DYNAMIC MODELLING OF A NON-LINEARLY CONSTRAINED FLEXIBLE MANIPULATOR WITH A TIP MASS BY HAMILTON'S PRINCIPLE

✍ Scribed by R.-F Fung; H.-C. Chang

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 299 KB
• Volume: 216
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1998.1718

✦ Synopsis

In this paper, the equations of motion for a non-linearly constrained flexible manipulator with a tip mass are derived by using Hamilton's principle. Dynamic formulation is based on expressing the kinetic and potential energies of the manipulator system in terms of generalized co-ordinates. Four dynamic models, based on Timoshenko, Euler, simple flexure and rigid body beam theories are used to describe the flexible two-link and single-link manipulators. The Lagrange multiplier method is employed to treat the problem with geometric constraint. The emphasis of this paper is that the generalized friction force is taken into account only whilst the manipulator is in contact with the constrained surface. It is found that the rigid body motion and flexible vibrations are non-linearly coupled in the equations of motion. Some observations are also discussed.