The Monte Carlo method is used to solve a number of manipulator link shape design, task space, and obstacle placement problems. 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. For a specified operating environment, the spaces within which a given manipulator may be installed in order to perform the required tasks are identified. For a given enclosure, the allowable task spaces, and regions within which obstacles may be placed are mapped. By defining weighted distributions for the task and/or obstacle spaces, weighted allowable link shapes, and task and obstacle spaces are determined. The information can be used for optimal link shape synthesis, and for optimal task, obstacle, and manipulator placement purposes. The developed methods are very simple, numeric in nature, and readily implemented on computer. Several examples are presented.

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