Build Your Own Combat Robot

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OLLOWING are formulas that you might find helpful in calculating
drive, timing belt, and V-belt centerline distances.
Chain Drive Centerline Distances
When calculating the center distance, the first step is to estimate the center distance
between the two sprockets, as shown in Figure C-1. Start with a distance in
which you would like the sprockets to be spaced.
The center distance is in terms of number of pitches, so divide the physical distance
by the chain and sprocket pitch. For example, if you are using a #40 chain that has
a 1/2-inch pitch, and the first estimate center distance is 12 inches, the first value
of C is 24 pitches (24 pitches = 12 inches / [1/2” inch per pitch]). If the large
sprocket has 20 teeth and the small sprocket has 10 teeth, chain length from Equation
1 (from Martin Sprocket and Gear Incorporated Catalog No. 60, 1987) is
63.106 pitches long. Now chains can only be in integer pitch lengths, so you either
round this number up or down to the nearest integer. In this case, since the final value
is closer to 63, you will use this value in Equation 2 to determine the final center
distance. The final center distance is now 23.947 pitches long. To convert this
back into actual inches, multiply this value by the pitch length. In this case, you are
using a 1/2-inch pitch; thus, the center distance is 11.974 inches.
FIGURE C-1
Sprocket center
distances
C is equal to shaft center distances in pitches, L is the chain length in pitches, N
is the number of teeth of the larger sprocket, and n is the number of teeth of the
smaller sprocket. You can see that these formulas can be rather complex.
When building the actual robot, if you use a center distance value that is slightly
larger than the theoretical center distance, it might not be possible to assemble the
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