An effective method is presented for modeling the full three-dimensional dynamics of high performance spatial machine systems, including the vibrations of their links, supporting structure and enclosures, and impacts in their connection clearances. The method combines four-by-four matrix modeling techniques with finite-element techniques. The system’s elements can be described in rich detail, including detailed models of the internal structure of the connections, yet the dynamic calculations are performed efficiently. The method is formulated for implementation on computer-aided design systems. Examples are presented.
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Dubowsky et al. (1987) studied this question.