Zimmerman—Instant Angular and Linear Velocities. 517 
from tli© velocity of the given point the velocity of the common 
point, then the velocity of the required point from that of the 
common point.” This rule enables ns to omit from considera¬ 
tion all intermediate links in the more complex mechanisms, as 
will be shown later. In Mg. 3, the rocker arm B and cam D 
move with respect to each other. At this position of the mech¬ 
anism 
V°B bd—ad 
V°D bd—ab 
when A is stationary. In Big. 4, the same equation holds, the 
difference being that here the directional motion of the two 
links is opposite, whereas in Fig. 3 it is the same. The relative 
directional rotation is very clear after noting the position of the 
common point with respect to the centros of rotation. In this 
position of the mechanism, the two centrodes vary in opposite 
direction when motion occurs. The dotted position indicates 
where the directional motion is changing from one to another 
hence Bi has a zero angular velocity for the instant. 
Figures 5, 6, 7 and 8 represent the slides crank chain with 
various links held stationary and with comparisons made of 
angular and linear velocities. 
In Fig. 5, A is stationary. 
V°B bc—ae 
V°C as be—ab 
The linear velocity of point 
QY) 
y — -V velocity of x, 
mn 
the velocities being compared through that of the common point. 
The centrode of B has a constant diameter, while the centrode 
of C varies. 
In Fig. 6 B is stationary. 
V°C ac-ab 
V°A ac—bc 
Here the t\Vo centrodes vary together, the distance between 
centers being a constant. 
In Fig. 7, O is stationary. 
y°D_ bd—be 
V°B ~bd-de 
