### Overview

Needing a Flat Belt style Pulley transmission system for my turbine I found this book titled – A treatise on belts and pulleys By John Howard Cromwell published 1885.

I was just wanting a general outline of the style and dimensions for a pulley and this book pretty much will answer any question I have. Like many book from the period it is very wordy – I think they were probably paid by how many words were in the book. This blog gives me a chance to winnow out the bits that I need.

Geeze. Trying to make sense of this is fun – in a .. hitting your finger with a hammer feels better when you stop – kinda way.

### Horsepower

I just realized that while I go about calculating the pulley size it is based on a pre-determined belt width and pulley dia – meaning I haven’t done any calculation on what horsepower that combination would transmit.

### Rim Dimensions

-Rounding-
The rim of a pulley intended to carry a flat belt is generally rounded (Figs. 48 and 49), in order that the belt may remain in the centre of the pulley-fact, instead of working to one side, as is the case with flat-faced pulleys. The amount of this rounding (s) may be taken equal to $\frac{1}{20}$ the width of the belt.

For isolated pulleys the face-width B is taken some-what greater than the width of the belt b; often we take –
$B = \frac{5}{4}b$

B = Face Width
b = Belt Width

– Rim Edge Thickness –
The thickness k of the edge of the rim, or the thickness at the ends of the face-width, may be easily calculated from the formula –
$k = 0.08 + \frac{B}{100}$

k = Rim Thickness
B = Face Width

– Rounding at Pulley Face –
For the amount of rounding at the pulley-face

$s=\frac{1}{20}*b$

s = Rounding at the pulley face
b = Belt Width

The thickness of the rim at the center is therefore the rounding + thickness at the rim

$2*k+s$

k = Rim Thickness
s = Rounding at the pulley face

### Pulley-Nave

The thickness of a pulley-nave is given by the formula –
$w = 0.4 + \frac{d}{6} + \frac{R}{50}$
in which d represents the diameter of the shaft upon which the pulley is keyed, and R the radius of the pulley.
The length of the nave should not be taken less than
$L = 2.50w$
Often (in idle pulleys, for example) the length L is taken equal to the face-width B of the pulley.

### Arms of Pulleys

Ordinarily the arms of pulleys have oval cross-sections, the diameter in the plane of the pulley being twice the smaller diameter.

Fig. 57 shows a cross-section of the arm but that was simply how to draw an oval that is half the width.

The axes of pulley-arms may be straight as in Fig. 58, curved as in Fig. 59, or double curved in the form of a letter S. Single-curved arms may be drawn in the following manner: Take (Fig. 59) the arc AE equal to 2/8 the arc EF, determined by the centre s of the arms at the rim of the pulley, and draw AO perpendicular to AO. From the centre D draw CD perpendicular to AO. From the centre D draw CD perpendicular to OE, and the point C of intersection of DC and OC is the centre for the curved axis of the arm.
– Number of Arms –
The number of arms (N) necessary for pulleys of different sizes may be determined by means of the formula$N = \frac{1}{2} (5+\frac{R}{b})$N = Number of Arms
$h = 0.24 + \frac{b}{4} + \frac{R}{10N})$
$\frac{2}{3}h$
$h_1 = \frac{2}{3} X h$