An Alternative Approach towards Optimisation Design of Coupler Curve based Four-bar Mechanisms

This paper discusses a new methodology for the synthesis of planar four-bar linkages with rotary joints based on a desired coupler curve. This was performed by first deriving a closed-form expression relating the coupler points to the corresponding crank orientations, which in turn evaluated to zero when the desired point is reached exactly at the specified crank angle. The residual values of this expression, evaluated at a number of crank locations, were used to construct an objective function. The minima of the formulated objective function with respect to the geometry of the linkage yielded the desired solutions. Addition of penalty terms (constraints) to the above objective function ensured full-cycle mobility of the crank along with practically achievable linkage proportions. A genetic algorithm, namely the Non dominated Sorting Genetic Algorithm-II (NSGA-II) had been used to rectify the problem of unconstrained optimization. A local optimisation process using the lsqnonlin procedure of Matlab overcome the usual sluggishness of convergence by the process of refinement while the global exploration capabilities of the GA were exploited to arrive quickly at multiple candidate solutions. The stated method had been illustrated in this paper using three numerical examples. It has been observed that the proposed method has resulted in better solutions than those reported in recent literature.