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| | كتاب Machines and Mechanisms Applied Kinematic Analysis - Fourth Edition | |
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كاتب الموضوع | رسالة |
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rambomenaa كبير مهندسين
عدد المساهمات : 2041 التقييم : 3379 تاريخ التسجيل : 21/01/2012 العمر : 47 الدولة : مصر العمل : مدير الصيانة بشركة تصنيع ورق الجامعة : حلوان
| موضوع: كتاب Machines and Mechanisms Applied Kinematic Analysis - Fourth Edition السبت 16 يونيو 2012, 6:33 am | |
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تذكير بمساهمة فاتح الموضوع : أخواني في الله أحضرت لكم كتاب Machines and Mechanisms Applied Kinematic Analysis Fourth Edition David H. Myszka University of Dayton
و المحتوى كما يلي :
CONTENTS 1 Introduction to Mechanisms and Kinematics 1 Objectives 1 1.1 Introduction 1 1.2 Machines and Mechanisms 1 1.3 Kinematics 2 1.4 Mechanism Terminology 2 1.5 Kinematic Diagrams 4 1.6 Kinematic Inversion 8 1.7 Mobility 8 1.7.1 Gruebler’s Equation 8 1.7.2 Actuators and Drivers 12 1.8 Commonly Used Links and Joints 14 1.8.1 Eccentric Crank 14 1.8.2 Pin-in-a-Slot Joint 14 1.8.3 Screw Joint 15 1.9 Special Cases of the Mobility Equation 16 1.9.1 Coincident Joints 16 1.9.2 Exceptions to the Gruebler’s Equation 18 1.9.3 Idle Degrees of Freedom 18 1.10 The Four-Bar Mechanism 19 1.10.1 Grashof’s Criterion 19 1.10.2 Double Crank 20 1.10.3 Crank-Rocker 20 1.10.4 Double Rocker 20 1.10.5 Change Point Mechanism 20 1.10.6 Triple Rocker 20 1.11 Slider-Crank Mechanism 22 1.12 Special Purpose Mechanisms 22 1.12.1 Straight-Line Mechanisms 22 1.12.2 Parallelogram Mechanisms 22 1.12.3 Quick-Return Mechanisms 23 1.12.4 Scotch Yoke Mechanism 23 1.13 Techniques of Mechanism Analysis 23 1.13.1 Traditional Drafting Techniques 24 1.13.2 CAD Systems 24 1.13.3 Analytical Techniques 24 1.13.4 Computer Methods 24 Problems 25 Case Studies 29 2 Building Computer Models of Mechanisms Using Working Model Software 31 Objectives 31 2.1 Introduction 31 2.2 Computer Simulation of Mechanisms 31 2.3 Obtaining Working Model Software 32 2.4 Using Working Model to Model a Four-Bar Mechanism 32 2.5 Using Working Model to Model a SliderCrank Mechanism 37 Problems 41 Case Studies 42 3 Vectors 43 Objectives 43 3.1 Introduction 43 3.2 Scalars and Vectors 43 3.3 Graphical Vector Analysis 43 3.4 Drafting Techniques Required in Graphical Vector Analysis 44 3.5 CAD Knowledge Required in Graphical Vector Analysis 44 3.6 Trigonometry Required in Analytical Vector Analysis 44 3.6.1 Right Triangle 44 3.6.2 Oblique Triangle 46 3.7 Vector Manipulation 48 3.8 Graphical Vector Addition 48 3.9 Analytical Vector Addition : Triangle Method 50 3.10 Components of a Vector 52 3.11 Analytical Vector Addition : Component Method 53 3.12 Vector Subtraction 55 3.13 Graphical Vector Subtraction 55 3.14 Analytical Vector Subtraction : Triangle Method 57 3.15 Analytical Vector Subtraction : Component Method 59 3.16 Vector Equations 60 (- 7) (- 7) (- 7) (- 7) (+ 7) (+ 7) (+ 7) ivContents v 3.17 Application of Vector Equations 62 3.18 Graphical Determination of Vector Magnitudes 63 3.19 Analytical Determination of Vector Magnitudes 66 Problems 67 Case Studies 71 4 Position and Displacement Analysis 72 Objectives 72 4.1 Introduction 72 4.2 Position 72 4.2.1 Position of a Point 72 4.2.2 Angular Position of a Link 72 4.2.3 Position of a Mechanism 73 4.3 Displacement 73 4.3.1 Linear Displacement 73 4.3.2 Angular Displacement 73 4.4 Displacement Analysis 74 4.5 Displacement: Graphical Analysis 74 4.5.1 Displacement of a Single Driving Link 74 4.5.2 Displacement of the Remaining Slave Links 75 4.6 Position: Analytical Analysis 79 4.6.1 Closed-Form Position Analysis Equations for an In-Line Slider-Crank 81 4.6.2 Closed-Form Position Analysis Equations for an Offset SliderCrank 84 4.6.3 Closed-Form Position Equations for a Four-Bar Linkage 87 4.6.4 Circuits of a Four-Bar Linkage 87 4.7 Limiting Positions: Graphical Analysis 87 4.8 Limiting Positions: Analytical Analysis 91 4.9 Transmission Angle 93 4.10 Complete Cycle: Graphical Position Analysis 94 4.11 Complete Cycle: Analytical Position Analysis 96 4.12 Displacement Diagrams 98 4.13 Coupler Curves 101 Problems 101 Case Studies 108 5 Mechanism Design 109 Objectives 109 5.1 Introduction 109 5.2 Time Ratio 109 5.3 Timing Charts 110 5.4 Design of Slider-Crank Mechanisms 113 5.4.1 In-Line Slider-Crank Mechanism 113 5.4.2 Offset Slider-Crank Mechanism 114 5.5 Design of Crank-Rocker Mechanisms 115 5.6 Design of Crank-Shaper Mechanisms 117 5.7 Mechanism to Move a Link Between Two Positions 118 5.7.1 Two-Position Synthesis with a Pivoting Link 118 5.7.2 Two-Position Synthesis of the Coupler of a Four-Bar Mechanism 118 5.8 Mechanism to Move a Link Between Three Positions 119 5.9 Circuit and Branch Defects 119 Problems 120 Case Studies 121 6 Velocity Analysis 123 Objectives 123 6.1 Introduction 123 6.2 Linear Velocity 123 6.2.1 Linear Velocity of Rectilinear Points 123 6.2.2 Linear Velocity of a General Point 124 6.2.3 Velocity Profile for Linear Motion 124 6.3 Velocity of a Link 125 6.4 Relationship Between Linear and Angular Velocities 126 6.5 Relative Velocity 128 6.6 Graphical Velocity Analysis: Relative Velocity Method 130 6.6.1 Points on Links Limited to Pure Rotation or Rectilinear Translation 130 6.6.2 General Points on a Floating Link 132 6.6.3 Coincident Points on Different Links 135 6.7 Velocity Image 137 6.8 Analytical Velocity Analysis: Relative Velocity Method 137 6.9 Algebraic Solutions for Common Mechanisms 142 6.9.1 Slider-Crank Mechanism 142 6.9.2 Four-Bar Mechanism 142 6.10 Instantaneous Center of Rotation 142vi Contents 6.11 Locating Instant Centers 142 6.11.1 Primary Centers 143 6.11.2 Kennedy’s Theorem 144 6.11.3 Instant Center Diagram 144 6.12 Graphical Velocity Analysis: Instant Center Method 149 6.13 Analytical Velocity Analysis: Instant Center Method 152 6.14 Velocity Curves 155 6.14.1 Graphical Differentiation 157 6.14.2 Numerical Differentiation 159 Problems 161 Case Studies 168 7 Acceleration Analysis 170 Objectives 170 7.1 Introduction 170 7.2 Linear Acceleration 170 7.2.1 Linear Acceleration of Rectilinear Points 170 7.2.2 Constant Rectilinear Acceleration 171 7.2.3 Acceleration and the Velocity Profile 171 7.2.4 Linear Acceleration of a General Point 173 7.3 Acceleration of a Link 173 7.3.1 Angular Acceleration 173 7.3.2 Constant Angular Acceleration 173 7.4 Normal and Tangential Acceleration 174 7.4.1 Tangential Acceleration 174 7.4.2 Normal Acceleration 175 7.4.3 Total Acceleration 175 7.5 Relative Motion 177 7.5.1 Relative Acceleration 177 7.5.2 Components of Relative Acceleration 179 7.6 Relative Acceleration Analysis: Graphical Method 181 7.7 Relative Acceleration Analysis: Analytical Method 188 7.8 Algebraic Solutions for Common Mechanisms 190 7.8.1 Slider-Crank Mechanism 190 7.8.2 Four-Bar Mechanism 191 7.9 Acceleration of a General Point on a Floating Link 191 7.10 Acceleration Image 196 7.11 Coriolis Acceleration 197 7.12 Equivalent Linkages 201 7.13 Acceleration Curves 202 7.13.1 Graphical Differentiation 202 7.13.2 Numerical Differentiation 204 Problems 206 Case Studies 213 8 Computer-Aided Mechanism Analysis 215 Objectives 215 8.1 Introduction 215 8.2 Spreadsheets 215 8.3 User-Written Computer Programs 221 8.3.1 Offset Slider-Crank Mechanism 221 8.3.2 Four-Bar Mechanism 221 Problems 222 Case Study 222 9 Cams: Design and Kinematic Analysis 223 Objectives 223 9.1 Introduction 223 9.2 Types of Cams 223 9.3 Types of Followers 224 9.3.1 Follower Motion 224 9.3.2 Follower Position 224 9.3.3 Follower Shape 225 9.4 Prescribed Follower Motion 225 9.5 Follower Motion Schemes 227 9.5.1 Constant Velocity 228 9.5.2 Constant Acceleration 228 9.5.3 Harmonic Motion 228 9.5.4 Cycloidal Motion 230 9.5.5 Combined Motion Schemes 236 9.6 Graphical Disk Cam Profile Design 237 9.6.1 In-Line Knife-Edge Follower 237 9.6.2 In-Line Roller Follower 238 9.6.3 Offset Roller Follower 239 9.6.4 Translating Flat-Faced Follower 240 9.6.5 Pivoted Roller Follower 241 9.7 Pressure Angle 242 9.8 Design Limitations 243 9.9 Analytical Disk Cam Profile Design 243 9.9.1 Knife-Edge Follower 244 9.9.2 In-Line Roller Follower 246 9.9.3 Offset Roller Follower 249 9.9.4 Translating Flat-Faced Follower 249 9.9.5 Pivoted Roller Follower 250Contents vii 9.10 Cylindrical Cams 251 9.10.1 Graphical Cylindrical Cam Profile Design 251 9.10.2 Analytical Cylindrical Cam Profile Design 251 9.11 The Geneva Mechanism 252 Problems 254 Case Studies 258 10 Gears: Kinematic Analysis and Selection 260 Objectives 260 10.1 Introduction 260 10.2 Types of Gears 261 10.3 Spur Gear Terminology 262 10.4 Involute Tooth Profiles 264 10.5 Standard Gears 266 10.6 Relationships of Gears in Mesh 268 10.6.1 Center Distance 268 10.6.2 Contact Ratio 269 10.6.3 Interference 270 10.6.4 Undercutting 271 10.6.5 Backlash 272 10.6.6 Operating Pressure Angle 273 10.7 Spur Gear Kinematics 273 10.8 Spur Gear Selection 275 10.8.1 Diametral Pitch 276 10.8.2 Pressure Angle 276 10.8.3 Number of Teeth 276 10.9 Rack and Pinion Kinematics 281 10.10 Helical Gear Kinematics 282 10.11 Bevel Gear Kinematics 285 10.12 Worm Gear Kinematics 286 10.13 Gear Trains 288 10.14 Idler Gears 290 10.15 Planetary Gear Trains 290 10.15.1 Planetary Gear Analysis by Superposition 291 10.15.2 Planetary Gear Analysis by Equation 293 Problems 295 Case Studies 299 11 Belt and Chain Drives 302 Objectives 302 11.1 Introduction 302 11.2 Belts 302 11.3 Belt Drive Geometry 304 11.4 Belt Drive Kinematics 305 11.5 Chains 308 11.5.1 Types of Chains 308 11.5.2 Chain Pitch 309 11.5.3 Multistrand Chains 309 11.5.4 Sprockets 310 11.6 Chain Drive Geometry 310 11.7 Chain Drive Kinematics 311 Problems 313 Case Studies 315 12 Screw Mechanisms 316 Objectives 316 12.1 Introduction 316 12.2 Thread Features 316 12.3 Thread Forms 316 12.3.1 Unified Threads 317 12.3.2 Metric Threads 317 12.3.3 Square Threads 317 12.3.4 ACME Threads 317 12.4 Ball Screws 317 12.5 Lead 317 12.6 Screw Kinematics 318 12.7 Screw Forces and Torques 322 12.8 Differential Screws 324 12.9 Auger Screws 325 Problems 325 Case Studies 328 13 Static Force Analysis 330 Objectives 330 13.1 Introduction 330 13.2 Forces 330 13.3 Moments and Torques 330 13.4 Laws of Motion 333 13.5 Free-Body Diagrams 333 13.5.1 Drawing a Free-Body Diagram 333 13.5.2 Characterizing Contact Forces 333 13.6 Static Equilibrium 335 13.7 Analysis of a Two-Force Member 335 13.8 Sliding Friction Force 341 Problems 343 Case Study 345 14 Dynamic Force Analysis 346 Objectives 346 14.1 Introduction 346viii Contents 14.2 Mass and Weight 346 14.3 Center of Gravity 347 14.4 Mass Moment of Inertia 348 14.4.1 Mass Moment of Inertia of Basic Shapes 348 14.4.2 Radius of Gyration 350 14.4.3 Parallel Axis Theorem 350 14.4.4 Composite Bodies 351 14.4.5 Mass Moment of Inertia— Experimental Determination 352 14.5 Inertial Force 352 14.6 Inertial Torque 357 Problems 363 Case Study 366 Answers to Selected Even-Numbered Problems 367 References 370 Index 371 370 REFERENCES 1. Barton, Lyndon, Mechanism Analysis: Simplified Graphical and Analytical Techniques, 2nd ed., Marcel Dekker Inc., New York, 1993. 