Stewart六自由度运动平台自振频率的分析与计算研究

Study on the analysis and caculation of the natural frequencies of the stewart motion platform with six degree of freedom

提出了一种对重载的Stewart六自由度运动平台动力学模型局部线性化的新方法,将其六个作动杆简化成质量-弹簧系统。然后采用转移矩阵法将各局部坐标系中建立的质量矩阵、刚度矩阵、阻尼矩阵以及系统的位移和所受外力均转移到总的固定坐标系,运用D’Alembert原理建立其振动的线性运动微分方程。最后通过结合Stewart平台的运动学反解计算方法,对该平台在运动过程中的自振频率进行了分析和计算,计算结果表明对于这种重载的Stewart运动平台,其各个自振频率在整个工作空间内的变化幅度不大,该结果为重载Stewart平台的设计和控制提供了理论依据,已被成功应用于作者单位的某型船舶操纵模拟器运动平台的研制。

In this paper a novel approach to linearize the dynamic model locally by treating six struts of the Stewart platform as simple springs connected in parallel is proposed. All parameters on the local coordinate frames are transformed to the global coordinate frame. The linear motion differential equations have been developed using D＇Alembert principle. The method is applied to calculate the natural frequencies of the Stewart platform combining with the algorithm for solving the inverse kinematics. The numerical simulation results show that the natural frequencies of the Stewart platform vary slowly while the platform moves throughout the workspace.