Control and dynamic analysis of multilink flexible manipulator

Lagrange´s finite element approach is used to formulate the dynamic model of a flexible manipulator system in three-dimensional space. All manipulator links are considered as slim beams connected in one degree-of-freedom frictionless revolute joints. Beam type finite elements, with third-order interpolating polynomials and six generalized perturbation coordinates per finite element nodal point, are used for description of the link small displacement field. The Denavit-Hartenberg matrix method is used to describe the flexible manipulator kinematics. Joint and link transformation matrices, describing the transformation of coordinate systems between the ends of the deformed manipulator link, are applied. The resulting equations of motion take into account a coupling between the rigid body motion and elastic deformations of links