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PROFESSOR T. A. HEAR SOFT OH THE KINEMATICS OF MACHINES. 
that period, the angular velocity ratio will remain constant, or the curvature of the 
slotway may be so designed as to cause a specially desired change in the angular 
velocity ratio. 
An exceedingly important advantage is thus obtainable from the mechanism of 
fig 4 as compared with 1 and 2 ; moreover, it is obtained by the use of one less link 
or moving piece. But these advantages are purchased at the cost of requiring that 
the consecutive links V and Z be in contact at a point, or along a line of points only 
instead of over an area, so that, if considerable pressure is transmitted from one link 
to the other, there is liability to undue abrasion and rapid wear. 
If the action of the forces is such as to keep the link V always in contact with one 
side of the slotway, the other side may be omitted, as shown in fig. 5. In this case 
the pin w need not be cylindrical, but any shape. 
The relative motion of V and Z in fig. 5 is comparable to that of two teeth of a pair 
of spur wheels or two cam surfaces. It will thus be seen to be an amalgamation of 
two adjacent OU or I motions. 
The mechanism may be regarded as a mechanical artifice, whereby we get the 
movements which would be due to a four-linked mechanism in which the length of 
the links were capable, during the movement, of being varied in a desired way. 
According to this point of view the same two geometrical laws will be applicable to 
mechanisms containing these motions. For example, from Law I. it will follow that 
the angular velocity of Z relatively to V must equal the algebraical difference of the 
angular velocities of Z and V relatively to T. 
A convenient and expressive notation for such movements may be derived by 
suppressing the absent link and joining up the two simple adjacent OUI motions into 
one more complex. The letter W will naturally stand for an amalgamation of two 
U’s, and the figure eight on its side, or the sign of infinity co for two O’s, or would 
be useful to indicate rolling motion. 
The Greek letters and F are also available. 
A mechanism consisting of two spur wheels, mounted in a link and in outside gear 
with one another, may be represented by OWO, and an inversion of it WOO. If 
the outside of one wheel gears with the inside of the other (an annular wheel), the 
formula should be OWo. 
By the use of pulleys with ropes, belts, or other flexible links, another mechanical 
device is provided, whereby the angular velocity ratio in consecutive positions of the 
mechanism may be maintained constant, or caused to vary in a desired way. In this 
case the result may be considered to be achieved by a perpetual substitution of new 
links, exactly like the previous ones, and in the previous positions, when those have 
moved out of place, instead of regarding the movement to be continued by links of 
altered length, adapted to the new positions as we conceived to be the case with spur- 
wheels. 
The relative motion of' a belt to a pulley, which it wraps, is such that every point 
