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National Advisory Committee for Aeronautics, Technical Notes - Analytical Determination of Control System Pulley Axis Angles

The ideas developed in this paper are presented as a H
means of saving the designer's time and as a method of re— _ _
duction of control— system friction by an accurate calcula—
tion of pulley—axis angles without the errors and difficult
checking incident to any graphical methéd.'

The growing realization of the necessity for greater .
care and refinement in the design.of control systems is M
justification for the more accurate analytical methods
given. Saving in layout and checking time is also of im~
pertance, although probably secondary to the greater re—
finement obtainable by the use of a calculating machine
even in the hands of inexperienced personnel. It is sug—
gested that the formulas given here are worthy of careful
trial by any engineering department that is n.ot already
using an equivalent method of design.

Two mathematical laws are employed in the derivation
of the formulas for pulley-axis angles to givehcorrect
alinement with control cables and therefore avoid binding,
and_to reduce friction. These laws are:

1. Any two intersecting straight lines determine a m
single plane.

2. The first partial differentials of the equation ,
of a surface are proportional to the direc—
tion cosines of the normal to that surface
at any point chosen for investigation.

Since any pulley, to operate properly, must have its
center plane coincident with the plane containing the
cables leading around it, the location and angles of the
pulley axis, with reference to the coordinate planes, are
the values required to properly construct and locate a
pulley bracket.