Mechanical Technology Mechanical Advantage Build Challenge: Crane or Rescue Vehicle

Key Ideas Mechanical Advantage Efficiency Equilibrium Moment/Torque IMA AMA Efficiency Equilibrium Moment/Torque Machine Principle Machine Simple Machine Complex/Compound Machine Work Power

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 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 => 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

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 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)

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”

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 Load Resistance Output Driver Effort Input

Like a disconnected W&A system Load Effort

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 Load Effort

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

Therefore…

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