Elements of descriptive geometry, with applications to isometric projection and othe forms of one-plane projection; a text-book for colleges and ingineering schools by O. E. Randall.

REPRESENTATION OF WARPED SURFACES 113

of the sides of the generating triangle when occupying positions
parallel to V.
283. Problem 168. To represent a square-threaded screw.
In Fig. 116 let A-B represent the axis of a helicoid, and let D-E
and F-G, equal in length, perpendicular to the axis, parallel to
V, and at astated distance apart,
represent two generating ele- // - \
ments of the surface. / /
Make D-K and F-L each / \ \
equal to D-F. Through D and dir ---at -— id!
Fdraw the indefinite vertical k, a,,
line D-zlf, and through K and \
L draw the vertical line K-N. \! / /
While the generating lines | i
D-K and F-L generate their G - aj-. L
respective helicoidal surfaces, q- Id'
the four points D, F, L, and (< 2i4f'
K will generate their respec- d'J k~ -Hw'
tive helices, and the two verti- /f c --- ' —x
cal lines D-M and K-N will A _<' d"'
generate cylindrical surfaces f'I
whose diameters are equal to
d,-d,, and k,-k,, respectively.
If in this particular case the I I
pitch of the helicoidal surfaces I b' In'
is made equal to twice, or four FIG. 116
times, or six times, etc., the distance D-F, the surface generated
by the three sides K-D, D-F, and F-L of the square K-D-F-L
will be the surface of a square-threaded screw.
In Fig. 116 the pitch is made equal to four times the distance
D-F. After a half revolution the three generating lines D-K,
D-F, and F-L will take the positions indicated in vertical projection
by d"-kf", dJ-f", and f"-l"; and after a complete revolution they
will take the positions indicated in vertical projection by d"'-k"',
d"'-f"', and f"-'l".
We may regard the thread of a square-threaded screw as generated by the surface of a square which moves uniformly around and