非惯性系折叠式并联稳定平台机构建模及分析

Modeling and Analysis of Foldable Parallel Stabilized Platform in Non-inertial System

以折叠式6自由度并联机构为例,提出一种非惯性系舰载稳定平台机构建模及分析方法。该方法通过分析舰船及稳定平台在惯性系中的运动,导出动平台位姿、速度及加速度由惯性系到非惯性系的合成变换公式,并给出了伴随变换矩阵;基于并联机构影响系数法建立并联式稳定平台输入运动与非惯性系及动平台广义运动之间的映射,获得表征这种映射关系的非惯性系一、二阶影响系数矩阵;以此为基础,给出了稳定平台各质点虚位移之间的关系式,并利用虚功原理建立稳定平台在非惯性系下的动力学模型。通过数值算例考察稳定平台在非惯性系中位姿、速度及加速度的变化规律,并分析非惯性系运动对系统的影响程度。提出的合成变换及映射关系不仅适用于机构学建模及分析,还可进一步用于非惯性系下稳定平台优化设计与控制。

By taking a foldable 6-dof parallel mechanism as an example,an approach of mechanism modelling and analysis of the ship-based stabilized platform in non-inertial system is presented.This approach can be implemented by three steps.By analysing the motions of ship and stabilized platform in inertial system,the synthesize transformation formulae of pose,velocity and acceleration of the moving platform between inertial system and non-inertial system are deduced,and the adjoin transformation matrixes are given.The mapping between input motions and generalized motions of the moving platform in non-inertial system is derived based on the influence coefficient method,and the influence coefficient matrixes in non-inertial system are built respectively.The relationship between virtual displacements of each particle of stabilized platform is given,and the coupling dynamic model of stabilized platform in non-inertial system is built by virtual work principle.The performance distributions of the stabilized platform in non-inertial system are depicted by numerical examples,and the effect of the motions in non-inertial system to the system is analysed.The method is not only available for the mechanism modelling and analysis,but also can be extended to optimization design and control of parallel stabilized platform in non-inertial system.