Optimum exact/approximate point synthesis of planar mechanisms

An optimization approach is herein presented for mixed exact–approximate dimensional synthesis of planar mechanisms. Any number of points along a closed path may be traversed exactly while the rest approximately. Ant-gradient search is applied to an objective function based on log10 of the error between the desired positions and the generated ones. The log10 function results in miniscule errors being generated at the exact points. The algorithm is tested by way of four case studies in three examples that focus on four-bar and Watt-I six-bar mechanisms involving path and function generation tasks.