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

2. Key Ideas Mechanical Advantage Efficiency Equilibrium Moment/Torque
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 => dEFE = dLFL
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 Behaves as Class 3 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 => dEFE = dLFL
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.) 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