This chapter presents a dynamics modelling approach for flexible robotic manipulators. The driving motivation for this chapter is to understand the dynamics of such systems from a control point of view. A general framework is presented that provides an adequate basis for analysis and control of flexible manipulators aimed at terrestrial or orbital applications. To this end, the generalized coordinates chosen to describe the elastic deformation are based on the Ritz approximation, and the approach to arrive at the dynamics model of a single flexible link is the principle of virtual powers, or Jourdain's principle, leading to a Lagrangian description for the elastic deformation and a Eulerian description for the rigid-body motion. A rigid flexible-rigid body is modelled. The evolution to the multi-link case is then natural considering the topology of a serial link manipulator. Two procedures are presented, the first is the O(N³) composite inertia method and the second is the O(N) articulated body method.

Inspec keywords: elastic deformation; flexible manipulators; shear modulus; classical mechanics

Other keywords: Ritz approximation; rigid-body motion; classical mechanics; rigid flexible-rigid body; virtual powers; Jourdain principle; Lagrangian description; multi-link flexible manipulators; flexible robotic manipulators; Eulerian description; elastic deformation

Subjects: Manipulators