Abstract—This paper is proposed a new analytical method for studying the functionality and synthesis of the Stephenson II crank-slider mechanism according to a given slider change coefficient in average speed and the optimal pressure angle to ensure the highest force transfer from the input link to the functional body (output link). The formulas obtained in the work and their graphs reflect the operational capabilities of the kinematic structure of the Stephenson II crank-slider mechanism. These formulas and graphs authors used when designing this type of crank press. As a result, it is proposed to include them in the technical reference books on mechanisms (or the database on mechanisms). Such reference books about mechanisms that provide a structural diagram and formulas between parameters and their purpose are actively used in engineering and design practice. Disseminating the new mechanism through technical reference books or a mechanisms database contributes to the more significant practical application of the proposed mechanism structure. The application program in the Delphi 7 visual system for determining the parameters of the synthesized crank-slider mechanism by the optimal pressure angle and conducting a kinematic movement analysis of the links in the dialog mode is developed based on the above method.