Theory of vibrations in Stewart platforms

Abstract

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.

A Study on Vibrations of Hexarot-Based High-G Centrifugal Simulators

“…The virtual work methodology gives the relationship between the different parts of the mechanism and its end effector. Lee and Geng, 19 and Selig and Ding 20 presented an analytical vibration model for a parallel mechanism. Yoshikawa 21 introduced manipulability to consider the manipulator's dynamic parameters.…”

Influence of strut inertia on the vibrations in initially symmetric Gough–Stewart Platforms—an analytical study

“…Specifically regarding the modal analysis of GSPs, only a limited number of papers have been published which can be categorized into finite element [32], semi-parametric [19,[33][34][35][36][37][38][39][40] and parametric [9,22,40] approaches and none of them parametrically takes the strut inertia into account. Among the semi-parametric approaches, Wang et al [36] take the inertia of the struts into account for a hydraulic GSP with a semi-analytical approach where the equivalent inertia matrix and the eigenvalue problem are solved numerically.…”