MAY 72 1898 
KANSAS UNIVERSITY QUARTERLY. 
Vor. Vil: ARIE 2 1893: Nor 2: 
The Designing of Cone Pulleys. 
BY WALTER K. PALMER. 
Copyright. 1897. 
INTRODUCTION. 
Probably no other minor operation of machine designing involves 
such a complex mathematical analysis as the apparently simple 
one of proportioning a pair of cone pulleys. 
The question of determining a single pair of pulleys to give a 
desired velocity ratio for their shafts, is so elementary and so easily 
solved by the simplest application of arithmetic, that it is difficult 
at first to realize that there can be anything at all to make impossible 
an equally simple treatment of the problem of a series of pulleys 
on one shaft, paired to run with a corresponding series on another, 
? 
which constitute what are commonly called ‘‘cone,”’ or ‘‘step cone”’ 
pulleys—the several pulleys of each being the ‘‘steps.”’ 
But the one condition which must be observed when propor- 
tioning the series of steps of a cone pulley, and which is not 1m- 
posed in the case of a series of independent pairs of pulleys—that 
the same de/¢ must fit with an equal degree of tension on each one 
of the pairs of the series—introduces complications which make the 
problem a most difficult one for exact solution; and one which, it 
is believed, has not yet been treated in full by an exact method, 
either analytical or graphical. At least no method, not involving 
some kind of an approximation, or tentative process, has been of- 
fered, which is of a satisfactory form to use in the course of every 
day practice. 
A purely analytical solution is not to be expected, owing to the 
form of the equations, as will appear. And such a solution is not 
(41) KAN. UNIV. QUAR., VOL. VII, NO, 2. APRIL, 1898. SERIES A, 
