Gear Theory

  •  http://www.technologystudent.com/gears1/geardex1.htm

    This activity familiarizes students with gears of different sizes and how these relate. There are excellent mathematics connections, such as relating the number of times a small gear turns to that of a larger gear. Students can also compare circumferences. Students should discover the ratio of gear teeth, such as 8 teeth on the smaller gear and 40 on the larger gear, means that the small gear must turn 5 times to move the larger gear once. You might ask students to create a table and record their results. 

    Brain Pop      Ballston /Scotties   Gears

    Gears
    Gears are toothed or pegged wheels meshed together to transmit motion and force. In any pair of gears the larger one will rotate more slowly than the smaller one, but will rotate with greater force. Each gear in a series reverses the direction of rotation of the previous gear.

     

    Circumference of Drive Wheels

    Wheel  Diameter Formula for Circumference Circumference of the wheel
    1 2pi x r or pi x d 3.141
    1 1/2 where pi = 3.14159 4.712
    2 d= diameter of wheel 6.283
    2 1/2 r = radius of wheel 7.853
    3   9.424
    3 1/4   10.210
    3 1/2   10.995
    3 3/4   11.780
    4   12.566

     

    Gear Ratios

      

    http://www.technologystudent.com/gears1/gears1.htm

     

    Gear 1 Gear 2 distance between centers
    12 20 5/8"
    12 30 13/16"
    12 40 1"
    20 30 1"
    20 40 1 3/16"
    30 40 1 3/8"

    Combinations from the following gears 12t, 20t, 30t & 40t

    2 gears in combination - [Driver:Driven]

    12:20 3:5 12:30 2:5 12:40 3:10
    20:12 5:3 20:30 2:3 20:40 1:2
    30:12 5:2 30:20 3:2 30:40 3:4
    40:12 10:3 40:20 2:1 40:30 4:3

     

     http://www.technologystudent.com/gears1/gears2.htm

    Another look at Compound Gears

     http://www.technologystudent.com/gears1/gears3.htm

    Compound gear Calculator

    4 gears in combination      12:20 ; 30:40  =  3/5 x 3/4 = 9/20 or 9:20 the 20t and 30t are on the same "axle"

    12:20; 30:40 9:20 20:12; 30:40 5:4 30:12; 20:40 5:4 40:12; 20:30 20:9
    12:20; 40:30 4:5 20:12; 40:30 20:9 30:12; 40:20 5:1 40:12; 30:20 5:1
    12:30; 20:40 1:5 20:30; 12:40 1:5 30:20; 12:40 9:20 40:20; 12:30 4:5
    12:30; 40:20 4:5 20:30; 40:12 20:9 30:20; 40:12 5:1 40:20; 30:12 5:1
    12:40; 20:30 1:5 20:40; 12:30 1:5 30:40; 12:20 9:20 40:30; 12:20 4:5
    12:40; 30:20 9:20 20:40, 30:12 5:4 30:40; 20:12 5:4 40:30; 20:12 20:9

     

     http://www.technologystudent.com/gears1/pulley2.htm

     

    Our Pulleys for class project:

    Pulley 1 Pulley 2 Pulley 3 Pulley 4
    3/8 diameter (0.375) 6/8 diameter (0.750) 9/8 diameter (1.125) 12/8 diameter (1.500)

    Distance Between Pulleys

    Pulley A Pulley B  Distance
    1 2 2.375 inches
    1 3 2.125 inches
    1 4 1.750 inches
    2 3 1.750 inches
    2 4 1.375 inches
    3 4 1.375 inches

    Speed Chart Circumference is pi (3.14159) x Diameter

    Device How Far Unit
    Motor 11000 RPM's
    Drive Wheel 1.5 inches diameter
    Drive Wheel 1 turn 4.71 inches
    Drive Wheel 51810 Inches Per Minute
    Drive Wheel 4317.5 Feet Per MInute
    Drive Wheel 0.8177083 Miles Per Minute
    Drive Wheel 49.0625 Miles Per Hour

     

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