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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

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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


Like a disconnected w a system

Like a disconnected W&A system

Load

Effort


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


Compound pulley systems

Compound Pulley Systems

Load

Effort


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


Therefore1

Therefore…


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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