BASIC CONCEPTS OFMACHINES AND MECHANISMS PARTS Kinematics – Analysis – Synthesis Kinetics ANALYSIS AND SYNTHESIS Analysis Synthesis: Design – Science & Art – Tools to compare – Analysis: helpful tool Synthesis: the real goal MECHANICS Assumption: Rigid Bodies DEFINITIONS Machine Mechanism Difference with structures MECHANISMS .MACHINES VS. DEFINITIONS Link Driver and Follower Kinematic pairs: joints Rigidity . SCHEMATIC DIAGRAMS . DEFINITIONS Kinematic chain Binary links Open or closed Frame: reference link . JOINTS Kinds of joints Surfaces Pin joint . PAIR VARIABLES Way of measuring the motion Degrees of freedom . USUAL PAIRS . . 3 Planar . y. 3 Spheric Flat F x.TABLE Pair Symbo Pair Variable l Degrees of freedom Relative motion Revolute R 1 Circular Prism P s 1 Rectilinear Helical H or s 1 Helical Cylinder C and s 2 Cylindric Sphere S . REVOLUTE JOINTS Ball Bearings Journal Bearings . WRAPPING PAIRS Belts. pulleys. chains – One of the links has one-way rigidity . PLANAR MECHANISMS Planar motion Graphical Techniques . SPHERICAL MECHANISMS Spherical Motion Representation technique Only revolute pairs . SPATIAL MECHANISMS No restrictions Special representation techniques . MOBILITY Input variables Determined from the joints and number of links . MOBILITY Free link: 3 degrees of freedom 3(n-1) without joints 1-degree of freedom joint: 2 constraints 2-degree of freedom joint: 1 constraint . KUTZBACH CRITERION n: number of links j1: number of 1-degree of freedom joints j2: number of 2-degree of freedom joints . EXAMPLES . MOBILITY m > 1: m degrees of freedom m = 0: motion impossible m < 0: statically indeterminate structure . EXCEPTIONS . CLASSIFICATION Motion transformation Torfason outlines 262 mechanisms . LINEAR ACTUATORS Stationary screws with traveling nuts Stationary nuts with traveling screws Hydraulic and pneumatic cylinders . worm gearing. .FINE ADJUSTMENTS Screws. etc. INDEXING MECHANISMS They count number of revolutions They must have low inertia . SWINGING OR ROCKING MECHANISMS The output motion is an oscillation The input member is a crank Examples: – Toothed rack – Crank-and-rocker mechanism – Quick-return mechanism . SWINGING OR ROCKING MECHANISMS . SWINGING OR ROCKING MECHANISMS . RECIPROCATING MECHANISMS Repetitive motions Straight-line motion in both directions Typical mechanisms: – Offset slider-crank mechanism – Scotch-yoke mechanism – Shaper mechanism . RECIPROCATING MECHANISMS . RECIPROCATING MECHANISMS . RECIPROCATING MECHANISMS Working stroke and return stroke Advance-to-return time ratio: . r3 = 209 mm .4 mm. r2 = 4.2 r4 = 60 mm Angle of oscillation = 60º Position and length of the other links? r1 = 155 mm.EXAMPLE OF DESIGN Crank-rocker four-bar linkage Q = 1. RECIPROCATING MECHANISMS Crank-driven toggle High mechanical advantage . REVERSING MECHANISMS Output rotation in either direction Two-way clutch . COUPLINGS AND CONNECTORS Transmit motion between shafts Gears Other mechanisms – Belts – Four-bar mechanism – Hooke’s joint . COUPLINGS AND CONNECTORS . COUPLINGS AND CONNECTORS . CURVE GENERATORS Infinite plane moving with the coupler Coupler curve Pivots make circles Algebraic equation of 6th order: wide variety of curves Design by intuitive procedures . CURVE GENERATORS . STRAIGHT-LINE GENERATORS There weren’t prismatic pairs Straight-line motion as a part of a coupler curve Watt’s linkage Roberts’ mechanism . STRAIGHT-LINE GENERATORS . KINEMATIC INVERSION Different frame links chosen for a kinematic chain Their absolute motions change n-link kinematic chain yields n kinematic inversions . KINEMATIC INVERSION Slider-crank mechanism: combustion engine or compressor . KINEMATIC INVERSION . GRASHOF’S LAW Ensure that one of the links make a complete revolution Grashof’s law states that for a planar four-bar linkage. the sum of the shortest and longest link lengths cannot be greater than the sum of the remaining two link lengths if there is to be continuous relative rotation between two . GRASHOF’S LAW It does not specify the order of the links or the frame link Link s is the one which rotates Four inversions . GRASHOF’S LAW . GRASHOF’S LAW Crank-rocker mechanisms Double crank or drag-link mechanism Double rocker mechanism . EXAMPLES . MECHANICAL ADVANTAGE It is the ratio of the torque exerted by the follower and the input torque Continuously changing Extreme positions . MECHANICAL ADVANTAGE . MECHANICAL ADVANTAGE : transmission angle When it becomes 0 the linkage locks Extreme positions: line AD Measure of quality . SUMMARY The Science of Mechanisms Definitions Planar. Spherical and Spatial Mechanisms Mobility Classification of Mechanisms Kinematic Inversion Grashof’s law Mechanical Advantage .