To aid in our delineations we draw from the center _A_ the radial lines
_A d'_ and _A m'_, passing through the points _d m_. The arc _a_ is next
drawn as in former instructions and establishes the length of the
addendum of the escape-wheel teeth, the outer angle of our escape-wheel
tooth being located at the intersection of the arc _a_ with the radial
line _A d'_.
As shown in Fig. 92, the impulse planes of the tooth _D_ and pallet _C_
are in contact and, consequently, in parallel planes, as mentioned on
page 91. It is not an easy matter to determine at exactly what degree of
angular motion of the escape wheel such condition takes place; because
to determine such relation mathematically requires a knowledge of higher
mathematics, which would require more study than most practical men
would care to bestow, especially as they would have but very little use
for such knowledge except for this problem and a few others in dealing
with epicycloidal curves for the teeth of wheels.
For all practical purposes it will make no difference whether such
parallelism takes place after eight or nine degrees of angular motion of
the escape wheel subsequent to the locking action.
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