Description : A systematic and automatic modeling of robots requires an appropriate method for the description of their morphology. Several methods and notations have been proposed. The most widely used one is that of Denavit-Hartenberg . However, this method, developed for simple open structures, presents ambiguities when it is applied to closed or tree-structured robots. Hence, we recommend the notation of Khalil and Kleinfinger which enables the unified description of complex and serial structures of articulated mechanical systems Link C0 indicates the robot base and link Cn, the link carrying the end-effector. Joint j connects link Cj to link Cj-1.
In this chapter we presented a coherent approach to the geometric, kinematic and dynamic modeling of a flexible robot. The approach is based on the floating frame method. The deformation fields are reduced through “clamped-free” modes. The dynamic model suggested performs a generalization of the Newton-Euler model for the rigid robot manipulators. This generalization is conceptually guided by the concept of formalism of description of a motion applied as defined in the continuous medium mechanics.
This concept, contrary to the current practices in rigid robotics, is dissociated from the means of obtaining the dynamic equations (Newton-Euler theorems, Lagrange equations, Hamel equations, etc.). After considering this point, the principle of virtual powers proved to be best adapted to an Eulerian-Lagrangian mixed description, as imposed by the generalization of the Newton-Euler models within the framework of the floating frame. Based on this model, we developed two algorithms for the calculation of the direct and inverse dynamic models for a deformable robot manipulator. These two algorithms are in o(n), and can be
numerically or symbolically calculated.
In this chapter we presented a coherent approach to the geometric, kinematic and dynamic modeling of a flexible robot. The approach is based on the floating frame method. The deformation fields are reduced through “clamped-free” modes. The dynamic model suggested performs a generalization of the Newton-Euler model for the rigid robot manipulators. This generalization is conceptually guided by the concept of formalism of description of a motion applied as defined in the continuous medium mechanics.
This concept, contrary to the current practices in rigid robotics, is dissociated from the means of obtaining the dynamic equations (Newton-Euler theorems, Lagrange equations, Hamel equations, etc.). After considering this point, the principle of virtual powers proved to be best adapted to an Eulerian-Lagrangian mixed description, as imposed by the generalization of the Newton-Euler models within the framework of the floating frame. Based on this model, we developed two algorithms for the calculation of the direct and inverse dynamic models for a deformable robot manipulator. These two algorithms are in o(n), and can be
numerically or symbolically calculated.
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