Zimmermmii—Instant Angular a/nd Linear Velocities. 519 
Take the three links B, G and O. Let O be stationary, then 
we have 
V°B Jbg—cg 
V°G~bg—bc 
the two links B and G have opposite directional rotation with 
respect to the stationary link C. 
When considering 
V°E 
V°H 
when A is held stationary we have 
V°E _ eh—ah 
V°H ~eh—ae 
the four points ah and ae at the top of the plate are the centers 
of the rotation and the common point of the two links is at °o 
hence the angular velocities of E; and H with respect to A show 
themselves to he equal. 
In conclusion then, we employ here a more simple set of 
centrodes; we have a rapid graphical solution in which a direct 
method of comparing angular and linear velocities is involved, 
a method where directional rotation is made less intricate, where 
the relative value of instant angular and linear velocities can 
be represented by a simple equation and where solutions of a 
complex nature are brought down to a plane with those less 
complex. 
University of Wisconsin, December, 190S. 
