MACHINES AND MECHANISMS

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1 MACHINES AND MECHANISMS APPLIED KINEMATIC ANALYSIS Fourth Edition David H. Myszka University of Dayton PEARSON ж rentice Hall Pearson Education International Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo

CONTENTS iv 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.

2 CONTENTS iv 1 Introduction to Mechanisms and Kinematics 1 Objectives Introduction Machines and Mechanisms Kinematics Mechanism Terminology Kinematic Diagrams Kinematic Inversion Mobility Gruebler's Equation Actuators and Drivers Commonly Used Links and Joints Eccentric Crank Pin-in-a-Slot Joint Screw Joint Special Cases of the Mobility Equation Coincident Joints Exceptions to the Gruebler's Equation Idle Degrees of Freedom The Four-Bar Mechanism Grashof's Criterion Double Crank Crank-Rocker Double Rocker Change Point Mechanism Triple Rocker Slider-Crank Mechanism Special Purpose Mechanisms Straight-Line Mechanisms Parallelogram Mechanisms Quick-Return Mechanisms Scotch Yoke Mechanism Techniques of Mechanism Analysis Traditional Drafting Techniques CAD Systems Analytical Techniques Computer Methods 24 Problems 25 Case Studies 29 2 Building Computer Models of Mechanisms Using Working Model Software 31 Objectives Introduction Computer Simulation of Mechanisms Obtaining Working Model Software Using Working Model to Model a Four-Bar Mechanism Using Working Model to Model a Slider- Crank Mechanism 37 Problems 41 Case Studies 42 3 Vectors 43 Objectives Introduction Scalars and Vectors Graphical Vector Analysis Drafting Techniques Required in Graphical Vector Analysis CAD Knowledge Required in Graphical Vector Analysis Trigonometry Required in Analytical Vector Analysis Right Triangle Oblique Triangle Vector Manipulation Graphical Vector Addition ( + >) Analytical Vector Addition (+ >): Triangle Method Components of a Vector Analytical Vector Addition (+ >): Component Method Vector Subtraction (->) Graphical Vector Subtraction ( >) Analytical Vector Subtraction ( >): Triangle Method Analytical Vector Subtraction ( > ): Component Method Vector Equations 60

Contents v 3.17 Application of Vector Equations 62 3.18 Graphical Determination of Vector Magnitudes 63 3.

3 Contents v 3.17 Application of Vector Equations Graphical Determination of Vector Magnitudes Analytical Determination of Vector Magnitudes 66 Problems 67 Case Studies 71 4 Position and Displacement Analysis 72 Objectives Introduction Position Position of a Point Angular Position of a Link Position of a Mechanism Displacement Linear Displacement Angular Displacement Displacement Analysis Displacement: Graphical Analysis Displacement of a Single Driving Link Displacement of the Remaining Slave Links Position: Analytical Analysis Closed-Form Position Analysis Equations for an In-Line Slider-Crank Closed-Form Position Analysis Equations for an Offset Slider- Crank Closed-Form Position Equations for a Four-Bar Linkage Circuits of a Four-Bar Linkage Limiting Positions: Graphical Analysis Limiting Positions: Analytical Analysis Transmission Angle Complete Cycle: Graphical Position Analysis Complete Cycle: Analytical Position Analysis Displacement Diagrams Coupler Curves 101 Problems 101 Case Studies Mechanism Design 109 Objectives Introduction Time Ratio Timing Charts Design of Slider-Crank Mechanisms In-Line Slider-Crank Mechanism Offset Slider-Crank Mechanism Design of Crank-Rocker Mechanisms Design of Crank-Shaper Mechanisms Mechanism to Move a Link Between Two Positions Two-Position Synthesis with a Pivoting Link Two-Position Synthesis of the Coupler of a Four-Bar Mechanism Mechanism to Move a Link Between Three Positions Circuit and Branch Defects 119 Problems 120 Case Studies Velocity Analysis 123 Objectives Introduction Linear Velocity Linear Velocity of Rectilinear Points Linear Velocity of a General Point Velocity Profile for Linear Motion Velocity of a Link Relationship Between Linear and Angular Velocities Relative Velocity Graphical Velocity Analysis: Relative Velocity Method Points on Links Limited to Pure Rotation or Rectilinear Translation General Points on a Floating Link Coincident Points on Different Links Velocity Image Analytical Velocity Analysis: Relative Velocity Method Algebraic Solutions for Common Mechanisms Slider-Crank Mechanism Four-Bar Mechanism Instantaneous Center of Rotation 142

vi 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.

