Mechanical Advantage Build Challenge: Crane or Rescue Vehicle
Mechanical Technology
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Key Ideas Mechanical Advantage IMA AMA Efficiency Equilibrium
Moment/Torque Machine Principle Machine Simple Machine
Complex/Compound Machine Work Power
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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
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Equilibrium Assumes a perfect world Efficiency = 1 AMA = IMA D
E F E = D L F L F E :F L = D L :D E Ratio of Forces is INVERSE of
Ratio between Distances
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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
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Class 1 Lever Fulcrum between Load and Effort EFL
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Class 2 Lever Load between Fulcrum and Effort FLE
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Class 3 Lever Effort between Fulcrum and Load FEL
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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 = (thats a lower-case Greek
letter, tau.) Measured (USCMS) in Foot-Pounds (ftlbs)
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Lever Equilibrium D = Distance travelled by Force Assume
rotation doesnt stop D = pi*2*radius (distance from fulcrum to
force) => d E F E = d L F L Distance between Effort and Fulcrum
* Force of Effort Distance between Load and Fulcrum * Force of Load
Compare these equations to Moment => d E :d L = h E :h L Height
travelled = d sin is the same for both sides of the lever, so d E
sin = d L sin Therefore d E = d L > h E = h L
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Ideal Mechanical Advantage Theoretical Mechanical Advantage
Levers can be FORCE MULTIPLERS or DISTANCE MULTIPLERS IMA of a
Lever: d E / d L >1 - Force Multiplier =1 - neutral system
Wheel & Axle D = Distance travelled by Force D =
pi*2*radius (distance from CoR to force) D = pi*diam. = pi*2*rad. =
Circum => d E F E = d L F L Distance between Effort and CoR *
Force of Effort Distance between Load and CoR * Force of Load
Compare these equations to Moment
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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 D E measured by length of
rope D L measured by lift of load
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Pulley as Direction Changer Open pulley systems leave
disconnected the ends of the rope/cable/chain/belt IMA of Fixed
Pulley: 1
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Pulley as a Force Multiplier IMA of fixed pulley: 1 IMA of
moving pulley: 2 IMA = 4?!!? AH!! 2 Pulleys!
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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 MA T = MA 1 * MA 2 * * MA n
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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
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Like a disconnected W&A system Effort Load
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Therefore SEVERAL equivalent equations!! New Variables!! d =
diameter = torque = Rotational Velocity (rotations-per-minute;
revolutions-per- minute; RPM) IMA = d out /d in = in / out AMA =
out / in
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Compound Pulley Systems Effort Load
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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! Height Length of Slope
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Therefore
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Wedge Basically two inclined planes connected Functions as
moving IP Face Length of Slope Face
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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
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Screw Theoretical Mechanical Advantage: pi*d m / l pi = (appx.)
3.1415 or 22/7 d m = 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
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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
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Therefore SEVERAL equivalent equations!! New Variables!! d =
diameter = torque = Rotational Velocity (rotations-per-minute; RPM)
n = number of teeth IMA = n out /n in = d out /d in = out / in = in
/ out IMA = GEAR RATIO
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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
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She cant 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 its 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