Understanding how manufacturing variation affects manipulator fit and function is of the utmost importance. There are currently many techniques to determine these effects. Many of them for robotic manipulators only apply to the static analysis, but there is a need to determine the dynamic effects. This paper outlines how polynomial chaos theory (PCT) can be utilized to solve both the static (aka tolerance stack-up) and dynamic analyses. To show the power of the procedure, it is applied to a simple planar two link manipulator with geometric variation of the link lengths.
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Voglewede et al. (2006) studied this question.