4 vi Contents 6.11 Locating Instant Centers Primary Centers Kennedy's Theorem Instant Center Diagram Graphical Velocity Analysis: Instant Center Method Analytical Velocity Analysis: Instant Center Method Velocity Curves Graphical Differentiation Numerical Differentiation 159 Problems 161 Case Studies Acceleration Analysis 170 Objectives Introduction Linear Acceleration Linear Acceleration of Rectilinear Points Constant Rectilinear Acceleration Acceleration and the Velocity Profile Linear Acceleration of a General Point Acceleration of a Link Angular Acceleration Constant Angular Acceleration Normal and Tangential Acceleration Tangential Acceleration Normal Acceleration Total Acceleration Relative Motion Relative Acceleration Components of Relative Acceleration Relative Acceleration Analysis: Graphical Method Relative Acceleration Analysis: Analytical Method Algebraic Solutions for Common Mechanisms Slider-Crank Mechanism Four-Bar Mechanism Acceleration of a General Point on a Floating Link Acceleration Image Coriolis Acceleration Equivalent Linkages Acceleration Curves Graphical Differentiation Numerical Differentiation 204 Problems 206 Case Studies Computer-Aided Mechanism Analysis 215 Objectives Introduction Spreadsheets User-Written Computer Programs Offset Slider-Crank Mechanism Four-Bar Mechanism 221 Problems 222 Case Study Cams: Design and Kinematic Analysis 223 Objectives Introduction Types of Cams Types of Followers Follower Motion Follower Position Follower Shape Prescribed Follower Motion Follower Motion Schemes Constant Velocity Constant Acceleration Harmonic Motion Cycloidal Motion Combined Motion Schemes Graphical Disk Cam Profile Design In-Line Knife-Edge Follower In-Line Roller Follower Offset Roller Follower Translating Flat-Faced Follower Pivoted Roller Follower Pressure Angle Design Limitations Analytical Disk Cam Profile Design Knife-Edge Follower In-Line Roller Follower Offset Roller Follower Translating Flat-Faced Follower Pivoted Roller Follower 250

5 Contents vii 9.10 Cylindrical Cams Graphical Cylindrical Cam Profile Design Analytical Cylindrical Cam Profile Design The Geneva Mechanism 252 Problems 254 Case Studies Gears: Kinematic Analysis and Selection 260 Objectives Introduction Types of Gears Spur Gear Terminology Involute Tooth Profiles Standard Gears Relationships of Gears in Mesh Center Distance Contact Ratio Interference Undercutting Backlash Operating Pressure Angle Spur Gear Kinematics Spur Gear Selection Diametral Pitch Pressure Angle Number of Teeth Rack and Pinion Kinematics Helical Gear Kinematics Bevel Gear Kinematics Worm Gear Kinematics Gear Trains Idler Gears Planetary Gear Trains Planetary Gear Analysis by Superposition Planetary Gear Analysis by Equation 293 Problems 295 Case Studies Belt and Chain Drives 302 Objectives Introduction Belts Belt Drive Geometry Belt Drive Kinematics Chains Types of Chains Chain Pitch Multistrand Chains Sprockets Chain Drive Geometry Chain Drive Kinematics 311 Problems 313 Case Studies Screw Mechanisms 316 Objectives Introduction Thread Features Thread Forms Unified Threads Metric Threads Square Threads ACME Threads Ball Screws Lead Screw Kinematics Screw Forces and Torques Differential Screws Auger Screws 325 Problems 325 Case Studies Static Force Analysis 330 Objectives Introduction Forces Moments and Torques Laws of Motion Free-Body Diagrams Drawing a Free-Body Diagram Characterizing Contact Forces Static Equilibrium Analysis of a Two-Force Member Sliding Friction Force 341 Problems 343 Case Study Dynamic Force Analysis 346 Objectives Introduction 346

viii 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.

6 viii Contents 14.2 Mass and Weight Center of Gravity Mass Moment of Inertia Mass Moment of Inertia of Basic Shapes Radius of Gyration Parallel Axis Theorem Composite Bodies Mass Moment of Inertia Experimental Determination Inertial Force Inertial Torque 357 Problems 363 Case Study 366 Answers to Selected Even-Numbered Problems 367 References 370 Index 371

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