2. Baumeister, Theodore III, Avallone, Eugene, and Sadegh, Ali, Mark’s Standard Handbook for Mechanical Engineers, 11th ed., McGraw-Hill Book Company, New York, 2006. 3. Chironis, Nicholas and Sclater, Neil, Mechanisms and Mechanical Drives Sourcebook, 4th ed., McGraw-Hill Book Company, New York, 2007. 4. Erdman, Aurthur, Sandor, George, and Kota, Sridhar, Mechanism Design, Vol 1: Analysis and Synthesis, 4th ed., Prentice Hall, Upper Saddle River, NJ, 2001. 5. Kepler, Harold, Basic Graphical Kinematics, 2nd ed., McGraw-Hill Book Company, New York, 1973. 6. Jensen, Preben, Cam Design and Manufacture, 2nd ed., Marcel Dekker, New York, 1987. 7. Jensen, Preben, Classical Modern Mechanisms for Engineers and Inventors, Marcel Dekker, Inc., New York, 1991. 8. Jones, Franklin, Holbrook, Horton, and Newell, John, Ingenious Mechanisms for Designers and Inventors, Vols. I–IV, Industrial Press Inc, New York, 1930. 9. Mabie, Hamilton and Reinholtz, Charles, Mechanisms and Dynamics of Machinery, 4th ed., John Wiley and Sons Inc., New York, 1987. 10. Martin, George, Kinematics and Dynamics of Machines, 2nd ed., Waveland Press Inc., Long Groove, IL, 2002. 11. Norton, Robert, Design of Machinery, 4th ed., McGraw-Hill Book Company, New York, 2008. 12. Uicker, John, Pennock, Gordon, and Shigley, Joseph, Theory of Machines and Mechanisms, 4th ed., Oxford University Press, New York, 2010. 13. Townsend, Dennis and Dudley, Darle, Dudley’s Gear Handbook, 2nd ed., McGraw-Hill Book Company, New York, 1991. 14. Waldron, Kenneth and Kinzel, Gary, Kinematics, Dynamics, and Design of Machinery, 2nd ed., John Wiley and Sons Inc., Hoboken, NJ, 2004. 15. Wilson, Charles and Sadler, Peter, Kinematics and Dynamics of Machinery, 3rd ed., Pearson Education, Upper Saddle River, NJ, 2003. 16. Working Model Demonstration Guide, Knowledge Revolution Inc., San Mateo, CA, 1995.A Absolute motion, 128 Acceleration. See also Coriolis acceleration, Normal acceleration, Relative acceleration, Tangential acceleration, Total acceleration analysis of, 175 general summary problems, 206 kinematic analysis, 2 paths of, 179–180, 180i point of interest, 4 vector, 43 velocity profile, 178–179, 179t, 206–207, 207i Working Model, 208i–209i, 213 Acceleration curves description of, 202 graphical differentiation, 202–203, 203i numerical differentiation, 204–205, 205 summary problems, 206i–209i, 212–213 Acceleration images, description of, 196–197 ACME thread types, 314, 315i, 317t Actuators definition of, 4 role of, 12–13 types of, 12–13 Addendum, gear terminology, 260, 260i, 263i Air/hydraulic motors, actuator type, 12 Algebraic solution, common mechanism, 142, 190–191 American Gear Manufacturer’s Association (AGMA) diametrical pitch, 261 gear quality, 273, 273t gear standardization, 264–266, 264t American National Standards Institute (ANSI), gear standardization, 265 Analytical method cam follower displacement diagrams summary problems, 253–254 cycle position analysis, 96–98, 97i, 98i cylindrical cam profile design, 250, 255 disk cam profile design, 242–249, 243i–245i, 247i, 249i disk cam profile design summary problems, 254i–255i, 255 displacement analysis, 79, 79i, 80–81 displacement analysis summary problems, 101i–105i, 106 instant center location summary problems, 162i–164i, 164–165 instant center method, 123, 152, 153i instant center method summary problems, 162i–164i, 165 limiting positions analysis, 91–93, 92i limiting positions summary problems, 101i–105i, 105–106 mechanism analysis technique, 24 motion curves summary problems, 254 relative acceleration analysis, 188i, 188–190, 190t relative acceleration summary problems, 208i–209i, 210 relative velocity method, 137–141, 138i, 140i, 140i relative velocity method summary problems, 162i–164i, 164–165 vector component addition, 53–55, 54i, 54t vector component subtraction, 55–60, 56i–57i, 59t vector magnitude determinations, 66–71, 67i–70i, 66t vector triangle addition, 50–51, 51i, 53–54, 59–60, 59i, 759, 69, 69i vector triangle subtraction, 57i, 55–57 velocity curves summary problems, 162i–164i, 165 Angle method, 50–51 Angle of contact belt drive, 303–304, 303t chain drive, 308–309 Angular acceleration, 173, 174i Angular displacement, 73, 73i Angular inertia of a body, 355 Angular position vector, 72–73 Angular velocity and linear velocity, 126–127, 127i links, 125–126, 126i and relative velocity, 128–129 Annular gears, 259 “Archimedes Screw,” See Auger screws Assembly circuit branch defect, 120 circuit defect, 119 Auger screws, 323, 323i Automatic Dynamic Analysis of Mechanical Systems (ADAMS), 24, 31 Avoirdupois pound, 328 B Backlash gear mesh relationship, 270–271 gear terminology, 260 Ball screws, 315, 317i, 321 Base circle cam profile design, 237, 237i gear terminology, 260i, 262i–263i Base diameter, 260 Bellcrank, 3i, 4 Belt drive geometry, 302–303, 302i, 311 Belt drive kinematics, 303–306, 303i, 305i, 311 Belt drives description of, 300–301 selection summary problems, 310 types of, 300–301 Belt length, 302, 303t Belt speed, 303–304 Belts, 300–302, 301i–302i, 301t Bevel gear kinematics, 283–284, 283i Bevel gears, 259–260, 259i, 283 Bull gear, 266 INDEX Note: The letter ‘i’ and ‘t’ followed by locators refers to illustrations and tables cited in the text 371 C Cam follower displacement diagrams analytical summary problems, 253–254 description of, 224–225, 238i graphical summary problems, 252–253 Cam followers, 223 motion scheme nomenclature, 227–228 prescribed motion, 225–226 types of, 224–225, 224i Cam followers motion scheme constant acceleration, 228, 228t, 229t, 230i constant velocity, 228, 228t cycloidal motion, 230–236, 233i, 234i, 235i, 236i harmonic motion, 228–230, 228t, 230i Cam joint definition of, 3, 3i kinematic diagram symbol, 5t–6t Cams description of, 223, 224i, 226–227, 226i, types of, 223–224, 224i Case studies acceleration analysis, 213–214, 213i–214i belt/chain drives, 312–313, 312i–313i cam design/analysis, 255–257, 256i–257i displacement/position analysis, 108, 108i dynamic force analysis, 364, 364i gears, 297–299, 298i–299i kinematic motion/classification, 29–30, 30i machine analysis, 42, 42i machine design, 121–122, 121i–122i screw mechanisms, 326–327, 326i–327i spread sheets, 222, 222i static force analysis, 343, 343i vectors, 71, 71i velocity, 168–169, 168i–169i Center distance belt drive, 302–303 chain drive, 308–309, 308i gear mesh relationship, 266i, 267 Center of gravity, 345–346, 345i, 346t Chain drive description of, 300, 306–309 selection summary problems, 312 Chain drive geometry, 308i, 308–309, 312 Chain drive kinematics, 309–310, 309 Chain length, 308–309, 308i Chain pitch, 307, 307t Chain speed, 309 Chains, types of, 306i, 306–307 Change point, 19t, 20, 21 Circular pitch, 260, 260i Clearance, 260 Clockwise, 125 Closed-form position analysis four-bar linkage, 87 in-line slider-crank, 81–83, 81i–82i offset slider-crank, 84–86, 84i–85i Coarse pitch, 261t, 264t Cog belt, 301, 301iCoincident joint, 16–18 Combined motion schemes comparisons, 237t computer software for, 236 description, 236 goals of, 236 jerk, 236 modified sinusoidal acceleration, 237 modified trapezoidal acceleration, 236 polynomial displacement, 236 trapezoidal acceleration, 236 Common mechanisms, algebraic solutions, 142, 190–191 Common units, 173, 329, 346, 348 Commutative law of addition, 49 Complex link, 3i, 4 Component method analytical addition, 53–55, 754i, 54t analytical subtraction, 59–60, 59i, 59t Components, 4, 12 Composite bodies, 349–350, 349i Computer methods/programs dynamic analysis programs, 31 mechanism analysis technique, 24–25 user–written programs, 221–222, 221i value of, 31 Computer-aided design (CAD) systems mechanism analysis technique, 24–25 vector analysis, 44 Configuration, 74–75 Connecting arm, 19 Constant acceleration, 228, 229i–230i, 229t Constant angular acceleration, 173–174, 174i Constant rectilinear acceleration, 171 Constant velocity, 228, 228t Contact forces, 331–332, 331i, 339–340 Contact line, 262 Contact ratio, 267–268 Coriolis acceleration description of, 197–201 summary problems, 210–212, 210i–211i Cosine, 44, 47 Counterclockwise, 126 Coupler, 19 Coupler curve, 101, 101i Crank definition of, 3–4, 3i eccentric, 14, 14i slider-crank mechanism, 22 Crank-rockers circuits of, 87, 87i four-bar mechanism, 19–20, 19t, 20i, 22 machine design, 115–117, 117i summary problems, 120 Crank-shapers analytical methods, 118 graphical procedure, 117–118 machine design, 117–118, 117i summary problems, 120 Cross drives, 303, 303i Crossed helical gears, 280 Cycle analysis analytical position, 96, 97i, 99, 100i description of, 94 displacement diagram, 101–106, 101i–105i graphical position, 94–96, 94i–96i Cycloidal motion, follower motion scheme, 230–236, 231t–232t, 231i–236i Cylinders, actuator type, 4 Cylindrical cams analytical profile design, 250 description of, 224, 224i, 362 graphical profile design, 249–250, 250ii D D’Alembert’s principle, 351 Dedendum, 260i, 260 Degree of freedom beer crusher computation, 10i, 10–11 description of, 8 equation for, 74 four-bar mechanism calculation, 19, 19i lift table computation, 15–16, 15i–16i mechanism types, 8, 8i outrigger computation, 13–14, 13i–14i shear press computation, 11–12, 11i–12i toggle clamp computation, 9i, 9–10 Degree of freedom mechanical press, 17–18, 17i–18i Diametral pitch gear terminology, 261 spur gear selection, 273–279, 273t, 276i, 278i Differential screw, description of, 322–323, 322i–323i, 326 Disk cam profile design analytical method, 242–249 design limitations, 241–242, 242i flat-faced follower, 239–240, 239i graphical features, 237i, 237 in-line knife-edge follower, 238i, 237–238 in-line roller follower, 238i, 238 offset roller follower, 239, 239i pivoted roller follower, 240–241, 240i Disk cams, 223–224, 224i Displacement analytical method, 79–81, 80i analytical summary problems, 101i–105i, 106 description of, 74 general summary problems, 101, 101i–105i and linear velocity, 123 graphical driver analysis, 74i, 74–75 graphical problems, 76–78, 76i, 78i–79i, 80 graphical slave links analysis, 75–76, 75i, 76i graphical summary problems, 101–106, 101i–105i kinematic analysis, 2 point of interest, 4 types of, 73 vector, 43 Working Model problems, 101i–103i, 105i, 107–108 Displacement diagrams. See also Cam follower displacement diagrams cycle position analysis, 98–99, 99i–100i summary problems, 101i–103i, 105i, 107 velocity curves, 155, 156i, 157–158, 158i Double crank, 20, 19t, 20i Double enveloping worm gear set, 284, 285i Double rocker, 20, 19t, 20i Drafting as technique, 24 vector analysis, 43–44 Driver, 98 