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Mechanical Technology

Mechanical Technology. Mechanical Advantage Build Challenge: Crane or Rescue Vehicle. Key Ideas. Mechanical Advantage IMA AMA Efficiency Equilibrium Moment/Torque Machine Principle Machine Simple Machine Complex/Compound Machine Work Power. Mechanical Advantage.

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Mechanical Technology

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  1. Mechanical Technology Mechanical Advantage Build Challenge: Crane or Rescue Vehicle

  2. Key Ideas • Mechanical Advantage • IMA • AMA • Efficiency • Equilibrium • Moment/Torque • Machine • Principle Machine • Simple Machine • Complex/Compound Machine • Work • Power

  3. Mechanical Advantage • An expression of the ratio of force output to force input • Ideal Mechanical Advantage • Assumes a “perfect world” • No friction or Thermodynamics • Distance Travelled by Effort / Distance Travelled by Load • Actual Mechanical Advantage • Considers friction and Thermodynamics • Force applied by Load / Force applied by Effort • Efficiency • A measure of the useable portion of energy in a system • AMA / IMA

  4. Equilibrium • Assumes a “perfect world” • Efficiency = 1 • AMA = IMA • DEFE = DLFL • FE:FL = DL:DE • Ratio of Forces is INVERSE of Ratio between Distances

  5. Lever • Beam (LEVER ARM) supported by pivot point (FULCRUM) • 3 classifications • One of two PRINCIPLE MACHINES • Force Multiplier or Distance Multiplier • “Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.” Archimedes 

  6. Class 1 Lever • Fulcrum between Load and Effort • EFL

  7. Class 2 Lever • Load between Fulcrum and Effort • FLE

  8. Class 3 Lever • Effort between Fulcrum and Load • FEL

  9. 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 rotation” • This is virtually the same concept as “Torque” • This is NOT the same thing as “Torsion,” the structural stress resulting from moment/torque • Torque = Moment = F * D = τ • (that’s a lower-case Greek letter, “tau.”) • Measured (USCMS) in Foot-Pounds (ftlbs)

  10. Lever Equilibrium • D = Distance travelled by Force • Assume rotation doesn’t stop • D = pi*2*radius (distance from fulcrum to force) • => dEFE = dLFL • Distance between Effort and Fulcrum * Force of Effort • Distance between Load and Fulcrum * Force of Load • Compare these equations to “Moment” • => dE:dL = hE:hL • Height travelled = d sin ß • ß is the same for both sides of the lever, so… • dE sin ß = dL sin ß • Therefore dE = dL<<implies>>hE = hL

  11. Ideal Mechanical Advantage • Theoretical Mechanical Advantage • Levers can be FORCE MULTIPLERS or DISTANCE MULTIPLERS • IMA of a Lever: dE / dL • >1 - Force Multiplier • =1 - neutral system • <1 - Distance Multiplier

  12. Wheel-and-Axle • Behaves as Class 2 Lever • ONLY WHEN EFFORT IS APPLIED TO WHEEL!!!!!!!!! • Behaves as Class 3 Lever • WHEN EFFORT IS APPLIED TO AXLE!!!!!!!!! • Force Multiplier, distance reducer • (steering wheel) • Distance Multiplier, force reducer • (automotive transmission)

  13. Wheel & Axle • D = Distance travelled by Force • D = pi*2*radius (distance from CoR to force) • D = pi*diam. = pi*2*rad. = Circum • => dEFE = dLFL • Distance between Effort and CoR * Force of Effort • Distance between Load and CoR * Force of Load • Compare these equations to “Moment”

  14. Pulley • Grooved wheels attached to an axle • Grooves runs concentrically around the outer rim of the wheel • Behave like Class 2 Levers • Direction Changer, Force Multiplier, or Distance Multiplier • “Open” system or “Closed” system • DE measured by length of rope • DL measured by lift of load

  15. Pulley as Direction Changer • Open pulley systems leave disconnected the ends of the rope/cable/chain/belt IMA of Fixed Pulley: 1

  16. Pulley as a Force Multiplier IMA of fixed pulley: 1 IMA of moving pulley: 2 IMA = 4?!!? AH!! 2 Pulleys!

  17. Compound Machines • When two or more simple machines are used in conjunction with one another • Can be same machine (pulleys and pulleys) • Can be different machines (lever, w/a, pulley) • Total IMA = Product of simple IMA • MAT = MA1 * MA2 * … * MAn

  18. Closed Pulley Systems • Closed pulley systems have connected the ends of the belt/cable/chain/cable • Behave somewhat like a wheel-and-axle… just in two pieces Follower Load Resistance Output Driver Effort Input

  19. Like a disconnected W&A system Load Effort

  20. Therefore… • SEVERAL equivalent equations!! • New Variables!! • d = diameter • τ = torque • ω = Rotational Velocity (rotations-per-minute; revolutions-per-minute; RPM) • IMA = dout/din = ωin/ωout • AMA = τout/τin

  21. Compound Pulley Systems Load Effort

  22. Inclined Plane • Second PRINCIPLE MACHINE • Reduces the force required to lift an object • Ideal Mechanical Advantage: length of slope / height of slope • NOT THE SAME AS CALCULATION OF SLOPE ANGLE • NOT A MOVING OBJECT! Length of Slope Height

  23. Therefore…

  24. Wedge • Basically two inclined planes connected • Functions as moving IP Length of Slope Length of Slope ½ Face Face

  25. Therefore… • EQUATION FOR Wedge EQUILIBRIUM • 2sE = fL • 2 * Length of Slope * Force of Effort • Width of Wedge Face * Force of Load • EQUATION FOR PULLEY MECHANICAL ADVANTAGE • 2s / f • 2 * Length of Slope / Width of Wedge Face

  26. Screw • Theoretical Mechanical Advantage: pi*dm / l • pi = (appx.) 3.1415 or 22/7 • dm = average diameter of the screw • l = “lead” of the screw • axial advance of a helix for one complete turn on a gear • In other words… the distance between threads

  27. Gears • Same basic idea as Pulleys • Gears have teeth or spurs extending radially outward from the outer or inner edge of the wheel • Gears do not slip, as pulleys can • Gears ALWAYS reverse the direction of rotation between adjacent gears • Use an “idler gear” between driver and follower to have follower turn in same direction as driver • Force Multiplier or Speed Multiplier

  28. Therefore… • SEVERAL equivalent equations!! • New Variables!! • d = diameter • τ = torque • ω = Rotational Velocity (rotations-per-minute; RPM) • n = number of teeth • IMA = nout/nin = dout/din = τout/τin = ωin/ωout • IMA = “GEAR RATIO”

  29. Arbeit macht frei • WORK = FORCE x DISTANCE • In a way, measures the conversion of “POTENTIAL ENERGY” into “KINETIC ENERGY” • No distance = no work. • No force = no work. • TORQUE = rotational work • TORQUE = FORCE x RADIUS

  30. She can’t do it, Captain! I need more power! • Power = Work / Time • Horsepower (hp) = (Force in pounds x Distance in feet) / (Time in seconds x 550) • Yep… the number (constant) 550… • HP was originally used by James Watt to describe the “power” equivalence of steam engines in terms we could understand • This number was chosen… for some reason… but it’s actually twice the number that it should be… the first motor was THAT powerful… • Electrical Power is measured in WATTS • 1 Watt = 1 Joule / 1 Second

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