The continuous belt of Example 1.48 has length L given by

Show that when R – r ≪ l, a good approximation to L is given by

Data from Example 1.48

A continuous belt of length L m passes over two wheels of radii r and R m with their centres a distance l m apart, as illustrated in Figure 1.32. The belt is sufficiently tight for any sag to be negligible. Show that L is given approximately by

Find the error inherent in this approximation and obtain error bounds for L given the rounded data R = 1.5, r = 0.5 and l = 3.5.

Figure 1.32

Transcribed Image Text:

L = 2[1 (Rr)]/ + (R + r) + 2(R - r) sin - R-r