For a long time, the study and design of biomimetic multifingered manipulators or robotic hands has been the target of many researchers. The small spaces between joints is a critical design constrain for including actuators during the design tasks, and therefore transmission mechanisms are often implemented on these robots. In this paper the Particle Swarm Optimization (PSO) and Differential Evolution (DE) bioinspired algorithms have been applied to a transmission mechanism of a robotic finger. In this case the goal is to achieve a previously modeled finger movement in order to make possible gripping tasks. Two cost functions have been explored, the first one for evaluating the fingertip trajectory and the second one for evaluating the joint's angles work. Tatistical results and test hypothesis are used for comparing the achieved results with the Genetic Algorithm (GA). For this approach the results show that the DE algorithm for both cost functions are not statistically different. Finally, it's proposed the use of the mean of the results of the DE implementations for the two cost functions, providing a better result than the separate ones.