Synthesis of mechanisms for single and hybrid tasks using differential evolution

The optimal dimensional synthesis for planar mechanisms using differential evolution (DE) is demonstrated. Four examples are included: in the first case, the synthesis of a mechanism for hybrid-tasks, considering path generation, function generation, and motion generation, is carried out. The second and third cases pertain to path generation, with and without prescribed timing. Finally, the synthesis of an Ackerman mechanism is reported. Order defect problem is solved by manipulating individuals instead of penalizing or discretizing the search space for the parameters. A technique that consists in applying a transformation in order to satisfy the Grashof and crank conditions to generate an initial elitist population is introduced. As a result, the evolutionary algorithm increases its efficiency.

► A weight factor that allows to solve the hybrid-task problem in an efficient manner is determined.
► The introduction of two transformations in the DE method, allows to solve the synthesis of mechanisms consistently.
► Penalization and/or search space discretization are both avoided.
► Path generation without prescribed timing using DE for 18 target points and 27 design variables is presented.
► The evolutionary algorithm increases its efficiency.