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Mechanical Concepts 101

Basic Concepts: Equations. Force = Mass * AccelerationTorque = Force * Distance = WorkPower = Work/TimePower = Torque * Angular Velocity. . . . The friction coefficient for any given contact with the floor, multiplied by the normal force, equals the maximum tractive force can be applied at th

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Mechanical Concepts 101

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    1. Mechanical Concepts 101 Shannon Schnepp Dennis Hughes Anthony Lapp 10/29/05

    2. Basic Concepts: Equations Force = Mass * Acceleration Torque = Force * Distance = Work Power = Work/Time Power = Torque * Angular Velocity

    3. Basic Concepts: Traction

    4. Basic Concepts: Traction Equations

    5. Basic Concepts: Coefficient of Friction Materials of the robot wheels (or belts) High Friction Coeff: soft materials, “spongy” materials, “sticky” materials Low Friction Coeff: hard materials, smooth materials,shiny materials Shape of the robot wheels (or belts) Want the wheel (or belt) surface to “interlock” with the floor surface Material of the floor surface Surface conditions Good: clean surfaces, “tacky” surfaces Bad: dirty surfaces, oily surfaces

    6. Basic Concepts: Free Body Diagrams

    7. Basic Concepts: Weight Distribution

    8. Basic Concepts: Weight Transfer

    9. Basic Concepts: Gears Gears are generally used for one of four different reasons: To reverse the direction of rotation To increase or decrease the speed of rotation (or increase/decrease torque) To move rotational motion to a different axis To keep the rotation of two axes synchronized

    10. Basic Concepts: Gears The Gear Ratio is a function of the number of teeth of the gears Consecutive gear stages multiply

    11. Basic Concepts: Gears

    12. Lifting/Moving Objects Example 1: A box weighs 130 lbs and must be moved 10 ft. The coefficient of friction between the floor and the box is .25. How much work must be done??

    13. Lifting/Moving Objects f = mu*N = .25*130 f = 65 lbs so… Work = f * dist Work = 65 * 10 = 650 ft lbs

    14. Lifting/Moving Objects Example 2: The arm weighs 10 lbs and moves 3 ft vertically. The mechanism that contains the balls weighs 5 lbs. The balls weigh 3 lbs. The mechanism and balls move 6 ft vert. Work = Force 1*Dist 1 + Force 2*Dist 2 = 10 lbs * 3 ft + 8 lbs * 6 ft = 30 + 48 = 78 ft lbs

    15. Lifting/Moving Objects Example 2A: Desire this motion to be completed in 10 seconds. Power = 78 ft lbs / 10 seconds *(60sec/1min) * .02259697 = 10.6 Watts Note: There is only a certain amount of power available.

    16. Lifting/Moving Objects Example 2B: Desire this motion to be completed in 3 seconds. Power = 78 ft lbs / 3 seconds *(60sec/1min) * .02259697 = 35.3 Watts

    17. Combined Motor Curves

    18. Motor Calculations Motor Power = Power Available = Free Speed / 2 * Stall Torq. / 2 * C.F. Where: Free Speed is in rad / min Stall Torque is in ft lbs Conversion Factor = .02259697

    19. Motor Calculations Free Speed (rad/min) = RPM * 2 Pi (rad/rev) Stall Torque (ft*lb) = (in oz)*(1 ft/12 in)*(1 lb/16 oz)

    20. Motor Calculations Drill Motor Free Speed = 20000(rev/min)*2PI(rad/rev) = 125664 rad/min Stall Torque = 650 (Nmm)*(1 lb/4.45 N)* (1 in/ 25.4mm)*(1 ft/12 in) = .48 ft lbs

    21. Motor Calculations Drill Motor Power = Free Speed / 2 * Stall Torque / 2 *Conv. Factor = 125664 / 2 * .48 / 2 *.02259697 = 340 W

    22. Choosing a Motor Need 78 ft lbs of Torque (ex 2) Try Globe Motor w/ Gearbox Working Torque = Stall Torque / 2 = (15 ft lbs @ 12 V) / 2 = 7.5 ft lbs

    23. Gear Ratios Gear Ratio = Torque Needed / Torque Available = 78 ft lbs / 7.5 ft lbs = 10.4 :1 Now time to find the gear train that will work!

    24. Choosing a Motor In Summary: All motors can lift the same amount (assuming 100% power transfer efficiencies) - they just do it at different rates BUT, no power transfer mechanisms are 100% efficient If you do not account for these inefficiencies, your performance will not be what you expected

    25. Materials Steel High strength Many types (alloys) available Heavy, rusts, Harder to processes with hand tools Aluminum Easy to work with for hand fabrication processes Light weight; many shapes available Essentially does not rust Lower strength

    26. Material Lexan Very tough impact strength But, lower tensile strength than aluminum Best material to use when you need transparency Comes in very limited forms/shapes PVC Very easy to work with and assemble prefab shapes Never rusts, very flexible, bounces back (when new) Strength is relatively low

    27. Structure Take a look at these two extrusions - both made from same Aluminum alloy: Which one is stronger? Which one weighs more?

    28. Structure The solid bar is 78% stronger in tension The solid bar weighs 78% more But, the hollow bar is 44% stronger in bending And is similarly stronger in torsion

    29. Structural Equations

    30. Stress Example Let's assume we have a robot arm (Woo hoo!) that's designed to pick up a few heavy weights. The arm is made out of Al-6061, and is 3/8" tall, 1" wide, and 3 feet long. The yield strength is about 40,000 PSI. In the competition they are hoping to to pick up 3 boxes of 15 lbs each. Will this arm be strong enough?

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