THEORY OF MACHINES AND MECHANISMS
CONTENTS INTRODUCTION TO KINEMATIC SYNTHESIS THE ROLE OF KINEMATIC SYNTHESIS IN MECHANICAL DESIGN GLOSSARY KINEMATIC ANALYSIS VERSUS KINEMATIC SYNTHESIS A SUMMARY OF SYSTEMS OF ALGEBRAIC EQUATIONS ALGEBRAIC AND COMPUTATIONAL TOOLS THE TWO-DIMENSIONAL REPRESENTATION OF THE CROSS PRODUCT ALGEBRA OF 2 × 2 MATRICES ALGEBRA OF 3 × 3 MATRICES LINEAR-EQUATION SOLVING: DETERMINED SYSTEMS LINEAR-EQUATION SOLVING: OVERDETERMINED SYSTEMS NONLINEAR-EQUATION SOLVING: THE DETERMINED CASE THE NEWTON–RAPHSON METHOD OVERDETERMINED NONLINEAR SYSTEMS OF EQUATIONS THE NEWTON–GAUSS METHOD PACKAGES RELEVANT TO LINKAGE SYNTHESIS REFERENCES THE QUALITATIVE SYNTHESIS OF KINEMATIC CHAINS NOTATION BACKGROUND KINEMATIC PAIRS THE KINEMATIC PAIR GRAPH REPRESENTATION OF KINEMATIC CHAINS GROUPS OF DISPLACEMENTS DISPLACEMENT SUBGROUPS KINEMATIC BONDS THE CHEBYSHEV–GRÜBLER–KUTZBACH–HERVÉ FORMULA TRIVIAL CHAINS EXCEPTIONAL CHAINS PARADOXICAL CHAINS APPLICATIONS TO ROBOTICS THE SYNTHESIS OF ROBOTIC ARCHITECTURES AND THEIR DRIVES LINKAGE SYNTHESIS FOR FUNCTION GENERATION INTRODUCTION INPUT-OUTPUT (IO) FUNCTIONS PLANAR FOUR-BAR LINKAGES THE DENAVIT-HARTENBERG NOTATION SPHERICAL FOUR-BAR-LINKAGES SPATIAL FOUR-BAR-LINKAGES EXACT SYNTHESIS PLANAR LINKAGES SPHERICAL LINKAGES SPATIAL LINKAGES ANALYSIS OF THE SYNTHESIZED LINKAGE SPHERICAL FOUR-BAR LINKAGES SPATIAL FOUR-BAR LINKAGES APPROXIMATE SYNTHESIS THE APPROXIMATE SYNTHESIS OF PLANAR FOUR-BAR LINKAGES THE APPROXIMATE SYNTHESIS OF SPHERICAL LINKAGES THE APPROXIMATE SYNTHESIS OF SPATIAL LINKAGES LINKAGE PERFORMANCE EVALUATION PLANAR LINKAGES: TRANSMISSION ANGLE AND TRANSMISSION QUALITY SPHERICAL LINKAGES: TRANSMISSION ANGLE AND TRANSMISSION QUALITY SPATIAL LINKAGES: TRANSMISSION ANGLE AND TRANSMISSION QUALITY DESIGN ERROR VERSUS STRUCTURAL ERROR MINIMIZING THE STRUCTURAL ERROR BRANCH-SWITCHING DETECTION INTRODUCING A MASSIVE NUMBER OF DATA POINTS SYNTHESIS UNDER MOBILITY CONSTRAINTS MOTION GENERATION DYAD SYNTHESIS FOR THREE POSES DYAD SYNTHESIS FOR FOUR POSES DYAD SYNTHESIS FOR FIVE POSES CASE STUDY: SYNTHESIS OF A LANDING GEAR MECHANISM THE PRESENCE OF A P JOINT IN DYAD SYNTHESIS DYAD SYNTHESIS FOR THREE ATTITUDES DYAD SYNTHESIS FOR FOUR ATTITUDES DYAD SYNTHESIS FOR FIVE ATTITUDES SPHERICAL DYADS WITH A P JOINT APPROXIMATE DYAD SYNTHESIS EXAMPLES GEOMETRIC CONSTRAINTS OF CC AND RC DYADS THE SYNTHESIS OF THE CC DYAD THE SYNTHESIS OF THE RC DYAD SYNTHESIS OF FOUR-BAR LINKAGES A SEMIGRAPHICAL SOLUTION OF THE DIRECTION EQUATIONS SOLVING THE LINEAR EQUATIONS OF THE MOMENT VARIABLES CONGRUENCES OF THE FIXED AND THE MOVING AXES SUMMARY TRAJECTORY GENERATION PLANAR PATH GENERATION WITH PRESCRIBED TIMING COUPLER-CURVE SYNTHESIS OF PLANAR FOUR-BAR LINKAGES TRAJECTORY GENERATION FOR SPHERICAL FOUR-BAR LINKAGES PATH SYNTHESIS WITH DISCRETE POSITIONS PATH SYNTHESIS WITH PRESCRIBED TIMING PATH GENERATION FOR RCCC LINKAGES A GENERIC RCCC LINKAGE AN ALTERNATIVE COORDINATE FRAME CONSTRAINT EQUATIONS OF THE CC AND RC DYADS N-POINT PATH SYNTHESIS EXAMPLE SYNTHESIS OF PLANAR COMPLEX LINKAGES SIX-BAR LINKAGES SYNTHESIS OF THE STEPHENSON-III LINKAGE ELIMINATION OF MOTION VARIABLES EXTENSION TO STEPHENSON-I AND II LINKAGES STEPHENSON-II LINKAGE PARAMETERIZED COORDINATES OF POINT D SYNTHESIS EQUATIONS FOR THE STEPHENSON-II LINKAGE STEPHENSON-I LINKAGE SYNTHESIS IN THE PRESENCE OF INCOMPLETE DATA SETS A DESIGN EXAMPLE A 10-BAR LINKAGE SYNTHESIS FOR M PRESCRIBED POSES SOLUTION OF THE 10-POSTURE SYNTHESIS EQUATIONS A SYNTHESIS EXAMPLE