A TREATMENT OF INSTANT ANGULAR AND LINEAR 
VELOCITIES IN COMPLEX MECHANISMS. 
OLIVER B. ZIMMERMAN, 
Assistant Professor of Machine Design , University of Wisconsin. 
To the engineer, it is usually desirable, in the treatment of 
kinematic motions, to obtain as simple and direct a solution of 
the problem as is possible. This simplicity requires either a 
rapid graphical solution or the simplest of equations to represent 
the relations that exist between parts of a mechanism, whatever 
these relations may be. 
It is to present a treatment of angular and linear velocities, 
somewhat different from that usually given that I submit the 
following. This method of solving such problems, especially 
those of a. complex nature, has been used by the classes in engi¬ 
neering kinematics for the past three years, and has been found 
more satisfactory than the older geometrical solutions. 
In Fig. I, take the four link, crossed link mechanism A. B. 
C. D., links A and B equal in length to G and D respectively, 
hold A stationary and follow the motion of O, keeping links B 
and I) crossed throughout the motion. 
We understand from our knowledge of centros that all points 
in C roll with respect to A about the instant center ac. Follow 
the path of this instant center and it will be found to describe, 
under the conditions named, the two elliptical centrodes, the 
body centrode and the space centrode. 
We. know further that if the two links B and D be removed, 
we can produce the same relative motion between links A and 
O if we replace links B and D by the two centrodes which point 
ac describes during its motion, and roll them together without 
slip. We can state also that links A and O are lines upon the 
