Dynamic Modeling of Systems With Translating Components

This paper summarizes a method for modeling the vibration response of mechanical systems whose configuration may vary during operation. A model of adjacent elements which experience relative translational motion is developed. System Differential equations are derived and then transformed to accept as input angular acceleration rather than torque information at the actuator shafts. A technique for determining this angular acceleration information from optical encoder signals is described. Finally, predicted and actual vibration response for a representative system, a cartesian robot, are presented and compared.