| In this thesis a general method for the formulation of the dynamical equations of general ;To ascertain the effects of link flexibility on the overall performance of the manipulator, the dynamic simulation of the flexible-link manipulator is compared with the dynamic simulation of the same manipulator considering all links to be rigid. Numerical examples, chosen from specialized literature are included to demonstrate the validity of the dynamical equations and the algorithms to solve them. The dynamic simulation, ranging from a single-link- to a six-link-manipulator, with all links flexible, is presented. The results of simulations for all these manipulators indicate that the effects of structural flexibility on the motion of the manipulator can be considerable even at low speeds. The simulation results also bring to light the effects of various joint torques on the elastic behaviour of the manipulator. Finally, it was found that the stability of the numerical integration schemes used depended largely on the type of input joint torques.;The formulation of the dynamical equations of flexible-link manipulators is carried out by considering each link as an unconstrained body and writing its EL equations disregarding kinematic couplings. These equations are expressed in terms of the body 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 to obtain the independent dynamical equations. These equations are then solved for accelerations using the Cholesky decomposition. The integration of the accelerations is performed using Gear's stiff method of backward differentiation. |