Driver link mechanism analysis, 73 position analysis, 74i, 74–75 Driver point, 73 372 Index Drivers, 12–13, 15 Drum cam, 224, 224i Dynamic Analysis of Dynamic Systems (DADS), dynamic analysis program, 31 Dynamic equilibrium, 328 Dynamic force analysis design questions, 2 purpose of, 344 static force analysis, 343, 343i and static equilibrium, 328 strategy for, 31 Dynamic force analysis programs, 24 E Eccentric crank, 14, 14i Efficiency, 321 Elastic parts, 2 Electric motors, 12 Engines, actuator type, 4, 12 Enveloping worm gear teeth, 284, 285i Epicyclic train, 288–293, 289i Equilibrium, 333–338, 334i–337i Equivalent linkage, 201 F Face width, 260i, 260 Fine pitch, 315, 316t Flat belt, 300, 301i Flat-faced follower analytical profile design, 248 description of, 224i, 225 profile design, 239–240, 239i Floating link relative acceleration analysis, 191i, 191–192, 193i–194i, 195–196 relative acceleration summary problems, 210, 210i relative velocity method, 132–135, 133i–134i Follower, 19. See also Cam followers Follower motion, 224, 224i Follower position, 224–225, 224i Follower shape, 224i, 225 Foot-pound, 328–329 Force definition of, 328 screw mechanisms, 320i–321i, 320–322 summary problems, 341, 341i vector, 43 Force analysis. See also Dynamic force analysis, Static force analysis and acceleration, 170 machine design, 1 Formula, spreadsheets, 215–218, 217i–218i Four-bar linkage, 87 Four-bar mechanisms algebraic solutions, 142, 190–191 categories of, 19t, 19–20 circuits of, 87, 87i coupler two–point synthesis, 119i, 118–119 description of, 19, 19i Grashof’s theorem, 19 motion classification, 20–21, 21i, 29, 29i nomenclature, 19 three-point synthesis, 119, 119i transmission angle, 93–94, 94i user-written programs, 221i, 221–222 Working Model tutorial, 32–37, 33i–34i, 36iFrame definition of, 2 four-bar mechanism, 19 kinematic diagram, 8 Free-body diagrams, 331–333, 331i–333i Friction coefficients of, 339, 339t force analysis, 1 screw mechanisms, 320 Friction force, 339 Full joints, 3, 3i G Gear joint, 3, 3i, 5t–6t Gear kinematics gear function, 271–273, 271i–272i, 293 Gear mesh relationship backlash, 270–271 center distance, 266–267, 266i contact ratio, 267–268 interference, 268–269, 268t operating pressure angle, 271 undercutting, 269–270, 270i Gear rack, 259, 259i, 262, 279 Gear selection, 294 Gear standardization, 264–266, 264t Gear trains description of, 286–288, 286i design summary problems, 296 summary problems, 295i–296i, 295–296 Gear-driven mechanisms, summary problems, 296, 296i Gears description of, 258–259, 258i–259i terminology, 260i, 260–262, 261t, 262i types of, 259–260, 259i, 284 General triangles, 46–48, 47i, 48i Geneva mechanism, 250–252, 250i, 252i, 255 Graphical analysis cam follower displacement diagrams summary problems, 252–253 cycle position, 94–96, 94i–96i cylindrical cam profile design, 250, 250i disk cam profile design, 237–242, 237i–242i disk cam profile design summary problems, 254i–255i, 254–255 displacement, 74–79, 74i–79i displacement diagrams summary problems,102i–105i, 107 displacement summary problems, 101–106, 101i–105i driver link displacement, 74i instant center location summary problems, 162i–164i, 165 instant center method, 123, 149–152, 150i, 152i instant center method summary problems, 162i–164i, 166 limiting positions, 88i, 87–88 mechanism analysis, 23–24 relative acceleration analysis, 181–187, 182i–183i, 185i–186i relative acceleration summary problems, 208–209, 208i–209i relative velocity method, 130–137, 130i–131i, 133i–136i relative velocity method summary problems, 162–164, 162i–164i slave links displacement, 75–76, 75i–76i vector addition, 48–50, 49i–50i vector magnitudes, 63–65, 63i–65i, 70–71, 70i–71i vector subtraction, 55–57, 55i–57i Graphical differentiation acceleration curves, 202–203, 203i velocity curves, 157i, 157 velocity curves summary problems, 162i–164i, 167 Graphical disk cam profile design features of, 237i, 237 flat-faced follower, 239–240, 239i in-line knife-edge follower, 238i, 237–238 in-line roller follower, 238i, 238 offset roller follower, 239, 239i pivoted roller follower, 240–241, 240i Grashof’s theorem, 19 Gruebler’s equation description of, 8 exceptions to, 18 special cases, 16–18, 16i–18i Gyration radius, 348 H Half joint, 3, 3i Harmonic motion, 228–230, 228t–229t, 229i–230i Helical gear kinematics, 280–282, 281i, 281t–282t Helical gears, 259, 259i, 294–295 Helix angle, 280, 281i Herringbone gears, 259, 259i Higher order joint, 3, 3i Hinge joint, 3, 3i Home position, 237, 237i Hydraulic cylinders, 13i, 12–13 Hydraulic motors, 12 I Idler gears, 288i, 288 Idler pulley, 301 In-line follower, 225, 224i In-line knife-edge follower, 238i, 237–238 In-line roller follower analytical profile design, 245–247, 245i, 247i graphical profile design, 238i, 238 In-line slider-crank closed-form analysis, 81–83, 81i–82i machine design, 113–114, 114i Inch-pound, 329 Included angle screw efficiency, 321 thread feature, 314, 314i Inertia, 170, 328 Inertia-force method of dynamic equilibrium, 351 Inertial forces description of, 350–355, 351i–352i, 354i summary problems, 362, 362i Inertial torques description of, 355–361, 355i–357i, 359i summary problems, 362–363, 362i–363i Input link, 19 Instant center, 142, 142i Instant center diagram, 144–145, 145i Instant center method Index 373 analytical velocity method, 123, 152–154, 153i analytical velocity method summary problems, 162i–164i, 166–167 graphical velocity method, 123, 149–152, 150i, 152i graphical velocity method summary problems, 162i–164i, 166 Instant centers locating, 142–149, 143i–149i, 146t, 148t summary problems, 162i–164i, 165–166 Instantaneous center of rotation, 142 Interference, 268–269, 268t Internal angle triangle addition problem, 51 triangle subtraction problem, 57–58, 58i Internal gears, 259, 259i International Organization for Standardization (ISO) force unit, 328 metric threads, 315 moment unit, 329 Inverted tooth/silent chain, 306i, 307 Involute tooth profile, 262–264, 262i, 263i J Joint, definition of, 3, 3i Joints coincident, 16i, 16–17 commonly used, 14–15 K Kennedy’s theorem, instant centers, 144–146, 147 Kinematic analysis, 1i, 2, 3 Kinematic diagram four-bar mechanism, 19, 19i manual water pump, 22 symbol system, 4, 5t–6t Kinematic diagram problems beer crusher, 10i, 10–11 lift table, 15i–16i, 15–16 mechanical press, 17i–18i, 17–18 nose wheel assemble, 20–21, 21i outrigger, 13–14, 13i–14i shear presses, 6–7, 6i–7i, 11–12, 11i–12i sketching diagrams, 25–28, 25i–28i toggle clamp, 9i, 9–10 vice grip, 7, 7i Kinematic inversion, 8 Kinematics, 2 Knife-edge follower analytical profile design, 242–244, 243i–244i description of, 224i, 225 L Law of cosines, oblique triangles, 46 Law of sines, oblique triangles, 46 Lead, 315–316 Lead angle screw threads, 316 thread feature, 314, 314i worm gears, 284, 285i Limiting positions analytical analysis, 91–93, 92i definition of, 87, 88iLimiting positions (Continued) graphical analysis, 88i, 87–88 graphical analysis problems, 88–91, 88i–90i summary problems, 101i–105i, 106–107 Line of center, 149, 150i Line of contact, 262, 262i Line of proportion, 149, 150i Linear acceleration, 170–173 Linear cam, 224, 224i Linear displacement, 73 Linear motion, 125i, 124–125 Linear velocity and angular velocity, 126–127, 127i definition of, 123 general point, 124, 124i rectilinear points, 124i, 123–124 Link, angular position, 72 Linkage acceleration. See also Timing charts Linkage, definition of, 2 Linkage velocity analysis. See also Timing charts Links acceleration analysis, 170, 173–174, 210, 210i angular velocity, 125–126, 126i commonly used, 14 definition of, 2 four-bar mechanism tutorial, 32–33, 33i relative velocity method, 130i, 130–135, 131i, 133i–134i resizing, 33 slider-crank mechanism tutorial, 37–38, 38i types of, 3 Locked mechanism, 8, 8i Long and short addendum system, 269 Lowering a load (screw drive), 321 Lubrication, chain drive kinematics, 309 M Machine design crank-shaper, 117–118, 117i crank-rocker, 115, 116i, 117, 120 slider-crank ratio, 113–115, 114i–115i, 120 three point synthesis, 119, 119i, 121 time ratio problems, 109–110, 120 two position links, 118–121, 118i–119i Machines, 1 Magnitude, 73, 73i Magnitude direction triangle addition, 52 triangle subtraction, 57, 58i Major diameter, 314, 314i Manual force, 13 Mass, 344, 361–362, 361i–362i Mass moment of inertia basic shapes, 346, 347i, 347t, 348 composite bodies, 349i, 349–350 description of, 346, 346i experiential determination, 350, 350i parallel axis theorem, 348i, 348–349 radius of gyration, 348 summary problems, 361–362, 361i–362i Mechanism basic components of, 2–4, 3i definition of, 1–2 degrees of freedom computation, 74 motion analysis, 73 phases of, 80 vectors, 43 Mechanism analysis, 2, 23 Metric thread, 314–315, 315i, 317t Minor diameter, 314, 314i Miter gears, 260, 259i, 283 Mobility (M) equation, 8 equation exceptions, 18 special cases, 16–18, 16i–18i Mobility (M) calculation can crusher, 11 four-bar mechanism, 19 graphical displacement analysis, 76 lift table, 16 manual water pump, 22 mechanical press, 17–18 outrigger, 14 shear press, 12 sketching diagrams, 25i–29i, 29 toggle clamp, 9–12, 14 Module, 261, 261t Moment description, 328–331, 329i–330i summary problems, 341, 341i Moment of inertia basic shapes, 346–348, 347i, 347t composite bodies, 349i, 349–350 description of, 346, 346i experiential determination, 350, 350i parallel axis theorem, 348i, 348–349 radius of gyration, 348 summary problems, 361–362, 361i Motion laws of, 331, 350 mechanism analysis, 1, 1i, 73 Motor actuator types, 4 four-bar mechanism tutorial, 35–36 slider-crank mechanism tutorial, 41 Multiple threads, 315–316, 317i Multiple-strand roller chain, 306, 306i Multi-strand chains, 307, 307t Multi-V-belt, 300, 301i N Newton, force magnitude unit, 328 Newton, Sir Isaac, 170, 331 Normal acceleration acceleration analysis, 174–177, 175i–176i description of, 173, 173i summary problems, 206–207, 207i Normal circular pitch, 281, 281i Normal diametral pitch, 281 Normal force, 339 Normal module, 281 Normal pressure angle, 281 Normal section, 281, 281i Numerical differentiation acceleration curves, 204–205, 205i velocity analysis, 159–160, 160i O Oblique triangle, 46–48, 46i–48i Offset follower, 225, 224i Offset roller follower analytical profile design, 248 graphical profile design, 239, 239i Offset sidebar roller chain, 306i, 307 374 Index Offset slider-crank, 221i, 221 closed-form analysis, 84–87, 84i–85i machine design, 114–115, 115i Off-set slider crank Mechanism, 221i, 221 Open, 32 Open-loop linkages, 8, 8i Operating pressure angle, 271 Output link, 19 P Parallel axis theorem, 248i, 348–349 Parallelogram mechanisms, 22, 23i Phase, 94 Pin, 3, 3i Pin joint kinematic diagram symbol, 5t four-bar mechanism tutorial, 33–35, 34i slider-crank mechanism tutorial, 38–41, 40i Pin-in-a-slot