Kinematic synthesis of Stephenson I mechanism for motion generation as a multi-objective optimization probleme

Abstract

In this paper a planar six-bar Stephenson I mechanism is synthetized which satisfies position, velocity, and acceleration conditions in three points for the motion generation problem, considering a unique angular velocity and acceleration for the crank. The synthesis equations were formulated by the vector method, and they were solved as a multiobjective optimization problem, applying the weighted sum method and the convex function combination, normalizing the objective functions and using the upper-lower bound approach and the Pareto maximum, and the absolute maximum as well. This enabled the driving point of the mechanism to be positioned approximately with respect to the desired values, synthetizing compact mechanisms with a unique crank that is able to rotate continuously.