In this thesis simple models of two- and threedimensional continuous robotic manipulators are presented. As a first step towards the control of such manipulators characterizations of their workspaces are determined. In order to describe the boundary of the workspaces we apply optimal control techniques. In the twodimensional case the equations investigated are the same as the equations of motion in Dubins' problem. First, the known results of Dubins' problem are extended by the solution of Dubins' problem for free terminal direction. Then these facts are applied in the solution of the optimal control problem connected to the determination of the workspaces. The workspaces for free and prescribed terminal orientation are presented for various upper bounds of the absolute value of the curvature. The threedimensional case is much more complicated since it affords at least two control inputs and more knowledge on differential geometry as well. Unfortunately, the optimal control problem cannot be completely solved. Nevertheless, many facts are given and under further assumptions the workspaces can be presented.