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

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