398 MOLESWORTH 8 POCKET-BOOK
Epicycloidal Teeth.
The curves of epicycloidal teeth are gencrflted
by a point in the circumference of a circle (called
the rolling circle) which rolls on the pitch line of
the teeth to be described.
To Delineate the Required Curves by Construction.
From the centre C, with radius C B, draw tho
pitch line A B. From any point, y, lay off on thø
pitch line, any convenient points, defy h, at any
distances from one another, and from them draw
the radial lines CdCeC/CøOA; and, with
tlicir centres on these radial lines, describe circles
equal to the rolling circle, and touching the pitch
line at the points d e f g h.
On the circumference of |at d get d j z=y d
„ „ at g „ g^-yg
„ at h „ h n = y h
The points y j k I m n form the required curve for
the root of the teeth.
Also set off, in like manner, the points p q r s,
and through these points draw radial lines, and,
with their centres on these radial lines, describe
circles equal to the rolling circle, and touching
the pitch line at the points p q r s.
On the circumference of j at lay off p t = y p
the circle _________J
„ at q „ q v = yq
’ „ at r „ r x = y r
„ at s „ s z = y s
Then ’the points ytvxz form the curve for the
point of the tooth.
For straight racks instead of radial lines, per-
pendicular lines are used.