This paper is a survey of our research on kinematic tolerance analysis of mechanical systems with parametric part tolerances. We present a general algorithm for planar systems and illustrate it with a design case study. The algorithm constructs a variation model for the system, derives worst-case bounds on the variation, and helps designers find unexpected failure modes, such as jamming and blocking. The variation model is a generalization of the configuration space representation of nominal part contacts. The algorithm handles general planar systems of curved parts with contact changes, including open and closed kinematic chains. It constructs a variation model for each interacting pair of parts then derives the overall system variation at a given configuration by composing the pairwise variation models via sensitivity analysis and linear programming. We demonstrate the algorithm on a gear selector mechanism in an automotive transmission with 100 functional parameters. The analysis, which takes less than a minute on a workstation, indicates that the critical kinematic variation occurs in third gear and identifies the parameters that cause the variation.