Abstract:

To obtain the kinematic and dynamic characteristics of a planar 5R parallel robot with physical flexible links and distributed mass, operating at higher prescribed input speeds, a finite element-based differential motion equation was proposed. Considering the kinematic coupling between the flexible links and rigid moving platform, a modeling method suitable for the mechanism systems which contained flexible bodies and rigid bodies was modified. The transformation matrices of element variables were derived from the system kinematics property. The governing equations for the deflections of the robot members were obtained using the Lagrange equation. The set of equations was discretized using the finite element method. The equations derived herein give a more accurate model by including additional terms as Coriolis damping, centrifugal stiffness and geometric stiffness. The element equations were transformed and assembled to generate the governing differential equations for the robot. In this manner the defects brought by kinematic and dynamic constraints equations were avoided. The procedure was illustrated by a detailed analysis of a planar flexible 5R parallel robot. The model can be used for Kineto-Elastodynamics analysis and optimal design. The flexibility of links is demonstrated to have significant impact on the performance and stability of the flexible robots.

Key words: flexible parallel robot, differential motion equation, rigid-flexible body coupling, finite element method, transformation matrix

摘要：

为了描述平面5R柔性并联机器人的运动学和动力学特性，需要建立机器人的运动微分方程。针对刚性活动平台和柔性杆件的运动学耦合特点，改进了一套适用于刚体、柔性体耦合的有限元建模方法，推导出单元弹性广义坐标相对于系统弹性广义坐标的转换矩阵，综合考虑了科氏阻尼、离心刚度和几何非线性的影响，利用运动弹性动力学理论，建立了平面5R柔性并联机器人的运动微分方程，避免了采用运动学和动力学约束方程的弊端，提高了建模精度。计算实例表明，该方程反映了机器人的弹性振动特性，杆件的弹性变形对机器人的运动误差具有重要影响。

关键词: 柔性并联机器人, 运动微分方程, 刚柔耦合, 有限元方法, 转换矩阵