PROFESSOR T. A. HEARSON ON THE KINEMATICS OF MACHINES. 
21 
In the most important examples the line of slide is parallel to the line joining the 
axes of the adjacent U and 0 motions, which is equivalent to requiring the two links 
joined by the I to be imagined equal as well as infinite. But the line of slide may 
be oblique to the line joining the axes of U and O, short of an amount which would 
cause the distance between those axes measured pependicularly to the line of slide to 
be equal to t-he difference in the lengths of the two finite links which join O and o 
and o and U. When the distance so measured is equal to the difference, a move¬ 
ment represented by 0 3 o 3 UI may take place, and if the distance exceeds this difference! 
then all 0 motions are precluded. All this follows from Law II., and is consistent 
with the statement, p. 18, of the conditions requisite for OoUU and OVUU. 
Next, if, for the other swing, we substitute a second slide we obtain the movement 
OoII. In the most important examples of this the two lines of slide are at right 
angles to one another ; but this is not necessary. It would be possible to increase 
the expressiveness of the formula by inclining the I’s to the actual angle employed. 
It is interesting to notice that the movement 0 3 o 3 II is not possible, for with I’s 
instead of U’s the conditions requisite for OVUU could not be satisfied, since the 
sum of a finite link and an infinite link cannot be equal to the sum of two infinites. 
It may also be noticed that inasmuch as we cannot have OUoU (p. 18), then, for the 
same reason, we cannot have OUol, or OIoI. 
From UUUU we may derive by substitution UUUI, and UUII, and XJIUI. 
In the last mentioned all the links are to be conceived of infinite length, but the 
axes of the two U’s are at a finite though variable distance apart. 
The combination UIII is not possible, for a slide is to be regarded as a swing through 
a zero angle about an infinitely distant centre, and there being no change in the 
angles of the imaginary quadrilateral at three of the joints, Law I. will preclude a 
change at the fourth joint. 
The movement IIII will be possible, but not only are all the links to be conceived 
of infinite length, as in UIUT, but there is no finite length whatever in the 
mechanism. This will permit of the movement being as indefinite as if there were 
five links of finite length joined by pins. 
One of the links and slides may he suppressed, and the mechanism will then provide 
a definite relative movement represented by III, which may otherwise be shown with 
the I’s inclined to one another, as the lines of slides are. 
The fourteen combinations of the OUI motions which have been mentioned exhaust 
the list of the different possible ways in which they can be associated together in one 
simple plane mechanism. 
The OUI motions permit of the possibility of the two pieces, which so move rela¬ 
tively to one another, being in contact with one another over an area which may be 
extended to any amount which may be deemed desirable. 
From this property great durability against wear is provided, and this advantage, 
combined with that due to the facility with which the necessary surfaces of contact 
