic and pneumatic actuators • • • • Modeling and analysis of actuators Practical performance and parameters of actuators Sizing and selection of actuators for practical applications Instrumentation, drive hardware, and control of actuators 7.1 Introduction This chapter introduces the subject of actuators, as related to mechatronics The actuator is the device that mechanically drives a mechatronic system Joint motors in a robotic manipulator are good examples of such actuators Actuators may be used as well to operate controller components ( nal control elements), such as servovalves, as well Actuators in this category are termed control actuators Actuators that automatically use response error signals from a process in feedback to correct the operation of the process (i.e., to drive the process to achieve a desired response) are termed servoactuators In particular, the motors that use measurements of position, speed, and perhaps load torque and armature current or eld current in feedback to drive a load to realize a speci ed motion are termed servomotors One broad classi cation separates actuators into two types: incremental-drive actuators and continuous-drive actuators Stepper motors, which are driven in xed angular steps, represent the class of incremental-drive actuators They can be considered to be digital actuators, which are pulse-driven devices Each pulse received at the driver of a digital actuator causes the actuator to move by a predetermined, xed increment of displacement Continuous-drive devices are very popular in mechatronic applications Examples are direct current (dc) torque motors, induction motors, hydraulic and pneumatic motors, and piston-cylinder drives (rams) Microactuators are actuators that are able to generate very small (microscale) actuating forces/torques and motions In general, they can be neither 465