The Monte Carlo method is used to solve a number of problems in manipulator link shape design, and in task space and obstacle placement. The shape of links of manipulators that are to operate within geometrically specified enclosures are determined. Within the enclosure, one or several obstacles may be present. The end effector operates within the task space, and may be required to reach points in different regions with different orientations. For a specified operating environment (enclosure geometry and obstacles), the spaces within which a given manipulator may be installed in order to perform the required tasks are identified. For a given enclosure, task space, and position of the fixed joint of the manipulator, regions within which obstacles may be placed are mapped. The developed methods are very simple, numeric in nature, and readily implemented on computer. Several examples are presented.