Simple Machines

Mechanical Advantage Build Challenge:Crane or Rescue VehicleMechanical TechnologyKey IdeasMechanical AdvantageIMAAMAEfficiencyEquilibriumMoment/TorqueMachinePrinciple MachineSimple MachineComplex/Compound MachineWorkPowerMechanical AdvantageAn expression of the ratio of force output to force inputIdeal Mechanical AdvantageAssumes a perfect worldNo friction or ThermodynamicsDistance Travelled by Effort / Distance Travelled by LoadActual Mechanical AdvantageConsiders friction and ThermodynamicsForce applied by Load / Force applied by EffortEfficiencyA measure of the useable portion of energy in a systemAMA / IMAEquilibriumAssumes a perfect worldEfficiency = 1AMA = IMADEFE = DLFLFE:FL = DL:DERatio of Forces is INVERSE of Ratio between DistancesLeverBeam (LEVER ARM) supported by pivot point (FULCRUM)3 classificationsOne of two PRINCIPLE MACHINESForce Multiplier or Distance MultiplierGive me a lever long enough and a fulcrum on which to place it, and I shall move the world.ArchimedesClass 1 LeverFulcrum between Load and EffortEFL

Class 2 LeverLoad between Fulcrum and EffortFLE

Class 3 LeverEffort between Fulcrum and LoadFEL

Wait a moment!Moment: a measure of the force inducing the tendency of an object to rotate within a system.measured by the application of a force some distance from the center of rotationThis is virtually the same concept as TorqueThis is NOT the same thing as Torsion, the structural stress resulting from moment/torqueTorque = Moment = F * D = (thats a lower-case Greek letter, tau.)Measured (USCMS) in Foot-Pounds (ftlbs)Lever EquilibriumD = Distance travelled by ForceAssume rotation doesnt stopD = pi*2*radius (distance from fulcrum to force)=> dEFE = dLFLDistance between Effort and Fulcrum * Force of EffortDistance between Load and Fulcrum * Force of LoadCompare these equations to Moment=> dE:dL = hE:hLHeight travelled = d sin is the same for both sides of the lever, sodE sin = dL sin Therefore dE = dL hE = hLIdeal Mechanical AdvantageTheoretical Mechanical AdvantageLevers can be FORCE MULTIPLERS or DISTANCE MULTIPLERSIMA of a Lever: dE / dL>1 - Force Multiplier=1 - neutral system dEFE = dLFLDistance between Effort and CoR * Force of EffortDistance between Load and CoR * Force of LoadCompare these equations to MomentPulley

Grooved wheels attached to an axleGrooves runs concentrically around the outer rim of the wheelBehave like Class 2 LeversDirection Changer, Force Multiplier, or Distance MultiplierOpen system or Closed systemDE measured by length of ropeDL measured by lift of load

Pulley as Direction ChangerOpen pulley systems leave disconnected the ends of the rope/cable/chain/belt

IMA of Fixed Pulley: 1Pulley as a Force Multiplier

IMA of fixed pulley: 1IMA of moving pulley: 2IMA = 4?!!?AH!! 2 Pulleys!Compound MachinesWhen two or more simple machines are used in conjunction with one anotherCan be same machine (pulleys and pulleys)Can be different machines (lever, w/a, pulley)Total IMA = Product of simple IMAMAT = MA1 * MA2 * * MAnClosed Pulley SystemsClosed pulley systems have connected the ends of the belt/cable/chain/cableBehave somewhat like a wheel-and-axle just in two pieces

FollowerLoadResistanceOutputDriverEffortInputLike a disconnected W&A system

EffortLoadThereforeSEVERAL equivalent equations!!New Variables!!d = diameter = torque = Rotational Velocity (rotations-per-minute; revolutions-per-minute; RPM)IMA = dout/din = in/outAMA = out/inCompound Pulley Systems

EffortLoad

Inclined PlaneSecond PRINCIPLE MACHINEReduces the force required to lift an objectIdeal Mechanical Advantage: length of slope / height of slopeNOT THE SAME AS CALCULATION OF SLOPE ANGLENOT A MOVING OBJECT!HeightLength of SlopeThereforeWedgeBasically two inclined planes connectedFunctions as moving IP

Face

Length of Slope

Length of SlopeFaceThereforeEQUATION FOR Wedge EQUILIBRIUM2sE = fL2 * Length of Slope * Force of EffortWidth of Wedge Face * Force of LoadEQUATION FOR PULLEY MECHANICAL ADVANTAGE2s / f2 * Length of Slope / Width of Wedge FaceScrewTheoretical Mechanical Advantage: pi*dm / lpi = (appx.) 3.1415 or 22/7dm = average diameter of the screwl = lead of the screwaxial advance of ahelixfor one complete turn on a gearIn other words the distance between threads

GearsSame basic idea as PulleysGears have teeth or spurs extending radially outward from the outer or inner edge of the wheelGears do not slip, as pulleys canGears ALWAYS reverse the direction of rotation between adjacent gearsUse an idler gear between driver and follower to have follower turn in same direction as driverForce Multiplier or Speed MultiplierThereforeSEVERAL equivalent equations!!New Variables!!d = diameter = torque = Rotational Velocity (rotations-per-minute; RPM)n = number of teethIMA = nout/nin = dout/din = out/in = in/outIMA = GEAR RATIOArbeit macht freiWORK = FORCE x DISTANCEIn a way, measures the conversion of POTENTIAL ENERGY into KINETIC ENERGYNo distance = no work.No force = no work.TORQUE = rotational workTORQUE = FORCE x RADIUSShe cant do it, Captain! I need more power!Power = Work / TimeHorsepower (hp) = (Force in pounds x Distance in feet) / (Time in seconds x 550)Yep the number (constant) 550HP was originally used by James Watt to describe the power equivalence of steam engines in terms we could understandThis number was chosen for some reason but its actually twice the number that it should be the first motor was THAT powerfulElectrical Power is measured in WATTS1 Watt = 1 Joule / 1 Second