230 
OF THE PARTS OF 
[sect. VII. 
Table of the Variation of Rotary Force, when a Crank is impelled 
by a Constant Force. 
Portion of 
circle de- 
Stress on 
Portion of 
Length of the connecting rod, the length of the crank being 1. 
the axis, 
when the 
the stroke 
scribed, in 
connecting 
rod is 6 
described, 
degrees 
the whole 
from the 
6 
times the 
being 1. 
beginning. 
2 
3 
4 
5 
7 
length of 
the crank. 
0-000 
0° 
0-00 
0-00 
0-00 
000 
0-00 
0-00 
1-000 
0-067 
30 
0-72 
0-65 
0-61 
0-59 
0-57 
0-56 
0-825 
0-146 
45 
0-97 
0-87 
0-83 
0-80 
0-78 
0-77 
0-624 
0-250 
60 
1-10 
1-01 
0-98 
0-95 
094 
0-93 
0-375 
0-500 
90 
1-00 
1-00 
1-00 
100 
1-00 
1-00 
0-169 
0-750 
120 
0-62 
0-75 
0-75 
0-78 
0-79 
0-80 
0-625 
0-854 
135 
0-43 
0-57 
0-57 
0-60 
0-62 
0-63 
0-790 
0-933 
150 
0-27 
0-39 
0-39 
0-42 
0-43 
0-44 
0-907 
1-000 
180 
0-00 
0-00 
0-00 
0-00 
0-00 
0-00 
1-000 
The length of the crank is supposed to be 1 ; and the table applies to any other 
length of crank, when the connecting rod is 2, 3, 4, 5, 6, or 7 times its length : 
the columns below these numbers show the rotary force corresponding to the posi 
tions indicated in the first and second column. The stress in the last column being 
greatest at each end, will have a tendency to wear the shaft into the form of an 
oval, having its longest diameter at right angles with the connecting rod. 
Parallel Motion. 
488. The next method to be described for communicating motion from a 
piston rod to a beam is that called the 4 Parallel Motion.’ It was invented by 
Mr. Watt, who first gave a notice on the subject in 4 Robison’s Mechanical Philo 
sophy ;’ and its theory has been since analytically investigated by Prony. We shall, 
by confining the enquiry to practical conditions, however, be able to treat it more 
briefly, and show how the best proportions for practice may be obtained. 1 
There are two cases, which for simplicity we shall investigate separately, 
though they are generally both in use in the same engine. 
489. First case. If each of two bars A B, C D, Plates x. (A) and (B) Fig. 4. has 
an axis at one end, round which it moves, and the other end be connected with a third 
bar B D, by moveable joints; then there is a point E in the middle bar which will 
nearly describe a straight line. The rectilinear movement of the air-pump rod, in 
1 A patent for the protection of the Parallel Motion was taken out by Mr. Watt in 1784, and 
the invention was in 1787 applied in its most perfect form to the engines of the Albion Mills.