Contact analysis is ubiquitous in many tasks in robotics, mechanical design, manufacturing, and computer graphics. The task is to compute the evolving sequence of part contacts and compliant motions given the part shapes and allowable motions. It is especially challenging for curved parts with multiple, changing contacts. Several disciplines have developed contact analysis algorithms for specialized systems, yet practical algorithms for most contact analysis applications are still not available. This situation leaves engineers, designers, and researchers unsure how to pick the right one for a given task. In this paper, we assess the effectiveness of current contact analysis algorithms for representative applications, identify the trade-offs between generality and efficiency, and propose directions for future research. We exemplify this selection with two applications: dynamical simulation and kinematic tolerance analysis.

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