Finite Element Dynamic Analysis of Flexible Spatial Mechanisms and Manipulators

摘要

A finite-element based method for the dynamic analysis of spatial mechanisms and manipulators with flexible links is presented. Finite element types, appropriate for modeling spatial mechanisms are presented. For each element, expressions for the deformation modes as analytical functions of the element nodal coordinates are defined. The angular orientations are described in terms of four Euler parameters; in contrast to Euler angles or any set of three angular generalized coordinates, these parameters display no singular behavior of the rotational transformations. The constraint condition for the Euler parameters can easily be incorporated in the theory as it is a condition similar to the constraint condition for undeformable finite elements. The kinematic description of multi degree of freedom mechanisms based on the geometric transfer function formalism is considered. The list of derivatives of the geometric transfer functions is extended up to the third order. The associated computation scheme for the kinematic analysis is described. The choice of the degrees of freedom is discussed.