The goal of this thesis is to provide systematic means to plan and follow a path for mechanical systems. Therefore, this thesis is divided into two main parts, one for each of these problems. Firstly, the path planning problem is introduced and then solved by using the so-called Rapidly Exploring Random Tree algorithm. To improve the so-found paths, a modification is introduced which renders the solutions optimal with respect to a specific criterion. To avoid high computation times, the algorithm was simplified by consistent assumptions on the mechanical system. Secondly, a path following controller is derived to follow the calculated path in presence of disturbances and to account for modelling errors. Using this controller, it is possible to control the velocity along the path with one control law and a second control law is defined to account for deviations from the path. To the best of the authors knowledge, this controller, unlike for any other approach, can be specified in fixed coordinates. This particularly simple approach is applicable to a wide variety of systems, in particular mechanical systems. In simulation the proposed concepts were tested for a number of mechanical systems. To underline its practical feasibility the path following approach was validated using a parallel kinematic robot.