joint, commonly used, 14, 15i Pinion, 266, 266i. See also Gear rack Piston, 3, 3i Pitch thread features, 315, 315i worm gears, 284, 285i Pitch circle, 260, 260i, 262, 262i Pitch curve, 237, 237i Pitch diameter belt drive, 301i–302i, 302–303 chain drive, 308, 308i gear terminology, 260, 260i thread feature, 314, 314i Pitch line gear terminology, 262, 262i spur gear kinematics, 271, 271i Pitch point, 260 Pivot link, 118i, 118 Pivoted followers, 224, 224i Pivoted roller follower analytical profile design, 249i, 248–249 profile design, 240–241, 240i Planar mechanism, 2 Planet gear, 288, 289i Planetary gear analysis equation, 291–292 summary problems, 292–293 superposition, 289 summary problems, 289–291 Planetary gear trains description of, 288–293, 289i, 290t–291t, 291i summary problems, 297, 297i Plate cams, 224, 224i Pneumatic cylinders, 13i, 12–13 Point (P), 73i, 72–73 Point of interest, 4 Point of interest path, 37, 37i Point position measurement, 36–37 Points linear acceleration, 173 linear velocity, 124, 124i relative acceleration analysis, 274, 191–196, 191i–194i relative acceleration summary problems, 210, 210i Points/floating link, 132–135, 133i–134i Points/multiple, relative velocity method, 135–137, 135i–136i Points/one link, relative velocity method, 130–132, 130i–131iPoints of interest four-bar mechanism tutorial, 33, 34i slider-crank mechanism tutorial, 55i Position, 2, 72 Position analysis analytical displacement, 80i, 80–81 graphical displacement, 74–76, 74i–76i graphical displacement problems, 76–79, 76i–79i in-line slider-crank, 81, 81i limiting positions, 91–93, 92i offset slider crank, 84, 84i purpose of, 72i, 72 Position vector, 73i, 72 Pound, 328 Pressure angle description of, 241, 241i gear terminology, 262, 262i spur gear selection, 274–279, 276i, 278i Primary centers locating problems, 145–149, 145i–149i, 146t, 148t rules of, 203i, 143–144, 143i–144i Primary joints, 3, 3i Prime circle, 237, 237i Prismatic joint, 3, 3i Pulleys, 301i, 301, 301t Pythagorean theorem, 45 Q Quick-return mechanisms, 23, 23i R Rack, 259, 259i, 279 Rack and pinion kinematics, 279–280, 280i, 294 Radian, description of, 125–126 Rectilinear points linear acceleration, 170–171 linear velocity, 123–124, 124i, Rectilinear translation, 130–132, 130i–131i Relative acceleration components, 179–181, 180i, 197–201, 197i–200i description of, 177–179, 178i, 179t summary problems, 207i, 207–208 Relative acceleration analysis analytical method, 188i, 188–190, 190t analytical summary problems, 208i–209i, 209–210 graphical method, 181–187, 182i–183i, 185i–186i graphical summary problems, 208–209, 208i–209i Relative displacement, 317 Relative motion definition of, 177 description of, 128, 177 Relative velocity, 128–129, 128i, 129i Relative velocity method analytical method, 137–141, 138i, 140i analytical method summary problems, 162i–164i, 164–165 graphical analysis, 130–137, 130i–131i, 133i–136i graphical analysis summary problems, 162–164, 162i–164i velocity analysis, 123, 137–141, 138i, 140i velocity image, 137, 137i Resultant definition of, 49 graphical addition problems, 49, 49i, 50 graphical subtraction problem, 56–57, 57i Resultant components, 53–55, 54i Resultant force, summary problems, 341, 341i Resultant magnitude triangle addition problem, 51 triangle subtraction problem, 58, 58i Reversible gearset, 285 Revolute joint, 3, 3i Richardson method (numerical differentiation) acceleration curves, 204 velocity curves, 159 Right triangle, 44–46, 44i–46i Ring gear, 288, 289i Rocker, 3i, 4 Rocker arm link, 4 Roller chain, 306, 306i Roller follower, 224i, 225 Rotation instantaneous center of, 142, 142i kinematic analysis, 2 relative velocity method, 130–132, 130i–131i S Scalar quantities, 43 Scotch Yoke mechanism, 23, 23i Screw actuators, 13 Screw forces/torques, 320–322, 320i–321i, 326 Screw joints, 15, 15i Screw kinematics, 316–320, 318i–320i Screw mechanisms, 314 Screw thread, 315, 314i–315i, 323–324 Screw-driven acceleration, 326, 324i–325i Screw-driven displacement, 324–325, 324i–325i Screw-driven velocity, 325–326, 324i–325i Self-locking, 316 Serpentine drives, 303, 303i Servomotors, 12 Shaft angle, 283, 283i Sheaves, 301i, 301, 301t Simple link, 3, 3i, 5t Simulation four-bar mechanism, 32–37, 33i–37i slider-crank mechanism tutorial, 37–41, 38i–40i Sine, 44, 46 Sketching, practice problems, 25–28, 25i–28i Slave links, 75–76, 75i–76i Slider-crank transmission angle, 93–94, 94i Slider joint, symbol, 6t Slider-crank mechanisms algebraic solutions, 142, 190–191 description of, 22 limiting positions, 88i machine design, 113–115, 114i–115i summary problems, 120 Working Model tutorial, 37–41, 38i–40i Sliding friction force, 339t, 339i–340i, 339–341 Sliding joint, 3, 3i Sliding link, 38, 38i–39i Slot joints, 38, 39i Slug, derivation of, 344 Software. See Computers methods/programs Solenoids, actuator type, 4 Speed, 2 Index 375 Spherical-faced follower, description of, 224i, 225 Spreadsheets acceleration curves, 205i cycle position analysis, 97, 98i cycloidal motion, 235i displacement curve, 155, 156i displacement diagram, 100i general description, 215–220, 215i–220i in-line roller follower design, 247i knife-edge follower design, 244i mechanism analysis technique, 24 summary problems, 222 velocity analysis, 160i Sprocket, 307, 307i, 308t Spur gear geometry, summary problems, 293 Spur gear kinematics gear function, 271–273, 271i–272i summary problems, 293 Spur gear selection diametral pitch, 273–279, 273t, 276i, 278i pressure angle, 274–279, 276i, 278i set center distance summary problems, 294 teeth number, 274–279, 276i, 278i Spur gears gear type, 259, 259i terminology, 260i, 260–262, 261t Square thread, 314–315, 315i Static equilibrium conditions of, 333 definition of, 328 Static machine forces, summary problems, 341–343, 341i–343i Straight-line mechanisms, 22 Peaucellier-Lipkin linkage, 22i Watt linkage, 22i Stroke, 88i, 88 Stub teeth, 269 Sun gear, 288, 289i Superposition method, 289 Swing arm followers, 224, 224i Synthesis, 109 T Tangent, right triangle, 44 Tangential acceleration acceleration analysis, 174–175 description of, 173, 173i, 175–177, 176i summary problems, 206–207, 207i Tangential velocity, 126 Teeth. See also Involute tooth profile chain drive, 308, 308i gear terminology, 260–262 spur gear selection, 273–279, 274t–275t, 276i, 278i worm gears, 284, 285i Thread features, 314, 314i Thread forms, 314–315, 315i, 316t–317t Thread number, 315–316, 317i Three-point synthesis, machine design, 119, 119i, 121 Throw angle, 115 Time ratio, 109–110, 120 Timing belt, 301, 301i Timing charts problems, 112–113 uses of, 110–111, 111i Tip-to-tail method, 48Torque definition of, 328, 329i screw mechanisms, 320–322, 320i–321i Total acceleration, 175–177, 176i Trace, 101 Trace point, 237, 237i Translating followers, 224, 224i Transmission angle definition, 93 mechanical advantage, 93 Transverse section, 281, 281i Triangles summary problems, 67–69, 67i–68i trigonometric relationships, 44, 44i types of, 44, 46 vector addition, 50–51, 51i vector subtraction, 57–60, 58i–60i, 59t Trigonometry, 44 Triple rocker, 19t, 20, 20i Truss, 8, 8i Two-armed synchro loader, 4, 5t Two-force member, 333–338, 334i–337i Two-point synthesis coupler of four-bar mechanism, 119i, 118–119 design class, 118 pivot link, 118–119, 118i–119i single pivot summary problems, 120–121 two pivots summary problems, 121 U Undercutting, 269–270, 270i Unified thread, 314–315, 315i, 316t United States Customary System force unit, 328 mass/weight, 344 moment unit, 328–329 threads per inch, 314 V V-belt, belt type, 300–302, 301i–302i Vector analysis analytical magnitude determination, 66–67, 66i, 66t, 71, 71i component addition, 53–55, 54i, 54t component subtraction, 59–60, 59i–60i, 59t graphical addition, 48–50, 49i–50i graphical magnitude determination, 63–65, 63i–65i graphical subtraction, 55–57, 55i–57i triangle addition, 50–51, 51i, 53–55, 54i, 54t, 69i, 69 triangle subtraction, 58i, 57–58 Vector components, 52i, 52 Vector diagram graphical addition problems, 49–50, 49i–50i graphical subtraction problems, 55–56, 56i magnitude determination, 65, 63i–65i triangle addition problem, 51 triangle subtraction problem, 58–59, 58i Vector equations, 60, 60i analytical magnitude determination, 66–67, 71 application of, 62 formation of, 60–62, 61i–62i graphical magnitude determination, 63–65, 70–71 subtraction, 59 Vector magnitude analytical determination, 66–67, 66i, 66t, 71, 71i graphical determination, 63–65, 63i–65i, 70–71, 70i–71i Vector problems analytical addition, 51–55, 51i–52i, 54i, 54t, 69i, 69 analytical magnitude determination, 66–67, 66i, 66t, 70–71, 70i–71i analytical subtraction, 57–60, 58i–60i, 59t, 69i, 70 equations, 61–62, 70, 70i graphical addition, 49–50, 49i–50i, 69i, 69 graphical magnitude determination, 63–65, 63i–64i, 70i–71i, 70–71 graphical subtraction, 55–57, 55i–57i, 69i, 69 triangle addition, 51i, 51, 53 triangle subtraction, 59–60, 59i–60i, 59t Vectors addition methods, 43, 48–55, 48i–52i, 54i, 54t mechanism characteristics, 43 oblique/general triangles, 46–48 right triangle, 44–46, 44i subtraction methods, 55–60, 55i–60i, 59t triangle types, 44–48, 44i–48i, 47i–48i Velocity kinematic analysis, 2 point of interest, 4 summary general problems, 161, 161i summary relative problems, 162, 162i vector property, 43 Working Model, 162i–164i, 168 Velocity analysis algebraic solutions, 142 analytical methods, 137–141, 138i, 140i description of, 123 graphical methods, 130–137, 130i–131i, 133i–136i 376 Index graphical methods summary problems, 162–164, 162i–164i instant center analytical method, 123, 152, 153i instant center graphical analysis, 123, 149–152, 150i, 152i Velocity curves analytical summary problems, 162i–164i, 167–168 description of, 155–157, 156i graphical differentiation, 157–158, 157i–158i graphical summary problems, 162i–164i, 167 numerical differentiation, 159–161, 160i Velocity image, 137, 137i Velocity profile acceleration, 171–172, 172i linear motion, 125i, 124–125 Velocity ratio belt drive kinematics, 303 chain drive kinematics, 309 spur gear kinematics, 271–273, 271i–272i Volume, 323 Volumetric acceleration, 323 Volumetric flow, 323 W Weight, 344 Whole depth, 260 Windshield wiper system, design concept, 1, 1i Wipe pattern, components, 1 Working Model software acceleration, 208i–209i, 213 computer simulation software, 31 displacement problems, 101i–105i, 107–108 four-bar mechanism tutorial, 32–37, 33i–37i practice problems, 41–42, 41i–42i purchase information, 32 slider-crank mechanism, 37–41, 38i–40i velocity problems, 162i–164i, 168 Worm, 284 Worm gear kinematics, 284–286, 285i Worm gears, 259i, 260, 295 Worm pitch diameter, 284, 285i Worm wheel, 284 X X–axis angle addition, 53 angle subtraction, 59t component determination, 66, 66t rotational equation, 15
