Build Your Own Combat Robot

Appendix C: Helpful Formulas 357
chain due to the high tension. If this is the case, add another master chain link to
the system.
Timing Belt Centerline Distances
The pulley centerline distances are computed in a similar manner to how the centerline
distances are computed with chain drive systems. The first step is to determine
a belt length. Equation 3 shows this relationship from the Martin sprocket and
gear catalog.
V-Belts
C is the center distance, L is the belt length, D is the pitch diameter of the larger
pulley, and d is the pitch diameter of the smaller pulley. Unlike equation 1, the center
distance and belt length are not in terms of pitches, but they are actual distances.
The pitch diameter of a timing belt pulley is always larger than the outside
diameter of the teeth on the pulley. The initial center distance, C, is estimated
based on preliminary robot designs. Belt lengths come only in finite lengths. Once
you determine the value for the belt length, you have to compare this with the
available belt lengths for the particular belt type. Then select the belt length that is
closest to the one calculated here. With this new belt length, you then need to calculate
the actual center distances of the pulleys. Equation 4 shows the relationship
that Martin uses to calculate these distances.
As with timing belts, a V-belt length is first estimated based on an initial sheave center
distance estimate. Spotts (Spotts, M.F., Design of Machine Elements, Prentice-Hall,
1985, pp 292) shows the relationship for determining the belt length in Equation 6
and then determining the actual center distance in Equation 7.
L is the belt length, C is the center distance, R 1 is the radius of the smaller diameter
sheave, and R 2 is the radius of the larger diameter sheave. The actual belt length
must match available belt lengths for the particular V-belt.
2
3
4
5
6
7