过约束并联机构动力学建模方法  

Research on the Dynamic Model of an Over-constrained Parallel Mechanism

作　　者：姜峣 李铁民[1] 王立平[1] 

机构地区：[1]清华大学精密仪器与机械学系,北京100084

出　　处：《机械工程学报》2013年第17期123-129,共7页Journal of Mechanical Engineering

基　　金：国家自然科学基金资助项目(51275260)

摘　　要：由于冗余支链和冗余约束力的存在,过约束并联机构的动力学建模一直未能得到很好的解决。以一台平面两自由度过约束并联机构为例,在运动学分析的基础上,利用牛顿-欧拉法并结合达朗贝尔原理,得到了该机构的力和力矩平衡方程,但由于方程少于未知数个数而无法直接进行求解。为此,提出变形协调性分析的方法,通过建立约束力与终端平台位置误差之间的关系作为补充方程,从而得到可求解的机构动力学模型。将该方法应用到一台混联机床并联部分的动力学建模分析中,通过数值算例,对驱动力和动平台位置误差进行仿真,结果表明该方法的可行性和合理性。该方法同样可以应用于其他过约束并联机构,为该类机构动力学建模分析提供了一种新的思路。Due to their redundant links and redundant restriction forces,it has been a different problem for dynamic modeling and analysis of over-constrained parallel mechanism.A planar 2-DOF over-constrained parallel mechanism is discussed as an example.On the basis of kinematics analysis,the equilibrium equations for the force and moment of this mechanism are established by using Newton Euler method and D＇Alembert principle.The model cannot be solved because the number of equations is less than that of unknown variables.So a novel method,which can provide feasible supplementary equations through analyzing the deformation compatibility to establish the relationships between constraint forces and position errors of terminal platform,is put forward.Thus the dynamic model can be solved.This method is applied to the dynamic modeling and analysis of parallel mechanism in a hybrid machine tool.By numerical example,driving forces and platform error are simulated.The result shows that this method is feasible and reasonable.The research provides a new method to the dynamic modeling and analysis of over-constrained parallel mechanism.

关 键 词：并联机构 过约束 动力学 变形协调性分析 

分 类 号：TH113[机械工程—机械设计及理论]