كلمة سر فك الضغط : books-world.net The Unzip Password : books-world.net أتمنى أن تستفيدوا من محتوى الموضوع وأن ينال إعجابكم رابط من موقع عالم الكتب لتنزيل كتاب Machines and Mechanisms Applied Kinematic Analysis - Fourth Edition رابط مباشر لتنزيل كتاب Machines and Mechanisms Applied Kinematic Analysis - Fourth Edition
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كاتب الموضوع | رسالة |
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rambomenaa كبير مهندسين
عدد المساهمات : 2041 تاريخ التسجيل : 21/01/2012
| موضوع: كتاب Machines and Mechanisms Applied Kinematic Analysis - Fourth Edition السبت 16 يونيو 2012, 6:33 am | |
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أخواني في الله أحضرت لكم كتاب Machines and Mechanisms Applied Kinematic Analysis Fourth Edition David H. Myszka University of Dayton
و المحتوى كما يلي :
CONTENTS 1 Introduction to Mechanisms and Kinematics 1 Objectives 1 1.1 Introduction 1 1.2 Machines and Mechanisms 1 1.3 Kinematics 2 1.4 Mechanism Terminology 2 1.5 Kinematic Diagrams 4 1.6 Kinematic Inversion 8 1.7 Mobility 8 1.7.1 Gruebler’s Equation 8 1.7.2 Actuators and Drivers 12 1.8 Commonly Used Links and Joints 14 1.8.1 Eccentric Crank 14 1.8.2 Pin-in-a-Slot Joint 14 1.8.3 Screw Joint 15 1.9 Special Cases of the Mobility Equation 16 1.9.1 Coincident Joints 16 1.9.2 Exceptions to the Gruebler’s Equation 18 1.9.3 Idle Degrees of Freedom 18 1.10 The Four-Bar Mechanism 19 1.10.1 Grashof’s Criterion 19 1.10.2 Double Crank 20 1.10.3 Crank-Rocker 20 1.10.4 Double Rocker 20 1.10.5 Change Point Mechanism 20 1.10.6 Triple Rocker 20 1.11 Slider-Crank Mechanism 22 1.12 Special Purpose Mechanisms 22 1.12.1 Straight-Line Mechanisms 22 1.12.2 Parallelogram Mechanisms 22 1.12.3 Quick-Return Mechanisms 23 1.12.4 Scotch Yoke Mechanism 23 1.13 Techniques of Mechanism Analysis 23 1.13.1 Traditional Drafting Techniques 24 1.13.2 CAD Systems 24 1.13.3 Analytical Techniques 24 1.13.4 Computer Methods 24 Problems 25 Case Studies 29 2 Building Computer Models of Mechanisms Using Working Model Software 31 Objectives 31 2.1 Introduction 31 2.2 Computer Simulation of Mechanisms 31 2.3 Obtaining Working Model Software 32 2.4 Using Working Model to Model a Four-Bar Mechanism 32 2.5 Using Working Model to Model a SliderCrank Mechanism 37 Problems 41 Case Studies 42 3 Vectors 43 Objectives 43 3.1 Introduction 43 3.2 Scalars and Vectors 43 3.3 Graphical Vector Analysis 43 3.4 Drafting Techniques Required in Graphical Vector Analysis 44 3.5 CAD Knowledge Required in Graphical Vector Analysis 44 3.6 Trigonometry Required in Analytical Vector Analysis 44 3.6.1 Right Triangle 44 3.6.2 Oblique Triangle 46 3.7 Vector Manipulation 48 3.8 Graphical Vector Addition 48 3.9 Analytical Vector Addition : Triangle Method 50 3.10 Components of a Vector 52 3.11 Analytical Vector Addition : Component Method 53 3.12 Vector Subtraction 55 3.13 Graphical Vector Subtraction 55 3.14 Analytical Vector Subtraction : Triangle Method 57 3.15 Analytical Vector Subtraction : Component Method 59 3.16 Vector Equations 60 (- 7) (- 7) (- 7) (- 7) (+ 7) (+ 7) (+ 7) ivContents v 3.17 Application of Vector Equations 62 3.18 Graphical Determination of Vector Magnitudes 63 3.19 Analytical Determination of Vector Magnitudes 66 Problems 67 Case Studies 71 4 Position and Displacement Analysis 72 Objectives 72 4.1 Introduction 72 4.2 Position 72 4.2.1 Position of a Point 72 4.2.2 Angular Position of a Link 72 4.2.3 Position of a Mechanism 73 4.3 Displacement 73 4.3.1 Linear Displacement 73 4.3.2 Angular Displacement 73 4.4 Displacement Analysis 74 4.5 Displacement: Graphical Analysis 74 4.5.1 Displacement of a Single Driving Link 74 4.5.2 Displacement of the Remaining Slave Links 75 4.6 Position: Analytical Analysis 79 4.6.1 Closed-Form Position Analysis Equations for an In-Line Slider-Crank 81 4.6.2 Closed-Form Position Analysis Equations for an Offset SliderCrank 84 4.6.3 Closed-Form Position Equations for a Four-Bar Linkage 87 4.6.4 Circuits of a Four-Bar Linkage 87 4.7 Limiting Positions: Graphical Analysis 87 4.8 Limiting Positions: Analytical Analysis 91 4.9 Transmission Angle 93 4.10 Complete Cycle: Graphical Position Analysis 94 4.11 Complete Cycle: Analytical Position Analysis 96 4.12 Displacement Diagrams 98 4.13 Coupler Curves 101 Problems 101 Case Studies 108 5 Mechanism Design 109 Objectives 109 5.1 Introduction 109 5.2 Time Ratio 109 5.3 Timing Charts 110 5.4 Design of Slider-Crank Mechanisms 113 5.4.1 In-Line Slider-Crank Mechanism 113 5.4.2 Offset Slider-Crank Mechanism 114 5.5 Design of Crank-Rocker Mechanisms 115 5.6 Design of Crank-Shaper Mechanisms 117 5.7 Mechanism to Move a Link Between Two Positions 118 5.7.1 Two-Position Synthesis with a Pivoting Link 118 5.7.2 Two-Position Synthesis of the Coupler of a Four-Bar Mechanism 118 5.8 Mechanism to Move a Link Between Three Positions 119 5.9 Circuit and Branch Defects 119 Problems 120 Case Studies 121 6 Velocity Analysis 123 Objectives 123 6.1 Introduction 123 6.2 Linear Velocity 123 6.2.1 Linear Velocity of Rectilinear Points 123 6.2.2 Linear Velocity of a General Point 124 6.2.3 Velocity Profile for Linear Motion 124 6.3 Velocity of a Link 125 6.4 Relationship Between Linear and Angular Velocities 126 6.5 Relative Velocity 128 6.6 Graphical Velocity Analysis: Relative Velocity Method 130 6.6.1 Points on Links Limited to Pure Rotation or Rectilinear Translation 130 6.6.2 General Points on a Floating Link 132 6.6.3 Coincident Points on Different Links 135 6.7 Velocity Image 137 6.8 Analytical Velocity Analysis: Relative Velocity Method 137 6.9 Algebraic Solutions for Common Mechanisms 142 6.9.1 Slider-Crank Mechanism 142 6.9.2 Four-Bar Mechanism 142 6.10 Instantaneous Center of Rotation 142vi Contents 6.11 Locating Instant Centers 142 6.11.1 Primary Centers 143 6.11.2 Kennedy’s Theorem 144 6.11.3 Instant Center Diagram 144 6.12 Graphical Velocity Analysis: Instant Center Method 149 6.13 Analytical Velocity Analysis: Instant Center Method 152 6.14 Velocity Curves 155 6.14.1 Graphical Differentiation 157 6.14.2 Numerical Differentiation 159 Problems 161 Case Studies 168 7 Acceleration Analysis 170 Objectives 170 7.1 Introduction 170 7.2 Linear Acceleration 170 7.2.1 Linear Acceleration of Rectilinear Points 170 7.2.2 Constant Rectilinear Acceleration 171 7.2.3 Acceleration and the Velocity Profile 171 7.2.4 Linear Acceleration of a General Point 173 7.3 Acceleration of a Link 173 7.3.1 Angular Acceleration 173 7.3.2 Constant Angular Acceleration 173 7.4 Normal and Tangential Acceleration 174 7.4.1 Tangential Acceleration 174 7.4.2 Normal Acceleration 175 7.4.3 Total Acceleration 175 7.5 Relative Motion 177 7.5.1 Relative Acceleration 177 7.5.2 Components of Relative Acceleration 179 7.6 Relative Acceleration Analysis: Graphical Method 181 7.7 Relative Acceleration Analysis: Analytical Method 188 7.8 Algebraic Solutions for Common Mechanisms 190 7.8.1 Slider-Crank Mechanism 190 7.8.2 Four-Bar Mechanism 191 7.9 Acceleration of a General Point on a Floating Link 191 7.10 Acceleration Image 196 7.11 Coriolis Acceleration 197 7.12 Equivalent Linkages 201 7.13 Acceleration Curves 202 7.13.1 Graphical Differentiation 202 7.13.2 Numerical Differentiation 204 Problems 206 Case Studies 213 8 Computer-Aided Mechanism Analysis 215 Objectives 215 8.1 Introduction 215 8.2 Spreadsheets 215 8.3 User-Written Computer Programs 221 8.3.1 Offset Slider-Crank Mechanism 221 8.3.2 Four-Bar Mechanism 221 Problems 222 Case Study 222 9 Cams: Design and Kinematic Analysis 223 Objectives 223 9.1 Introduction 223 9.2 Types of Cams 223 9.3 Types of Followers 224 9.3.1 Follower Motion 224 9.3.2 Follower Position 224 9.3.3 Follower Shape 225 9.4 Prescribed Follower Motion 225 9.5 Follower Motion Schemes 227 9.5.1 Constant Velocity 228 9.5.2 Constant Acceleration 228 9.5.3 Harmonic Motion 228 9.5.4 Cycloidal Motion 230 9.5.5 Combined Motion Schemes 236 9.6 Graphical Disk Cam Profile Design 237 9.6.1 In-Line Knife-Edge Follower 237 9.6.2 In-Line Roller Follower 238 9.6.3 Offset Roller Follower 239 9.6.4 Translating Flat-Faced Follower 240 9.6.5 Pivoted Roller Follower 241 9.7 Pressure Angle 242 9.8 Design Limitations 243 9.9 Analytical Disk Cam Profile Design 243 9.9.1 Knife-Edge Follower 244 9.9.2 In-Line Roller Follower 246 9.9.3 Offset Roller Follower 249 9.9.4 Translating Flat-Faced Follower 249 9.9.5 Pivoted Roller Follower 250Contents vii 9.10 Cylindrical Cams 251 9.10.1 Graphical Cylindrical Cam Profile Design 251 9.10.2 Analytical Cylindrical Cam Profile Design 251 9.11 The Geneva Mechanism 252 Problems 254 Case Studies 258 10 Gears: Kinematic Analysis and Selection 260 Objectives 260 10.1 Introduction 260 10.2 Types of Gears 261 10.3 Spur Gear Terminology 262 10.4 Involute Tooth Profiles 264 10.5 Standard Gears 266 10.6 Relationships of Gears in Mesh 268 10.6.1 Center Distance 268 10.6.2 Contact Ratio 269 10.6.3 Interference 270 10.6.4 Undercutting 271 10.6.5 Backlash 272 10.6.6 Operating Pressure Angle 273 10.7 Spur Gear Kinematics 273 10.8 Spur Gear Selection 275 10.8.1 Diametral Pitch 276 10.8.2 Pressure Angle 276 10.8.3 Number of Teeth 276 10.9 Rack and Pinion Kinematics 281 10.10 Helical Gear Kinematics 282 10.11 Bevel Gear Kinematics 285 10.12 Worm Gear Kinematics 286 10.13 Gear Trains 288 10.14 Idler Gears 290 10.15 Planetary Gear Trains 290 10.15.1 Planetary Gear Analysis by Superposition 291 10.15.2 Planetary Gear Analysis by Equation 293 Problems 295 Case Studies 299 11 Belt and Chain Drives 302 Objectives 302 11.1 Introduction 302 11.2 Belts 302 11.3 Belt Drive Geometry 304 11.4 Belt Drive Kinematics 305 11.5 Chains 308 11.5.1 Types of Chains 308 11.5.2 Chain Pitch 309 11.5.3 Multistrand Chains 309 11.5.4 Sprockets 310 11.6 Chain Drive Geometry 310 11.7 Chain Drive Kinematics 311 Problems 313 Case Studies 315 12 Screw Mechanisms 316 Objectives 316 12.1 Introduction 316 12.2 Thread Features 316 12.3 Thread Forms 316 12.3.1 Unified Threads 317 12.3.2 Metric Threads 317 12.3.3 Square Threads 317 12.3.4 ACME Threads 317 12.4 Ball Screws 317 12.5 Lead 317 12.6 Screw Kinematics 318 12.7 Screw Forces and Torques 322 12.8 Differential Screws 324 12.9 Auger Screws 325 Problems 325 Case Studies 328 13 Static Force Analysis 330 Objectives 330 13.1 Introduction 330 13.2 Forces 330 13.3 Moments and Torques 330 13.4 Laws of Motion 333 13.5 Free-Body Diagrams 333 13.5.1 Drawing a Free-Body Diagram 333 13.5.2 Characterizing Contact Forces 333 13.6 Static Equilibrium 335 13.7 Analysis of a Two-Force Member 335 13.8 Sliding Friction Force 341 Problems 343 Case Study 345 14 Dynamic Force Analysis 346 Objectives 346 14.1 Introduction 346viii Contents 14.2 Mass and Weight 346 14.3 Center of Gravity 347 14.4 Mass Moment of Inertia 348 14.4.1 Mass Moment of Inertia of Basic Shapes 348 14.4.2 Radius of Gyration 350 14.4.3 Parallel Axis Theorem 350 14.4.4 Composite Bodies 351 14.4.5 Mass Moment of Inertia— Experimental Determination 352 14.5 Inertial Force 352 14.6 Inertial Torque 357 Problems 363 Case Study 366 Answers to Selected Even-Numbered Problems 367 References 370 Index 371 370 REFERENCES 1. Barton, Lyndon, Mechanism Analysis: Simplified Graphical and Analytical Techniques, 2nd ed., Marcel Dekker Inc., New York, 1993. 