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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

Mechanical Technology

Mechanical Advantage Build Challenge:

Crane or Rescue Vehicle

key ideas
Key Ideas
  • Mechanical Advantage
    • IMA
    • AMA
  • Efficiency
  • Equilibrium
  • Moment/Torque
  • Machine
    • Principle Machine
    • Simple Machine
    • Complex/Compound Machine
  • Work
  • Power
mechanical advantage
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
equilibrium
Equilibrium
  • Assumes a “perfect world”
  • Efficiency = 1
  • AMA = IMA
  • DEFE = DLFL
  • FE:FL = DL:DE
      • Ratio of Forces is INVERSE of Ratio between Distances
lever
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 
class 1 lever
Class 1 Lever
  • Fulcrum between Load and Effort
    • EFL
class 2 lever
Class 2 Lever
  • Load between Fulcrum and Effort
    • FLE
class 3 lever
Class 3 Lever
  • Effort between Fulcrum and Load
    • FEL
wait a moment
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)
lever equilibrium
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
ideal mechanical advantage
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
wheel and axle
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)
wheel axle
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”
pulley
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
pulley as direction changer
Pulley as Direction Changer
  • Open pulley systems leave disconnected the ends of the rope/cable/chain/belt

IMA of Fixed Pulley: 1

pulley as a force multiplier
Pulley as a Force Multiplier

IMA of fixed pulley: 1

IMA of moving pulley: 2

IMA = 4?!!?

AH!! 2 Pulleys!

compound machines
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
closed pulley systems
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

therefore
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
inclined plane
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

wedge
Wedge
  • Basically two inclined planes connected
  • Functions as moving IP

Length of Slope

Length of Slope

½ Face

Face

therefore2
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
screw
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
gears
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
therefore3
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”
arbeit macht frei
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
she can t do it captain i need more power
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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