A reliability based robust multi-objective optimal synthesis of linkage mechanisms considering tolerances

The paper presents a methodology to synthesis simple planar linkage mechanism involving a multi objective optimization model considering cost associated with mechanical tolerances and the reliability based robustness of generating the intended path. An adapted probabilistic model for the deviation of the actual path generated by a coupler point from the desired one, by considering the structural and mechanical errors due to tolerances and clearances is considered. A synthesis procedure of the linkages is formulated as a multi objective non-linear optimization problem with robustness subject to a reliability level and cost as objectives. The reliability index of the mechanism is based on the probability with which a linkage will generate its intended design motion with specified precision. The robustness is based on the ratio of the mean to standard deviation of the error in the traced path with respect to the target. The cost index is based on manufacturing and assembly cost, which are functions of tolerances and clearances in joints. Multi objective genetic algorithm (Moga) is employed as the search tool. A Four-bar path generating mechanism is selected for numerical illustration.