Of all feasible designs, some are “better” than others. If this is assumed as true, then there must be some quality that the better designs have more of than the lees desirable ones do. This quality must be expressed as a computable function of the design variables, and it can consider optimizing to obtain a “best” design. The function with respect to which the design is optimized is called the objective function. In some design situations, there may appear to be two or more quantities which should be objective functions. The goal of the kinematics synthesis of the linkages is to establish the kinematics dimensions of the component elements provided that some conditions are imposed regarding movements of some points or elements. As a rule, only conditions about the positions of the points or elements are imposed. In the other words, only the transmission functions of the positions are used to write the synthesis equations. The solving of the kinematics synthesis problems is reduced to the solving of some nonlinear equation systems. As a result, the problems of the kinematics synthesis of linkages do not have the unique solutions. Only in some very simples particular cases the system of synthesis equations is linear and problem has a single solution. In the optimum synthesis of the gripper mechanisms, the objective function may express the positioning precision of the work pieces, the magnitude of the driving force, the domain of the stable fastening of the work pieces etc. In the work, some considerations about the optimum synthesis of the two fingered self centering grippers are shown.