2. Baumeister, Theodore III, Avallone, Eugene, and Sadegh, Ali, Mark’s Standard Handbook for Mechanical Engineers, 11th ed., McGraw-Hill Book Company, New York, 2006. 3. Chironis, Nicholas and Sclater, Neil, Mechanisms and Mechanical Drives Sourcebook, 4th ed., McGraw-Hill Book Company, New York, 2007. 4. Erdman, Aurthur, Sandor, George, and Kota, Sridhar, Mechanism Design, Vol 1: Analysis and Synthesis, 4th ed., Prentice Hall, Upper Saddle River, NJ, 2001. 5. Kepler, Harold, Basic Graphical Kinematics, 2nd ed., McGraw-Hill Book Company, New York, 1973. 6. Jensen, Preben, Cam Design and Manufacture, 2nd ed., Marcel Dekker, New York, 1987. 7. Jensen, Preben, Classical Modern Mechanisms for Engineers and Inventors, Marcel Dekker, Inc., New York, 1991. 8. Jones, Franklin, Holbrook, Horton, and Newell, John, Ingenious Mechanisms for Designers and Inventors, Vols. I–IV, Industrial Press Inc, New York, 1930. 9. Mabie, Hamilton and Reinholtz, Charles, Mechanisms and Dynamics of Machinery, 4th ed., John Wiley and Sons Inc., New York, 1987. 10. Martin, George, Kinematics and Dynamics of Machines, 2nd ed., Waveland Press Inc., Long Groove, IL, 2002. 11. Norton, Robert, Design of Machinery, 4th ed., McGraw-Hill Book Company, New York, 2008. 12. Uicker, John, Pennock, Gordon, and Shigley, Joseph, Theory of Machines and Mechanisms, 4th ed., Oxford University Press, New York, 2010. 13. Townsend, Dennis and Dudley, Darle, Dudley’s Gear Handbook, 2nd ed., McGraw-Hill Book Company, New York, 1991. 14. Waldron, Kenneth and Kinzel, Gary, Kinematics, Dynamics, and Design of Machinery, 2nd ed., John Wiley and Sons Inc., Hoboken, NJ, 2004. 15. Wilson, Charles and Sadler, Peter, Kinematics and Dynamics of Machinery, 3rd ed., Pearson Education, Upper Saddle River, NJ, 2003. 16. Working Model Demonstration Guide, Knowledge Revolution Inc., San Mateo, CA, 1995.A Absolute motion, 128 Acceleration. See also Coriolis acceleration, Normal acceleration, Relative acceleration, Tangential acceleration, Total acceleration analysis of, 175 general summary problems, 206 kinematic analysis, 2 paths of, 179–180, 180i point of interest, 4 vector, 43 velocity profile, 178–179, 179t, 206–207, 207i Working Model, 208i–209i, 213 Acceleration curves description of, 202 graphical differentiation, 202–203, 203i numerical differentiation, 204–205, 205 summary problems, 206i–209i, 212–213 Acceleration images, description of, 196–197 ACME thread types, 314, 315i, 317t Actuators definition of, 4 role of, 12–13 types of, 12–13 Addendum, gear terminology, 260, 260i, 263i Air/hydraulic motors, actuator type, 12 Algebraic solution, common mechanism, 142, 190–191 American Gear Manufacturer’s Association (AGMA) diametrical pitch, 261 gear quality, 273, 273t gear standardization, 264–266, 264t American National Standards Institute (ANSI), gear standardization, 265 Analytical method cam follower displacement diagrams summary problems, 253–254 cycle position analysis, 96–98, 97i, 98i cylindrical cam profile design, 250, 255 disk cam profile design, 242–249, 243i–245i, 247i, 249i disk cam profile design summary problems, 254i–255i, 255 displacement analysis, 79, 79i, 80–81 displacement analysis summary problems, 101i–105i, 106 instant center location summary problems, 162i–164i, 164–165 instant center method, 123, 152, 153i instant center method summary problems, 162i–164i, 165 limiting positions analysis, 91–93, 92i limiting positions summary problems, 101i–105i, 105–106 mechanism analysis technique, 24 motion curves summary problems, 254 relative acceleration analysis, 188i, 188–190, 190t relative acceleration summary problems, 208i–209i, 210 relative velocity method, 137–141, 138i, 140i, 140i relative velocity method summary problems, 162i–164i, 164–165 vector component addition, 53–55, 54i, 54t vector component subtraction, 55–60, 56i–57i, 59t vector magnitude determinations, 66–71, 67i–70i, 66t vector triangle addition, 50–51, 51i, 53–54, 59–60, 59i, 759, 69, 69i vector triangle subtraction, 57i, 55–57 velocity curves summary problems, 162i–164i, 165 Angle method, 50–51 Angle of contact belt drive, 303–304, 303t chain drive, 308–309 Angular acceleration, 173, 174i Angular displacement, 73, 73i Angular inertia of a body, 355 Angular position vector, 72–73 Angular velocity and linear velocity, 126–127, 127i links, 125–126, 126i and relative velocity, 128–129 Annular gears, 259 “Archimedes Screw,” See Auger screws Assembly circuit branch defect, 120 circuit defect, 119 Auger screws, 323, 323i Automatic Dynamic Analysis of Mechanical Systems (ADAMS), 24, 31 Avoirdupois pound, 328 B Backlash gear mesh relationship, 270–271 gear terminology, 260 Ball screws, 315, 317i, 321 Base circle cam profile design, 237, 237i gear terminology, 260i, 262i–263i Base diameter, 260 Bellcrank, 3i, 4 Belt drive geometry, 302–303, 302i, 311 Belt drive kinematics, 303–306, 303i, 305i, 311 Belt drives description of, 300–301 selection summary problems, 310 types of, 300–301 Belt length, 302, 303t Belt speed, 303–304 Belts, 300–302, 301i–302i, 301t Bevel gear kinematics, 283–284, 283i Bevel gears, 259–260, 259i, 283 Bull gear, 266 INDEX Note: The letter ‘i’ and ‘t’ followed by locators refers to illustrations and tables cited in the text 371 C Cam follower displacement diagrams analytical summary problems, 253–254 description of, 224–225, 238i graphical summary problems, 252–253 Cam followers, 223 motion scheme nomenclature, 227–228 prescribed motion, 225–226 types of, 224–225, 224i Cam followers motion scheme constant acceleration, 228, 228t, 229t, 230i constant velocity, 228, 228t cycloidal motion, 230–236, 233i, 234i, 235i, 236i harmonic motion, 228–230, 228t, 230i Cam joint definition of, 3, 3i kinematic diagram symbol, 5t–6t Cams description of, 223, 224i, 226–227, 226i, types of, 223–224, 224i Case studies acceleration analysis, 213–214, 213i–214i belt/chain drives, 312–313, 312i–313i cam design/analysis, 255–257, 256i–257i displacement/position analysis, 108, 108i dynamic force analysis, 364, 364i gears, 297–299, 298i–299i kinematic motion/classification, 29–30, 30i machine analysis, 42, 42i machine design, 121–122, 121i–122i screw mechanisms, 326–327, 326i–327i spread sheets, 222, 222i static force analysis, 343, 343i vectors, 71, 71i velocity, 168–169, 168i–169i Center distance belt drive, 302–303 chain drive, 308–309, 308i gear mesh relationship, 266i, 267 Center of gravity, 345–346, 345i, 346t Chain drive description of, 300, 306–309 selection summary problems, 312 Chain drive geometry, 308i, 308–309, 312 Chain drive kinematics, 309–310, 309 Chain length, 308–309, 308i Chain pitch, 307, 307t Chain speed, 309 Chains, types of, 306i, 306–307 Change point, 19t, 20, 21 Circular pitch, 260, 260i Clearance, 260 Clockwise, 125 Closed-form position analysis four-bar linkage, 87 in-line slider-crank, 81–83, 81i–82i offset slider-crank, 84–86, 84i–85i Coarse pitch, 261t, 264t Cog belt, 301, 301iCoincident joint, 16–18 Combined motion schemes comparisons, 237t computer software for, 236 description, 236 goals of, 236 jerk, 236 modified sinusoidal acceleration, 237 modified trapezoidal acceleration, 236 polynomial displacement, 236 trapezoidal acceleration, 236 Common mechanisms, algebraic solutions, 142, 190–191 Common units, 173, 329, 346, 348 Commutative law of addition, 49 Complex link, 3i, 4 Component method analytical addition, 53–55, 754i, 54t analytical subtraction, 59–60, 59i, 59t Components, 4, 12 Composite bodies, 349–350, 349i Computer methods/programs dynamic analysis programs, 31 mechanism analysis technique, 24–25 user–written programs, 221–222, 221i value of, 31 Computer-aided design (CAD) systems mechanism analysis technique, 24–25 vector analysis, 44 Configuration, 74–75 Connecting arm, 19 Constant acceleration, 228, 229i–230i, 229t Constant angular acceleration, 173–174, 174i Constant rectilinear acceleration, 171 Constant velocity, 228, 228t Contact forces, 331–332, 331i, 339–340 Contact line, 262 Contact ratio, 267–268 Coriolis acceleration description of, 197–201 summary problems, 210–212, 210i–211i Cosine, 44, 47 Counterclockwise, 126 Coupler, 19 Coupler curve, 101, 101i Crank definition of, 3–4, 3i eccentric, 14, 14i slider-crank mechanism, 22 Crank-rockers circuits of, 87, 87i four-bar mechanism, 19–20, 19t, 20i, 22 machine design, 115–117, 117i summary problems, 120 Crank-shapers analytical methods, 118 graphical procedure, 117–118 machine design, 117–118, 117i summary problems, 120 Cross drives, 303, 303i Crossed helical gears, 280 Cycle analysis analytical position, 96, 97i, 99, 100i description of, 94 displacement diagram, 101–106, 101i–105i graphical position, 94–96, 94i–96i Cycloidal motion, follower motion scheme, 230–236, 231t–232t, 231i–236i Cylinders, actuator type, 4 Cylindrical cams analytical profile design, 250 description of, 224, 224i, 362 graphical profile design, 249–250, 250ii D D’Alembert’s principle, 351 Dedendum, 260i, 260 Degree of freedom beer crusher computation, 10i, 10–11 description of, 8 equation for, 74 four-bar mechanism calculation, 19, 19i lift table computation, 15–16, 15i–16i mechanism types, 8, 8i outrigger computation, 13–14, 13i–14i shear press computation, 11–12, 11i–12i toggle clamp computation, 9i, 9–10 Degree of freedom mechanical press, 17–18, 17i–18i Diametral pitch gear terminology, 261 spur gear selection, 273–279, 273t, 276i, 278i Differential screw, description of, 322–323, 322i–323i, 326 Disk cam profile design analytical method, 242–249 design limitations, 241–242, 242i flat-faced follower, 239–240, 239i graphical features, 237i, 237 in-line knife-edge follower, 238i, 237–238 in-line roller follower, 238i, 238 offset roller follower, 239, 239i pivoted roller follower, 240–241, 240i Disk cams, 223–224, 224i Displacement analytical method, 79–81, 80i analytical summary problems, 101i–105i, 106 description of, 74 general summary problems, 101, 101i–105i and linear velocity, 123 graphical driver analysis, 74i, 74–75 graphical problems, 76–78, 76i, 78i–79i, 80 graphical slave links analysis, 75–76, 75i, 76i graphical summary problems, 101–106, 101i–105i kinematic analysis, 2 point of interest, 4 types of, 73 vector, 43 Working Model problems, 101i–103i, 105i, 107–108 Displacement diagrams. See also Cam follower displacement diagrams cycle position analysis, 98–99, 99i–100i summary problems, 101i–103i, 105i, 107 velocity curves, 155, 156i, 157–158, 158i Double crank, 20, 19t, 20i Double enveloping worm gear set, 284, 285i Double rocker, 20, 19t, 20i Drafting as technique, 24 vector analysis, 43–44 Driver, 