Robust parameter synthesis for planar higher pair mechanical systems

We present a parameter synthesis algorithm for planar, higher pair mechanical systems. The input is a parametric model of a mechanical system (part shapes and configurations) with nominal values and tolerance intervals for the parameters. The output is revised parameter ranges that guarantee correct kinematic function for all system variations. Nominal values are changed when possible and tolerance intervals are shrunk as a last resort. The algorithm consists of a three-step cycle that detects and eliminates system variations with incorrect kinematic function. The first step finds points in parameter space whose kinematic variation is maximal. The maximum of the higher pairs are derived by contact zone construction and are then combined into system maximums. The second step tests the points for correct kinematic function using configuration space matching and kinematic simulation. The third step adjusts the parameter ranges to exclude the points that fail the test. The cycle repeats until every point exhibits correct function. We demonstrate the algorithm on five real-world examples.

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