  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.