98 Driver link mechanism analysis, 73 position analysis, 74i, 74–75 Driver point, 73 372 Index Drivers, 12–13, 15 Drum cam, 224, 224i Dynamic Analysis of Dynamic Systems (DADS), dynamic analysis program, 31 Dynamic equilibrium, 328 Dynamic force analysis design questions, 2 purpose of, 344 static force analysis, 343, 343i and static equilibrium, 328 strategy for, 31 Dynamic force analysis programs, 24 E Eccentric crank, 14, 14i Efficiency, 321 Elastic parts, 2 Electric motors, 12 Engines, actuator type, 4, 12 Enveloping worm gear teeth, 284, 285i Epicyclic train, 288–293, 289i Equilibrium, 333–338, 334i–337i Equivalent linkage, 201 F Face width, 260i, 260 Fine pitch, 315, 316t Flat belt, 300, 301i Flat-faced follower analytical profile design, 248 description of, 224i, 225 profile design, 239–240, 239i Floating link relative acceleration analysis, 191i, 191–192, 193i–194i, 195–196 relative acceleration summary problems, 210, 210i relative velocity method, 132–135, 133i–134i Follower, 19. See also Cam followers Follower motion, 224, 224i Follower position, 224–225, 224i Follower shape, 224i, 225 Foot-pound, 328–329 Force definition of, 328 screw mechanisms, 320i–321i, 320–322 summary problems, 341, 341i vector, 43 Force analysis. See also Dynamic force analysis, Static force analysis and acceleration, 170 machine design, 1 Formula, spreadsheets, 215–218, 217i–218i Four-bar linkage, 87 Four-bar mechanisms algebraic solutions, 142, 190–191 categories of, 19t, 19–20 circuits of, 87, 87i coupler two–point synthesis, 119i, 118–119 description of, 19, 19i Grashof’s theorem, 19 motion classification, 20–21, 21i, 29, 29i nomenclature, 19 three-point synthesis, 119, 119i transmission angle, 93–94, 94i user-written programs, 221i, 221–222 Working Model tutorial, 32–37, 33i–34i, 36iFrame definition of, 2 four-bar mechanism, 19 kinematic diagram, 8 Free-body diagrams, 331–333, 331i–333i Friction coefficients of, 339, 339t force analysis, 1 screw mechanisms, 320 Friction force, 339 Full joints, 3, 3i G Gear joint, 3, 3i, 5t–6t Gear kinematics gear function, 271–273, 271i–272i, 293 Gear mesh relationship backlash, 270–271 center distance, 266–267, 266i contact ratio, 267–268 interference, 268–269, 268t operating pressure angle, 271 undercutting, 269–270, 270i Gear rack, 259, 259i, 262, 279 Gear selection, 294 Gear standardization, 264–266, 264t Gear trains description of, 286–288, 286i design summary problems, 296 summary problems, 295i–296i, 295–296 Gear-driven mechanisms, summary problems, 296, 296i Gears description of, 258–259, 258i–259i terminology, 260i, 260–262, 261t, 262i types of, 259–260, 259i, 284 General triangles, 46–48, 47i, 48i Geneva mechanism, 250–252, 250i, 252i, 255 Graphical analysis cam follower displacement diagrams summary problems, 252–253 cycle position, 94–96, 94i–96i cylindrical cam profile design, 250, 250i disk cam profile design, 237–242, 237i–242i disk cam profile design summary problems, 254i–255i, 254–255 displacement, 74–79, 74i–79i displacement diagrams summary problems,102i–105i, 107 displacement summary problems, 101–106, 101i–105i driver link displacement, 74i instant center location summary problems, 162i–164i, 165 instant center method, 123, 149–152, 150i, 152i instant center method summary problems, 162i–164i, 166 limiting positions, 88i, 87–88 mechanism analysis, 23–24 relative acceleration analysis, 181–187, 182i–183i, 185i–186i relative acceleration summary problems, 208–209, 208i–209i relative velocity method, 130–137, 130i–131i, 133i–136i relative velocity method summary problems, 162–164, 162i–164i slave links displacement, 75–76, 75i–76i vector addition, 48–50, 49i–50i vector magnitudes, 63–65, 63i–65i, 70–71, 70i–71i vector subtraction, 55–57, 55i–57i Graphical differentiation acceleration curves, 202–203, 203i velocity curves, 157i, 157 velocity curves summary problems, 162i–164i, 167 Graphical disk cam profile design features of, 237i, 237 flat-faced follower, 239–240, 239i in-line knife-edge follower, 238i, 237–238 in-line roller follower, 238i, 238 offset roller follower, 239, 239i pivoted roller follower, 240–241, 240i Grashof’s theorem, 19 Gruebler’s equation description of, 8 exceptions to, 18 special cases, 16–18, 16i–18i Gyration radius, 348 H Half joint, 3, 3i Harmonic motion, 228–230, 228t–229t, 229i–230i Helical gear kinematics, 280–282, 281i, 281t–282t Helical gears, 259, 259i, 294–295 Helix angle, 280, 281i Herringbone gears, 259, 259i Higher order joint, 3, 3i Hinge joint, 3, 3i Home position, 237, 237i Hydraulic cylinders, 13i, 12–13 Hydraulic motors, 12 I Idler gears, 288i, 288 Idler pulley, 301 In-line follower, 225, 224i In-line knife-edge follower, 238i, 237–238 In-line roller follower analytical profile design, 245–247, 245i, 247i graphical profile design, 238i, 238 In-line slider-crank closed-form analysis, 81–83, 81i–82i machine design, 113–114, 114i Inch-pound, 329 Included angle screw efficiency, 321 thread feature, 314, 314i Inertia, 170, 328 Inertia-force method of dynamic equilibrium, 351 Inertial forces description of, 350–355, 351i–352i, 354i summary problems, 362, 362i Inertial torques description of, 355–361, 355i–357i, 359i summary problems, 362–363, 362i–363i Input link, 19 Instant center, 142, 142i Instant center diagram, 144–145, 145i Instant center method Index 373 analytical velocity method, 123, 152–154, 153i analytical velocity method summary problems, 162i–164i, 166–167 graphical velocity method, 123, 149–152, 150i, 152i graphical velocity method summary problems, 162i–164i, 166 Instant centers locating, 142–149, 143i–149i, 146t, 148t summary problems, 162i–164i, 165–166 Instantaneous center of rotation, 142 Interference, 268–269, 268t Internal angle triangle addition problem, 51 triangle subtraction problem, 57–58, 58i Internal gears, 259, 259i International Organization for Standardization (ISO) force unit, 328 metric threads, 315 moment unit, 329 Inverted tooth/silent chain, 306i, 307 Involute tooth profile, 262–264, 262i, 263i J Joint, definition of, 3, 3i Joints coincident, 16i, 16–17 commonly used, 14–15 K Kennedy’s theorem, instant centers, 144–146, 147 Kinematic analysis, 1i, 2, 3 Kinematic diagram four-bar mechanism, 19, 19i manual water pump, 22 symbol system, 4, 5t–6t Kinematic diagram problems beer crusher, 10i, 10–11 lift table, 15i–16i, 15–16 mechanical press, 17i–18i, 17–18 nose wheel assemble, 20–21, 21i outrigger, 13–14, 13i–14i shear presses, 6–7, 6i–7i, 11–12, 11i–12i sketching diagrams, 25–28, 25i–28i toggle clamp, 9i, 9–10 vice grip, 7, 7i Kinematic inversion, 8 Kinematics, 2 Knife-edge follower analytical profile design, 242–244, 243i–244i description of, 224i, 225 L Law of cosines, oblique triangles, 46 Law of sines, oblique triangles, 46 Lead, 315–316 Lead angle screw threads, 316 thread feature, 314, 314i worm gears, 284, 285i Limiting positions analytical analysis, 91–93, 92i definition of, 87, 88iLimiting positions (Continued) graphical analysis, 88i, 87–88 graphical analysis problems, 88–91, 88i–90i summary problems, 101i–105i, 106–107 Line of center, 149, 150i Line of contact, 262, 262i Line of proportion, 149, 150i Linear acceleration, 170–173 Linear cam, 224, 224i Linear displacement, 73 Linear motion, 125i, 124–125 Linear velocity and angular velocity, 126–127, 127i definition of, 123 general point, 124, 124i rectilinear points, 124i, 123–124 Link, angular position, 72 Linkage acceleration. See also Timing charts Linkage, definition of, 2 Linkage velocity analysis. See also Timing charts Links acceleration analysis, 170, 173–174, 210, 210i angular velocity, 125–126, 126i commonly used, 14 definition of, 2 four-bar mechanism tutorial, 32–33, 33i relative velocity method, 130i, 130–135, 131i, 133i–134i resizing, 33 slider-crank mechanism tutorial, 37–38, 38i types of, 3 Locked mechanism, 8, 8i Long and short addendum system, 269 Lowering a load (screw drive), 321 Lubrication, chain drive kinematics, 309 M Machine design crank-shaper, 117–118, 117i crank-rocker, 115, 116i, 117, 120 slider-crank ratio, 113–115, 114i–115i, 120 three point synthesis, 119, 119i, 121 time ratio problems, 109–110, 120 two position links, 118–121, 118i–119i Machines, 1 Magnitude, 73, 73i Magnitude direction triangle addition, 52 triangle subtraction, 57, 58i Major diameter, 314, 314i Manual force, 13 Mass, 344, 361–362, 361i–362i Mass moment of inertia basic shapes, 346, 347i, 347t, 348 composite bodies, 349i, 349–350 description of, 346, 346i experiential determination, 350, 350i parallel axis theorem, 348i, 348–349 radius of gyration, 348 summary problems, 361–362, 361i–362i Mechanism basic components of, 2–4, 3i definition of, 1–2 degrees of freedom computation, 74 motion analysis, 73 phases of, 80 vectors, 43 Mechanism analysis, 2, 23 Metric thread, 314–315, 315i, 317t Minor diameter, 314, 314i Miter gears, 260, 259i, 283 Mobility (M) equation, 8 equation exceptions, 18 special cases, 16–18, 16i–18i Mobility (M) calculation can crusher, 11 four-bar mechanism, 19 graphical displacement analysis, 76 lift table, 16 manual water pump, 22 mechanical press, 17–18 outrigger, 14 shear press, 12 sketching diagrams, 25i–29i, 29 toggle clamp, 9–12, 14 Module, 261, 261t Moment description, 328–331, 329i–330i summary problems, 341, 341i Moment of inertia basic shapes, 346–348, 347i, 347t composite bodies, 349i, 349–350 description of, 346, 346i experiential determination, 350, 350i parallel axis theorem, 348i, 348–349 radius of gyration, 348 summary problems, 361–362, 361i Motion laws of, 331, 350 mechanism analysis, 1, 1i, 73 Motor actuator types, 4 four-bar mechanism tutorial, 35–36 slider-crank mechanism tutorial, 41 Multiple threads, 315–316, 317i Multiple-strand roller chain, 306, 306i Multi-strand chains, 307, 307t Multi-V-belt, 300, 301i N Newton, force magnitude unit, 328 Newton, Sir Isaac, 170, 331 Normal acceleration acceleration analysis, 174–177, 175i–176i description of, 173, 173i summary problems, 206–207, 207i Normal circular pitch, 281, 281i Normal diametral pitch, 281 Normal force, 339 Normal module, 281 Normal pressure angle, 281 Normal section, 281, 281i Numerical differentiation acceleration curves, 204–205, 205i velocity analysis, 159–160, 160i O Oblique triangle, 46–48, 46i–48i Offset follower, 225, 224i Offset roller follower analytical profile design, 248 graphical profile design, 239, 239i Offset sidebar roller chain, 306i, 307 374 Index Offset slider-crank, 221i, 221 closed-form analysis, 84–87, 84i–85i machine design, 114–115, 115i Off-set slider crank Mechanism, 221i, 221 Open, 32 Open-loop linkages, 8, 8i Operating pressure angle, 271 Output link, 19 P Parallel axis theorem, 248i, 348–349 Parallelogram mechanisms, 22, 23i Phase, 94 Pin, 3, 3i Pin joint kinematic diagram symbol, 5t four-bar mechanism tutorial, 33–35, 34i slider-crank mechanism tutorial, 38–41, 40i Pin-in-a-slot