Delta机器人动力学建模与弹性误差分析

Dynamics modeling and elastic error analysis of delta robot

针对Delta机器人运动过程中因弹性变形导致的误差问题,基于有限元理论对其弹性动力学问题建立了数学模型并进行了研究。根据机构特点,将机器人的各构件分别划分为刚性体与弹性体,形成了一个刚柔结合的系统,并充分考虑机构中平行四边形机构的运动协调关系,推导出了各构件的运动协调矩阵,由此装配出了系统的弹性动力学方程,在此基础上,采用Newmark积分方法对系统方程进行了求解,最后据此分析了Delta并联机器人杆件截面尺寸对其运动过程中弹性误差的影响。研究结果表明:增加驱动杆截面的尺寸时,其弯曲刚度随之增加,可以减少机器人弹性变形;而从动杆截面的尺寸增加时会因为机构自重增加导致变形增大。

Aiming at the problem of elastic deformation in Delta robot motion,the elastic dynamic model was established based on the finite element theory.According to characteristics of the structure,the components of the robot were divided into rigid parts and flexible parts,respectively,which consist of a rigid-flexible coupling system.The motion relation of the parallelogram structure was fully considered,and the motion compatible matrix of each component was deduced.Then the elastic dynamic equation of the system was obtained,on which was based,the influence of the cross-sectional dimension of Delta parallel robot＇s rods on the elasticity error in motion was analyzed.The results indicate that the bending stiffness increases with the increase of the cross section size of the drive rod,elastic deformation of the robot can be reduced.And the self – weight increases with the increase of the cross section size of the driven rod,which makes the deformation greater.