The vast majority of mechanical presses are using a crank mechanism for converting the main shaft's uniform rotation into a guided linear reciprocating motion. In many applications, the law of motion ensured by this mechanism is less than adequate, mainly because of the significant variation of slide velocity during the load stroke and the relatively small weighting of the duration of this part of the stroke in relation to the total time of a double stroke. Over time, researchers have conceived more complex conversion mechanisms for mechanical presses, like bar mechanisms that combine crank and four-bat mechanisms in various configurations in order to determine laws of motion of the slide as close as possible to an imposed or assumed optimum. Based on examples from patents and utility models, the paper presents conversion bar mechanisms, double composed and triple composed, designed for mechanical presses in order to ensure the most favourable law of motion of the slide for various applications.