CONTENTS 4.3 Translation,Rotation,and Complex Motion 149 Translation 749 Rotation 749 Complex Motion 4444 749 The0femS 750 4.4 Graphical Position Analysis of Linkages 151 4.5 Algebraic Position Analysis of Linkages 444……4.4。。+4……4444444…… 152 Vector Loop Representation of Linkages 753 Complex Numbers as Vectors. 754 The Vector Loop Equation for a Fourbar Linkage 756 4.6 The Fourbar Slider-Crank Position Solution 159 4.7 An Inverted Slider-Crank Position Solution 161 4.8 Linkages of More Than Four Bars 164 The Geared Fivebar Linkage 764 Sixbar Linkages.… 767 4.9 Position of Any Point on a Linkage 168 4.10 Transmission Angles 169 Extreme Values of the TransmissionAngle 769 4.11 Toggle Positions… 171 4.12 Circuits and Branches in Linkages 173 4.13 Newton-Raphson Solution Method 174 One-Dimensional Root-Finding (Newton's Method) 774 Multidimensional Root-Finding (Newton-Raphson Method) 776 Newton-Raphson Solution for the Fourbar Linkage 777 Equation Solvers. 778 4.14 References 178 4.15 Problems 178 Chapter 5 Analytical Linkage Synthesis..................... 188 5.0 Introduction 188 5.1 Types of Kinematic Synthesis 188 5.2 Precision Points 189 5.3 Two-Position Motion Generation by Analytical Synthesis 189 5.4 Comparison of Analytical and Graphical Two-Position Synthesis 196 5.5 Simultaneous Equation Solution 199 5.6 Three-Position Motion Generation by Analytical Synthesis 201 5.7 Comparison of Analytical and Graphical Three-Position Synthesis...206 5.8 Synthesis for a Specified Fixed Pivot Location 211 5.9 Center-Point and Circle-Point Circles......... 217 5.10 Four-and Five-Position Analytical Synthesis 219 5.11 Analytical Synthesis of a Path Generator with Prescribed Timing 220 5.12 Analytical Synthesis of a Fourbar Function Generator 220 5.13 Other Linkage Synthesis Methods 224 Precision Point Methods ... 226 CouplerCuNe Equation Methods 227 Optimization Methods 227 5.14 References 230 5.15 Problems 232 Chapter 6 Velocity Analysis.....241 6.0 Introduction 241 6.1 Definition of Velocity 241 6.2 Graphical Velocity Analysis 2444.3 Translation, Rotation, and Complex Motion .......................................... 149 Translation ................................................................................................ 749 Rotation .................................................................................................... 749 Complex Motion ...................................................................................... 749 Theorems .................................................................................................. 750 4.4 Graphical Position Analysis of Linkages .................................................. 151 4.5 Algebraic Position Analysis of Linkages .................................................. 152 Vector Loop Representation of Linkages ............................................. 753 Complex Numbers as Vectors ............................................................... 754 The Vector Loop Equation for a Fourbar Linkage ................................ 756 4.6 The Fourbar Slider-Crank Position Solution ............................................. 159 4.7 An Inverted Slider-Crank Position Solution ............................................. 161 4.8 Linkages of More Than Four Bars .............................................................. 164 The Geared Fivebar Linkage .................................................................. 764 Sixbar Linkages ......................................................................................... 767 4.9 Position of Any Point on a Linkage .......................................................... 168 4.10 Transmission Angles .................................................................................... 169 Extreme Values of the TransmissionAngle ............................................ 769 4.11 Toggle Positions ........................................................................................... 171 4.12 Circuits and Branches in Linkages ........................................................... 173 4.13 Newton-Raphson Solution Method ......................................................... 174 One-Dimensional Root-Finding (Newton's Method) ............................ 774 Multidimensional Root-Finding (Newton-Raphson Method) ............... 776 Newton-Raphson Solution for the Fourbar Linkage ............................. 777 Equation Solvers....................................................................................... 778 4.14 References ................................................................................................... 178 4.15 Problems ....................................................................................................... 178 Chapter 5 Analytical Linkage Synthesis........................................... 188 5.0 Introduction ................................................................................................. 188 5.1 Types of Kinematic Synthesis .................................................................... 188 5.2 Precision Points ............................................................................................ 189 5.3 Two-Position Motion Generation by Analytical Synthesis .................... 189 5.4 Comparison of Analytical and Graphical Two-Position Synthesis ..... 196 5.5 Simultaneous Equation Solution ............................................................... 199 5.6 Three-Position Motion Generation by Analytical Synthesis ................. 201 5.7 Comparison of Analytical and Graphical Three-Position Synthesis ... 206 5.8 Synthesis for a Specified Fixed Pivot Location ....................................... 211 5.9 Center-Point and Circle-Point Circles ..................................................... 217 5.10 Four- and Five-Position Analytical Synthesis .......................................... 219 5.11 Analytical Synthesis of a Path Generator with Prescribed Timing ..... 220 5.12 Analytical Synthesis of a Fourbar Function Generator ........................ 220 5.13 Other Linkage Synthesis Methods ............................................................ 224 Precision Point Methods .......................................................................... 226 CouplerCuNe Equation Methods ......................................................... 227 Optimization Methods ............................................................................. 227 5.14 References ................................................................................................... 230 5.15 Problems .............................................................. ,........................................ 232 Chapter 6 Velocity Analysis................................................................ 241 6.0 Introduction ........................................................ ,........................................ 241 6.1 Definition of Velocity ......................................... ,........................................ 241 6.2 Graphical Velocity Analysis ...................................................................... 244