Variation occurs in many closed loop multi-body dynamic (MBD) systems in the geometry, mass, or forces. Understanding how MBD systems respond to variation is imperative for the design of a robust system. However, simulation of how variation propagates into the solution is complicated as most MBD systems cannot be simplified into to a system of ordinary differential equations (ODE). This paper investigates polynomial chaos theory (PCT) as a means of quantifying the effects of uncertainty in a closed loop MBD system governed by differential algebraic equations (DAE). To demonstrate how PCT could be used, the motion of a two link slider-crank mechanism is simulated with variation in the link lengths. To validate and show the advantages and disadvantages of PCT in closed loop MBD systems, the PCT approach is compared to Monte Carlo simulations.

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