柔性并联机器人动力学建模

Dynamic Modeling of Flexible Parallel Robot

针对一般柔性并联机器人动力学模型,提出了一种精确而简单的动力学建模方法。根据并联机器人结构特点,将其划分为若个刚性子结构和弹性子结构,形成一个刚柔结合的系统。静平台和动平台相对其他构件变形较小,将它们作为刚性子结构,各个支链作为弹性子结构。分别建立各子结构的动力学方程,弹性子结构采用有限元法和模态综合法建立其动力学方程;考虑各个柔性支链弹性变形对刚性子结构的影响,建立刚性子结构动力学方程;推导出相邻的刚性子结构和弹性子结构之间的几何约束关系。通过相邻子结构的协调矩阵,将各个子结构的方程进行装配形成系统的弹性动力学方程。通过一种高速并联机械手的动力学特性比较分析,表明该方法的正确性和可行性。由于引入刚性子结构和采用了模态综合法,减少了系统自由度数,从而简化了计算模型,为柔性并联机器人提供一种实用的建模方法。

An accurate and simple method for dynamic modeling of general flexible parallel robot was proposed.According to the structural character of the parallel robot,it was devided into rigid sub-structure and elastic sub-structure,and the rigid-flexible coupling system was formed.The static platform and mobile platform were treated as rigid sub-structure because its deformations were smaller compared to the other part.The chains were treated as flexible sub-structure.The dynamic equations of each sub-structure were obtained,respectively.The dynamic equations of elastic sub-structure were obtained by using the finite element method and mode synthesis method.The dynamic equations of rigid sub-structure were built accounting for the effects of deformation of flexible sub-structure.The geometrical constraint relationship between three flexible sub-structures and the rigid platform was investigated to obtain a simple displacement and dynamic relation between them.The equations of all sub-structure were assembled to get the system dynamic equations.The comparative analysis of dynamic characteristics of a high-speed parallel manipulator show that the method is correct and feasible.Due to introducing the rigid sub-structure and application of the mode synthesis,the number of system freedom was reduced and the computational modeling was simplified.It provided a practical method for flexible parallel robot.