joint, commonly used, 14, 15i Pinion, 266, 266i. See also Gear rack Piston, 3, 3i Pitch thread features, 315, 315i worm gears, 284, 285i Pitch circle, 260, 260i, 262, 262i Pitch curve, 237, 237i Pitch diameter belt drive, 301i–302i, 302–303 chain drive, 308, 308i gear terminology, 260, 260i thread feature, 314, 314i Pitch line gear terminology, 262, 262i spur gear kinematics, 271, 271i Pitch point, 260 Pivot link, 118i, 118 Pivoted followers, 224, 224i Pivoted roller follower analytical profile design, 249i, 248–249 profile design, 240–241, 240i Planar mechanism, 2 Planet gear, 288, 289i Planetary gear analysis equation, 291–292 summary problems, 292–293 superposition, 289 summary problems, 289–291 Planetary gear trains description of, 288–293, 289i, 290t–291t, 291i summary problems, 297, 297i Plate cams, 224, 224i Pneumatic cylinders, 13i, 12–13 Point (P), 73i, 72–73 Point of interest, 4 Point of interest path, 37, 37i Point position measurement, 36–37 Points linear acceleration, 173 linear velocity, 124, 124i relative acceleration analysis, 274, 191–196, 191i–194i relative acceleration summary problems, 210, 210i Points/floating link, 132–135, 133i–134i Points/multiple, relative velocity method, 135–137, 135i–136i Points/one link, relative velocity method, 130–132, 130i–131iPoints of interest four-bar mechanism tutorial, 33, 34i slider-crank mechanism tutorial, 55i Position, 2, 72 Position analysis analytical displacement, 80i, 80–81 graphical displacement, 74–76, 74i–76i graphical displacement problems, 76–79, 76i–79i in-line slider-crank, 81, 81i limiting positions, 91–93, 92i offset slider crank, 84, 84i purpose of, 72i, 72 Position vector, 73i, 72 Pound, 328 Pressure angle description of, 241, 241i gear terminology, 262, 262i spur gear selection, 274–279, 276i, 278i Primary centers locating problems, 145–149, 145i–149i, 146t, 148t rules of, 203i, 143–144, 143i–144i Primary joints, 3, 3i Prime circle, 237, 237i Prismatic joint, 3, 3i Pulleys, 301i, 301, 301t Pythagorean theorem, 45 Q Quick-return mechanisms, 23, 23i R Rack, 259, 259i, 279 Rack and pinion kinematics, 279–280, 280i, 294 Radian, description of, 125–126 Rectilinear points linear acceleration, 170–171 linear velocity, 123–124, 124i, Rectilinear translation, 130–132, 130i–131i Relative acceleration components, 179–181, 180i, 197–201, 197i–200i description of, 177–179, 178i, 179t summary problems, 207i, 207–208 Relative acceleration analysis analytical method, 188i, 188–190, 190t analytical summary problems, 208i–209i, 209–210 graphical method, 181–187, 182i–183i, 185i–186i graphical summary problems, 208–209, 208i–209i Relative displacement, 317 Relative motion definition of, 177 description of, 128, 177 Relative velocity, 128–129, 128i, 129i Relative velocity method analytical method, 137–141, 138i, 140i analytical method summary problems, 162i–164i, 164–165 graphical analysis, 130–137, 130i–131i, 133i–136i graphical analysis summary problems, 162–164, 162i–164i velocity analysis, 123, 137–141, 138i, 140i velocity image, 137, 137i Resultant definition of, 49 graphical addition problems, 49, 49i, 50 graphical subtraction problem, 56–57, 57i Resultant components, 53–55, 54i Resultant force, summary problems, 341, 341i Resultant magnitude triangle addition problem, 51 triangle subtraction problem, 58, 58i Reversible gearset, 285 Revolute joint, 3, 3i Richardson method (numerical differentiation) acceleration curves, 204 velocity curves, 159 Right triangle, 44–46, 44i–46i Ring gear, 288, 289i Rocker, 3i, 4 Rocker arm link, 4 Roller chain, 306, 306i Roller follower, 224i, 225 Rotation instantaneous center of, 142, 142i kinematic analysis, 2 relative velocity method, 130–132, 130i–131i S Scalar quantities, 43 Scotch Yoke mechanism, 23, 23i Screw actuators, 13 Screw forces/torques, 320–322, 320i–321i, 326 Screw joints, 15, 15i Screw kinematics, 316–320, 318i–320i Screw mechanisms, 314 Screw thread, 315, 314i–315i, 323–324 Screw-driven acceleration, 326, 324i–325i Screw-driven displacement, 324–325, 324i–325i Screw-driven velocity, 325–326, 324i–325i Self-locking, 316 Serpentine drives, 303, 303i Servomotors, 12 Shaft angle, 283, 283i Sheaves, 301i, 301, 301t Simple link, 3, 3i, 5t Simulation four-bar mechanism, 32–37, 33i–37i slider-crank mechanism tutorial, 37–41, 38i–40i Sine, 44, 46 Sketching, practice problems, 25–28, 25i–28i Slave links, 75–76, 75i–76i Slider-crank transmission angle, 93–94, 94i Slider joint, symbol, 6t Slider-crank mechanisms algebraic solutions, 142, 190–191 description of, 22 limiting positions, 88i machine design, 113–115, 114i–115i summary problems, 120 Working Model tutorial, 37–41, 38i–40i Sliding friction force, 339t, 339i–340i, 339–341 Sliding joint, 3, 3i Sliding link, 38, 38i–39i Slot joints, 38, 39i Slug, derivation of, 344 Software. See Computers methods/programs Solenoids, actuator type, 4 Speed, 2 Index 375 Spherical-faced follower, description of, 224i, 225 Spreadsheets acceleration curves, 205i cycle position analysis, 97, 98i cycloidal motion, 235i displacement curve, 155, 156i displacement diagram, 100i general description, 215–220, 215i–220i in-line roller follower design, 247i knife-edge follower design, 244i mechanism analysis technique, 24 summary problems, 222 velocity analysis, 160i Sprocket, 307, 307i, 308t Spur gear geometry, summary problems, 293 Spur gear kinematics gear function, 271–273, 271i–272i summary problems, 293 Spur gear selection diametral pitch, 273–279, 273t, 276i, 278i pressure angle, 274–279, 276i, 278i set center distance summary problems, 294 teeth number, 274–279, 276i, 278i Spur gears gear type, 259, 259i terminology, 260i, 260–262, 261t Square thread, 314–315, 315i Static equilibrium conditions of, 333 definition of, 328 Static machine forces, summary problems, 341–343, 341i–343i Straight-line mechanisms, 22 Peaucellier-Lipkin linkage, 22i Watt linkage, 22i Stroke, 88i, 88 Stub teeth, 269 Sun gear, 288, 289i Superposition method, 289 Swing arm followers, 224, 224i Synthesis, 109 T Tangent, right triangle, 44 Tangential acceleration acceleration analysis, 174–175 description of, 173, 173i, 175–177, 176i summary problems, 206–207, 207i Tangential velocity, 126 Teeth. See also Involute tooth profile chain drive, 308, 308i gear terminology, 260–262 spur gear selection, 273–279, 274t–275t, 276i, 278i worm gears, 284, 285i Thread features, 314, 314i Thread forms, 314–315, 315i, 316t–317t Thread number, 315–316, 317i Three-point synthesis, machine design, 119, 119i, 121 Throw angle, 115 Time ratio, 109–110, 120 Timing belt, 301, 301i Timing charts problems, 112–113 uses of, 110–111, 111i Tip-to-tail method, 48Torque definition of, 328, 329i screw mechanisms, 320–322, 320i–321i Total acceleration, 175–177, 176i Trace, 101 Trace point, 237, 237i Translating followers, 224, 224i Transmission angle definition, 93 mechanical advantage, 93 Transverse section, 281, 281i Triangles summary problems, 67–69, 67i–68i trigonometric relationships, 44, 44i types of, 44, 46 vector addition, 50–51, 51i vector subtraction, 57–60, 58i–60i, 59t Trigonometry, 44 Triple rocker, 19t, 20, 20i Truss, 8, 8i Two-armed synchro loader, 4, 5t Two-force member, 333–338, 334i–337i Two-point synthesis coupler of four-bar mechanism, 119i, 118–119 design class, 118 pivot link, 118–119, 118i–119i single pivot summary problems, 120–121 two pivots summary problems, 121 U Undercutting, 269–270, 270i Unified thread, 314–315, 315i, 316t United States Customary System force unit, 328 mass/weight, 344 moment unit, 328–329 threads per inch, 314 V V-belt, belt type, 300–302, 301i–302i Vector analysis analytical magnitude determination, 66–67, 66i, 66t, 71, 71i component addition, 53–55, 54i, 54t component subtraction, 59–60, 59i–60i, 59t graphical addition, 48–50, 49i–50i graphical magnitude determination, 63–65, 63i–65i graphical subtraction, 55–57, 55i–57i triangle addition, 50–51, 51i, 53–55, 54i, 54t, 69i, 69 triangle subtraction, 58i, 57–58 Vector components, 52i, 52 Vector diagram graphical addition problems, 49–50, 49i–50i graphical subtraction problems, 55–56, 56i magnitude determination, 65, 63i–65i triangle addition problem, 51 triangle subtraction problem, 58–59, 58i Vector equations, 60, 60i analytical magnitude determination, 66–67, 71 application of, 62 formation of, 60–62, 61i–62i graphical magnitude determination, 63–65, 70–71 subtraction, 59 Vector magnitude analytical determination, 66–67, 66i, 66t, 71, 71i graphical determination, 63–65, 63i–65i, 70–71, 70i–71i Vector problems analytical addition, 51–55, 51i–52i, 54i, 54t, 69i, 69 analytical magnitude determination, 66–67, 66i, 66t, 70–71, 70i–71i analytical subtraction, 57–60, 58i–60i, 59t, 69i, 70 equations, 61–62, 70, 70i graphical addition, 49–50, 49i–50i, 69i, 69 graphical magnitude determination, 63–65, 63i–64i, 70i–71i, 70–71 graphical subtraction, 55–57, 55i–57i, 69i, 69 triangle addition, 51i, 51, 53 triangle subtraction, 59–60, 59i–60i, 59t Vectors addition methods, 43, 48–55, 48i–52i, 54i, 54t mechanism characteristics, 43 oblique/general triangles, 46–48 right triangle, 44–46, 44i subtraction methods, 55–60, 55i–60i, 59t triangle types, 44–48, 44i–48i, 47i–48i Velocity kinematic analysis, 2 point of interest, 4 summary general problems, 161, 161i summary relative problems, 162, 162i vector property, 43 Working Model, 162i–164i, 168 Velocity analysis algebraic solutions, 142 analytical methods, 137–141, 138i, 140i description of, 123 graphical methods, 130–137, 130i–131i, 133i–136i 376 Index graphical methods summary problems, 162–164, 162i–164i instant center analytical method, 123, 152, 153i instant center graphical analysis, 123, 149–152, 150i, 152i Velocity curves analytical summary problems, 162i–164i, 167–168 description of, 155–157, 156i graphical differentiation, 157–158, 157i–158i graphical summary problems, 162i–164i, 167 numerical differentiation, 159–161, 160i Velocity image, 137, 137i Velocity profile acceleration, 171–172, 172i linear motion, 125i, 124–125 Velocity ratio belt drive kinematics, 303 chain drive kinematics, 309 spur gear kinematics, 271–273, 271i–272i Volume, 323 Volumetric acceleration, 323 Volumetric flow, 323 W Weight, 344 Whole depth, 260 Windshield wiper system, design concept, 1, 1i Wipe pattern, components, 1 Working Model software acceleration, 208i–209i, 213 computer simulation software, 31 displacement problems, 101i–105i, 107–108 four-bar mechanism tutorial, 32–37, 33i–37i practice problems, 41–42, 41i–42i purchase information, 32 slider-crank mechanism, 37–41, 38i–40i velocity problems, 162i–164i, 168 Worm, 284 Worm gear kinematics, 284–286, 285i Worm gears, 259i, 260, 295 Worm pitch diameter, 284, 285i Worm wheel, 284 X X–axis angle addition, 53 angle subtraction, 59t component determination, 66, 66t rotational equation, 15
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