OverviewNeeding 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. 
HorsepowerI just realized that while I go about calculating the pulley size it is based on a predetermined belt width and pulley dia – meaning I haven’t done any calculation on what horsepower that combination would transmit. 
Rim DimensionsRounding For isolated pulleys the facewidth B is taken somewhat greater than the width of the belt b; often we take – B = Face Width – Rim Edge Thickness – k = Rim Thickness – Rounding at Pulley Face – s = Rounding at the pulley face The thickness of the rim at the center is therefore the rounding + thickness at the rim k = Rim Thickness 
PulleyNaveThe thickness of a pulleynave is given by the formula – 
Arms of PulleysOrdinarily the arms of pulleys have oval crosssections, the diameter in the plane of the pulley being twice the smaller diameter. Fig. 57 shows a crosssection of the arm but that was simply how to draw an oval that is half the width. 
The axes of pulleyarms may be straight as in Fig. 58, curved as in Fig. 59, or double curved in the form of a letter S. Singlecurved 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 formulaN = Number of Arms R = Pulley Radius b = Belt Width 
– Pulley Arm Widths – The formula gives the greater diameter for the pulleyarms (width of the arms in the plane of the pulley). The diameter or width h is taken at the nave as shown in Fig. 58, and the width h, at the rim may be conveniently taken equal to The width at right angles with the plane of the pulley is therefore
