Fl. Hu et Ag. Ulsoy, DYNAMIC MODELING OF CONSTRAINED FLEXIBLE ROBOT ARMS FOR CONTROLLER-DESIGN, Journal of dynamic systems, measurement, and control, 116(1), 1994, pp. 56-65
The modeling for controller design of a constrained rigid-flexible rob
ot arm is considered. The mathematical model is obtained as a set of n
onlinear hybrid ordinary-partial differential equations and an algebra
ic constraint equation. Galerkin's method is employed to discretize th
e partial differential equations. Because of the constrained environme
nt of the robot arm, the choice of approximating functions in the spat
ial discretization is crucial for obtaining accurate simulation result
s from a low order model. Several candidate approximating functions ar
e evaluated through convergence and accuracy studies. This work also i
nvestigates the effects of coupling between rigid- and flexible-body m
otion, and the effects of axial force (due to the contact force) on be
nding vibrations through axial shortening. It is shown that the use of
inappropriate spatial approximating functions with a low order model
can result in faulty predictions of the dynamic response, especially,
the axial force effects due to the contact force.