The mechanical conditions of mule directly related to spinning are the length
L of spinning field. the delivery-length
F of sliver from front roller and the revolutions
N of spindle, which are recorded against the elapsed time
t. The spinning-length
L is different from the horizontal displacement
l of spindle or carriage near the front roller, but almost equal to it in the later, effective part of spinning. The length
l or
L is generally represented as follows: The terms
F and
N may also be shown in the similar type of formula as
l(
t), and are also the functions of position
l, say; The terms except
l.
L,
F and
N are constant, and sometimes are regarded as
b=
k=β=1 or τ=κ=0 in the above equations. The displacement and also the delivery are more or less deformed from the shape of scroll because of the inertia of carriage, especially at the beginning of outward-run. At first the carriage-movement is delayed and then accelerated. The delivery is less deformed than the displacement. Mule has several discontinuos points of motions in its spinning process. The spindle-revolutions transit smoothly in the oil-box driving system employed in this experiment.
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