In this paper a selection of important problems, which occur in the layout of Flexible Manufacturing Systems (FMS), is considered and analyzed from a more computational geometry and knowledge engineering point of view. This includes the representation of proximity properties as well as applications in the layout of assembly lines, in machine layout and in robot vision/motion planning problems. Some recent results on monotonous bisector trees are given and their applicability in these fields are outlined. New results on motion planning in dynamic scenes are summarized.