Mechanical Technology

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# Mechanical Technology - PowerPoint PPT Presentation

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

Crane or Rescue Vehicle

Key Ideas
• IMA
• AMA
• Efficiency
• Equilibrium
• Moment/Torque
• Machine
• Principle Machine
• Simple Machine
• Complex/Compound Machine
• Work
• Power
• An expression of the ratio of force output to force input
• Assumes a “perfect world”
• No friction or Thermodynamics
• Distance Travelled by Effort / Distance Travelled by Load
• 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
• Assumes a “perfect world”
• Efficiency = 1
• AMA = IMA
• DEFE = DLFL
• FE:FL = DL:DE
• Ratio of Forces is INVERSE of Ratio between Distances
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
• Fulcrum between Load and Effort
• EFL
Class 2 Lever
• Load between Fulcrum and Effort
• FLE
Class 3 Lever
• Effort between Fulcrum and Load
• FEL
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
• 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
• 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
• 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
• 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
• 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
• Compare these equations to “Moment”
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
• Open pulley systems leave disconnected the ends of the rope/cable/chain/belt

IMA of Fixed Pulley: 1

Pulley as a Force Multiplier

IMA of fixed pulley: 1

IMA of moving pulley: 2

IMA = 4?!!?

AH!! 2 Pulleys!

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 have connected the ends of the belt/cable/chain/cable
• Behave somewhat like a wheel-and-axle… just in two pieces

Follower

Resistance

Output

Driver

Effort

Input

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

Length of Slope

Length of Slope

½ Face

Face

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
• 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
• 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
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
• 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!
• 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