DYNAMICAL SYSTEMS

By W. GIVAS

CONTENTS INTRODUCTION MOTIVATIONS A BRIEF HISTORY THE BOOK’S ORGANIZATION REFERENCES FUNDAMENTALS OF KINEMATICS DEGREES-OF-FREEDOM (DOF) TYPES OF MOTION LINKS, JOINTS, AND KINEMATIC CHAINS DETERMINATION OF DOF 2 4 1 REMARKS 2 4 2 PARADOXES 2 4 3 EXAMPLES EXERCISES PLANAR FOUR-BAR PIN-JOINTED LINKAGES EXISTENCE CONDITION GRASHOF CONDITION INVERSION TRANSMISSION ANGLES 3 4 1 DE?NITION 3 4 2 DETERMINATION OF 3 4 3 REASON FOR STUDYING TRANSMISSION ANGLES TOGGLE POSITIONS 3 5 1 TOGGLE POSITIONS 3 5 2 REASON FOR STUDYING TOGGLE POSITIONS CIRCUITS LIMITS OF ROTATION OF INPUT/OUTPUT LINKS 3 7 1 GRASHOF CRANK-ROCKER LINKAGES 3 7 2 GRASHOF DOUBLE-CRANK LINKAGES 3 7 3 GRASHOF ROCKER-CRANK LINKAGES 3 7 4 GRASHOF DOUBLE-ROCKER LINKAGES 3 7 5 NON-GRASHOF DOUBLE-ROCKER LINKAGES SUMMARY ANALYSIS OF PLANAR MECHANISMS ANALYSIS OF FOUR-BAR MECHANISMS ANALYSIS OF SIX-BAR MECHANISMS ANALYTICAL APPROACHES IN MOTION STUDIES METHOD OF COMPLEX NUMBER 5 1 1 REPRESENTATIONS OF A PLANAR VECTOR 5 1 2 EXAMPLE SUMMARY OF COMPLEX NUMBER APPROACH METHOD OF UNIT VECTORS 5 3 1 RATE OF CHANGE OF A VECTOR WITH RESPECT TO A FIXED FRAME 5 3 2 MOTION INVOLVED WITH CORIOLIS ACCELERATION 5 3 3 GENERAL MOTION INVOLVED MOVING FRAME OF REFERENCE QUESTIONS AND SOLUTIONS GRAPHICAL APPROACHES IN MOTION STUDIES INSTANTANEOUS CENTER METHOD 6 1 1 DETERMINATION OF INSTANT CENTERS (OF ROTATION) 6 1 2 APPLICATION OF INSTANT CENTERS IMAGE METHOD FOR MOTION STUDIES ANALYSIS AND DESIGN OF CAMS CLASSI?CATION OF CAMS CLASSI?CATION OF FOLLOWERS 7 2 1 FOLLOWER MOTIONS 7 2 2 FOLLOWER POSITIONS 7 2 3 FOLLOWER SHAPES FOLLOWER MOTION DESIGN 7 3 1 CONSTANT VELOCITY MOTION SCHEME 7 3 2 CYCLOIDAL MOTION SCHEMES 7 3 3 HARMONIC MOTION SCHEMES 7 3 4 REMARKS GRAPHICAL DESIGN OF CAMS 7 4 1 DISK CAM WITH RADIAL FLAT-FACED FOLLOWER 7 4 2 DISK CAM WITH RADIAL ROLLER FOLLOWER 7 4 3 CAM WITH O?SET ROLLER FOLLOWER ANALYTICAL APPROACHES TO CAM DESIGN 7 5 1 DISK CAM WITH FLAT-FACED FOLLOWER 7 5 2 DISK CAM WITH OSCILLATING ROLLER FOLLOWER 7A APPENDIX: CYCLOIDAL AND HARMONIC MOTION SCHEMES 7B APPENDIX: PROOF OF RADIUS OF CURVATURE OF PITCH SURFACE ANALYSIS AND DESIGN OF GEARS COMMON TYPES OF GEARS IN PRACTICE SPUR GEARS AND TERMINOLOGY 8 2 1 TERMINOLOGY 8 2 2 SPUR GEARS AND DESIGN PARAMETERS GEAR TRAINS 8 3 1 GEAR TRAINS WITH FIXED GEAR CENTERS AND TRAIN VALUE 8 3 2 PLANETARY GEAR TRAINS APPLICATION OF GEAR TRAINS IN AUTOMOTIVE TRANSMISSION ANALYSIS 8A APPENDIX: PROPERTIES OF INVOLUTE ANALYSIS OF DYNAMIC FORCES IN MACHINERY D’ALEMBERT’S PRINCIPLE AND INERTIA FORCE ANALYSIS OF MECHANISMS BY VIRTUAL WORK METHOD GYROSCOPIC FORCES C H A P T E R