Flexible-Link Robotic Manipulator Dynamics

In this paper the formulation of the dynamical equations of flexible-link manipulators is carried out by considering each link as an unconstrained body and writing its Euler-Lagrange (EL) equations disregarding the kinematic couplings. These equations are expressed in terms of the body´s flexible twist and its time derivative. The individual-link equations, along with the associated constraint wrenches, are assembled to obtain the constrained dynamical equations of the manipulator. The nonworking constraint wrenches are then efficiently eliminated by simple matrix multiplication of the said equations by the transpose of the natural orthogonal complement of the matrix of twist constraint to obtain the independent dynamical equations.