This chapter presents numerical approaches based on finite difference (FD) techniques for dynamic simulation of single-link flexible manipulator systems. A finite-dimensional simulation of the flexible manipulator system is developed using an FD discretisation of the dynamic equation of motion of the manipulator. Structural damping, hub inertia and payload are incorporated in the dynamic model, which is then represented in a state-space form. Case study simulation exercises and associated results characterising the dynamic behaviour of the manipulator are presented and assessed with experimental results in time and frequency domains.

Chapter Contents:

• 4.1 Introduction
• 4.2 Flexible manipulator system
• 4.3 Finite difference background
• 4.4 Finite difference for flexible manipulator
• 4.4.1 The hub displacement
• 4.4.2 The end-point displacement
• 4.4.3 Matrix formulation
• 4.4.4 State-space formulation
• 4.5 Case studies
• 4.5.1 Case study 4.1: flexible manipulator without hub inertia and payload
• 4.5.2 Case study 4.2: flexible manipulator with hub inertia and no payload
• 4.5.3 Case study 4.3: flexible manipulator with hub inertia and payload of 10 g
• 4.5.4 Case study 4.4: resonance frequency of the flexible manipulator
• 4.6 Summary

Inspec keywords: manipulator dynamics; damping; flexible manipulators; state-space methods; finite difference methods

Other keywords: hub inertia; numerical approaches; dynamic simulation; time domains; finite difference modelling; state-space form; frequency domains; single-link flexible manipulator systems; dynamic equation of motion; FD discretisation; payload; finite-dimensional simulation; FD techniques; structural damping

Subjects: Robot and manipulator mechanics; Vibrations and shock waves (mechanical engineering); Differential equations (numerical analysis); Manipulators; Numerical analysis