On Attempting to Reduce Undesirable Inertial Characteristics of the Schatz Mechanism

Abstract

Using the geometrical properties of the Schatz linkage, we develop expressions for the velocity and acceleration of the mass centre for each coupler and for the angular velocity and acceleration of each link. We attempt to reduce the serious inertial characteristics of the linkage by seeking an input pattern which decreases the magnitudes of acceleration components. We find that the most beneficial form of drive, under our criteria, is that which results from using a Hooke’s joint with a drive-shaft inclined at 45° to the input link. We employ the methods of classical mechanics to determine joint forces and input torque for a working model of the linkage for this case and for that with constant input angular velocity. We find that, despite the difference in acceleration characteristics, the consequent forces and torque for the two cases are practically identical. We subsequently determine locations of acceleration centres for the links as an indication of possible relationships with inertial properties. The result of this particular investigation leads us to also develop the equations of the axodes for the couplers.