The Lagrangian dynamic equation and statistical linearization for an n-dimensional manipulator subjected to both stochastic base and external excitations and geometric constraints in states are derived. The effects of utilizing a truncated Gaussian density in the linearization due to the geometry constraints are justified. The non-Gaussian effects due to the stochastic base excitation are also quantified to justify the accuracy in the prediction of the stationary output variances. Two examples of robot manipulators are selected to illustrate the accuracy of predicted variances by the linearization techniques.

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