In this contribution, a four-bar linkage having a variable input velocity is studied, traditionally it is assumed to be constant. The advantages of a variable input velocity mechanism, in contrast to a mechanism driven by constant velocity, are the flexibility of the output motion (and/or improved kinematic and dynamic characteristics). The velocity of the crank is controlled in order to obtain the desired output motion at the coupler point. The input velocity trajectory and the controller parameters are considered as design variables, such that the kinematic and dynamic requirements are fulfilled. Two numerical examples are provided to corroborate the result.
The problem of path generation for the spherical 4R mechanism is solved using the Differential Evolution algorithm (DE). Formulas for the spherical geodesics are employed in order to obtain the parametric equation for the generated trajectory. Direct optimization of the objective function gives the solution to the path generation task without prescribed timing. Therefore, there is no need to separate this task into two stages to make the optimization. Moreover, the order defect problem can be solved without difficulty by means of manipulations of the individuals in the DE algorithm. Two examples of optimum synthesis showing the simplicity and effectiveness of this approach are included.
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