This paper presents methods to obtain automatically the workspaces of mechanical manipulators and the corresponding feasible control paths. The workspaces depend on the tasks to be performed and therefore are different from the geometrical locus of the end point. Due to the strong non-linearities of the mathematical model, the extremum-finding problem may lead to several local solutions. A global search method and a recursive algorithm making use of the pseudoinverse of the jacobian matrix of the mechanism are presented. The means of obtaining trajectories from the corresponding workspaces is then discussed. The methods proposed in this paper have been developed to design and control an underwater robot devoted to manipulation of oil-pipes and assembly on wellheads.