Using extended assembly algorithm in finite element method in building dynamic equation process of flexible robot

Abstract

Dynamic equations of flexible robot in this paper are built by using finite
element method (FEM) and Lagrange’s equations of the second kind approach.
The generalized displacement vector in dynamic equations includes motion and
elastic displacement variables. Generalized inertia matrices and stiffness
matrices are established from assembling components matrices of elements.
Traditional assembly method is unsuitable to assemble for generalized inertia
and stiffness matrices of moving multi-body systems which have this
generalized displacement vector, especially when the number of elements is
incremental. Therefore, it is crucial to establish an extended general assembly
algorithm for building generalized matrices based on generalized displacement
vectors. This study proposed the extended general assembly algorithm which is
improved based on FEM theory. This algorithm is used temporarily for single
flexible link robot and two-link flexible robot with rotational or translational
joints. These configures robot are also used as illustrated examples. This
algorithm can serve as an useful tool for dynamics modeling of robots having
flexible links with different configurations and large amount of elements.