A probabilistic model and methods to determine the means and variances of the velocity and acceleration of stochastically-defined planar pin jointed kinematic chains are presented. The presented model considers the effect of tolerances on link length and radial clearance and uncertainty of pin location as a net effect on the link’s effective length. The determination of the mean values and variances of the output variables requires the calculation of sensitivities of secondary variables with respect to the random variables. It is shown that this computation is straightforward and can be accomplished by a conventional kinematic analysis package. Thus, the concepts of tolerance and clearance have been captured by the model and analysis. The only input data is the nominal linkage model and statistical information. The “effective link length” model is shown to be applicable to both analytical solution and Monte Carlo simulation. The results from both methods are compared. This paper solves the higher-order kinematics problem for the probabilistic design analysis of stochastically defined mechanisms.