Theory of vibrations in Stewart platforms

This article develops a simple linear model for the motion of a Stewart platform in a stationary position. That is, the situation where the platform is at rest and is then subject to an impulsive disturbance. The hydraulic actuators are modelled as simple spring-dashpot systems and the stiffness and damping matrices of the system are derived. It is found that the damping and stiffness matrices are simply proportional to each other and this simplifies the dynamics greatly. The general solution to the equations of motion is a linear combination of eigensolutions. The eigensolutions are damped oscillations about the harmonic screws of the undamped system. The characteristic values associated with each eigensolution can also be found in terms of the undamped frequencies. Finally some remarks are made concerning the possibility of the system being fully damped.