There is one great objection to worm gearing on account of
the friction due to the sliding action between the teeth. The
worm is a screw with threads shaped on the plan of the U. S.
S. except that the flats at the top are much wider and the
included angle of the sides is 29°. The thread of a worm
can be spoken of as having a lead and it can be of single,
double, triple, quadruple, etc., thread as in screw threads.
The tooth of the worm wheel, which meshes with the thread
of the worm, advances the distance of one tooth at each
revolution of a single thread worm; therefore if a worm
wheel has 30 teeth, the worm will have to revolve thirty
times for one complete revolution of the worm wheel.
The velocity ratio in the case of double, triple, etc., thread
worms will then be the number of teeth in the worm wheel
divided by 1, 2, 3, etc., according as it is a single, double,
triple, etc., thread worm.
42



SHOP MATHEMATICS




Fi^.34,



PROBLEMS

1. A, Fig. 34, is a double thread worm and B a worm

wheel with 80 teeth,
12f in. dia. fast to an
axle, a, 4 in. dia. The
crank C is 12 in. long.
What weight can be bal-
anced at W when 75 lbs.
of force is applied at xf

2. If A, Fig. 34, had
been a triple thread
worm and B had 45 teeth and 18 in. dia. with 5 in. axle, a,
what length of crank C will be required to lift 4,000 lbs.
with a force of 60 lbs. at xf

3. If a. Fig. 34, is a differential axle with 5 in. and 7 in.
