The paper describes research in computer-aided design of mechanical systems using configuration spaces. The research addresses the core design task of rigid-body contact analysis and related tasks. Contact analysis is a computational bottleneck in mechanical design, especially in systems with complex part shapes, tight fits, and contact changes. Manual analysis is error-prone and time-consuming, whereas automated analysis exceeds the capabilities of current design software. To address these problems, we have developed a general contact analysis method for planar mechanical systems based on configuration space computation. We have implemented a prototype design environment that integrates contact analysis with simulation, tolerance analysis, and visualization. The software helps designers study system function under a range of operating conditions, find and correct design flaws, and optimize performance.