Structural dynamics analysis of spatial robots with finite element approach

Abstract

This paper develops the generalized equations of motion for a robotic mechanism with elastic structures by using the finite element theory. The derivation and final form of the equations of motion can model two- or three-dimensional complex elastic mechanisms and include the nonlinear coupling terms of rigid body and elastic motions in a general representation. Here, the dynamic model of an R-R-R spatial robotic manipulator with the finite element approach is established. A robot mechanism consists of links and joint transmission systems. The equations of motion of elastic links are derived based on the displacement finite element method. The dynamic model of the flexible joint transmission systems are modeled as a general spherical joint with multi-degree of freedoms. The complete dynamic model of an elastic robotic structure can then be developed by combining the equations of motion of elastic links and joints. According to this dynamic model, we can investigate the structural dynamic properties of this robotic structure from the system dynamic responses. These data are useful for the controller design and optimal dynamic operation planning of robotic manipulator.