MINLP models for dimensional synthesis of planar four-bar linkages

Abstract

Most works on mechanism synthesis consider models that employ trigonometric functions and rely on derivative-free optimisation, such as bio-inspired and hybrid heuristics. Derivative-free strategies have the advantage of being applied directly to explore the design space. However, such strategies require tuning to achieve satisfactory results and do not provide certificates of solution quality. To this end, this work presents two alternative models: the first one consists of a trigonometric function-based model; while the second relies solely on natural coordinates, in which the nonlinear terms are bilinear. Both models result in mixed-integer nonlinear programming (MINLP) formulations. Mechanism constraints are conveniently expressed in this formulation, including Grashof's condition, prescribed timing, and increasing and decreasing angle sequence. In standard numerical cases of four-bar linkage path synthesis, global and local MINLP solvers yielded provably optimal designs in some cases and in others they outperformed works from the literature.