Optimization of multi-constrained linear coupler input four-bar and six-bar double rocker linkages for maximum rotational output

An analytical procedure is developed for the synthesis of four-bar and six-bar double rocker linkages with an approximate linear input for a maximum rotational output, while holding the transmission angle within a range of 45° to 135°. This method provides a means of synthesizing linear input linkages with controlled transmission angle and maximum rotational output within a specified regional size constraint. The method uses a program that finds the minimum of a multivariable, nonlinear function subject to nonlinear inequality and equality constraints. A model linkage that satisfies the inequality constraints is required for a starting point of the optimization technique. This linear input model is devised using an analytical means to determine an inflection circle for a coupler point that will give an approximate linear input. The solutions are graphically displayed to determine their validity.