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.

112

DESCRIPTIVE GEOMETRY

After a half revolution the two generating lines will take the positions indicated in vertical projection by d"-a" and d"-e" respectively, and after a complete revolution they will take the positions
indicated in vertical projection by d"'-a"' and d"'-e"' respectively.
We may regard the thread of a triangular-threaded screw as
generated by the surface of an isosceles triangle which moves uniformly around and along the surface of a right circular cylinder
in such a way that the base of the triangle always rests on the
surface of the cylinder, and the plane of the triangle always contains
the axis of the cylinder.
~ ~ [ -I ~~ ~ On account of this motion each
~/; ~ a\ pex of the triangle will gener| / \ \ ate a helix (see Section 213).
~I ~ ]d \ \ A If the downward movement
St a t g'f\?of the triangle per revolution
\ /& /l is equal to its base, the screw is, J-1n- / called single threaded; if equal
n L Ai / to twice the base of the triangle,
'0G____ _ L --- it is called double threaded;
a ' and if equal to three times the
I jI. -a"t/ I-, i base of the triangle, it is called!fl y-a" 'd' triple threaded.
l^..^d" d Fig. 115 represents a single|I." - ^ '~._,d"', t triangular-threaded screw.
("[^dr -t-^::^~f'" |<t The cylinder is represented in
I ^ e" / 1 plan by f,-n,-l,-o, and in eleva<a i~ tion by f'-k'-m'-l'. The gen|]= 2 = ~~~ ^ _ —'erating triangle, when its plane
I, M lb' is parallel to V, is represented
FIG. 115 in plan by f,-d, and in elevation by f'-d'-g'.
The helices generated by the points F, D, and G may be represented by Section 214, remembering that the pitch in each case is
equal to the length of the base of the triangle.
The extreme elements of the thread surface on the right and left
are represented in vertical projection by f'-d'-g'-d"'-gl"'- and
by f"-d"-g"-d9" —g#" -, which represent the vertical projections