Vector form description of hydraulic cylinders interaction with links of actuating unit

This paper describes interaction between mechanism links connected by a turning pair and the elements of hydraulic linear motion engine. This is done in a compact vector form. Expressions were derived for generalized driving force related to the angle of reciprocal link rotation and for transfer functions connecting displacement and velocity of the hydraulic-cylinder rod of the engine with the angle and angular velocity of relative link rotation. A vector-matrix form of these expressions simplifies their application in algorithms of automatic formation of multilink mechanism dynamic equations. A mathematical model of the actuator hydraulic part employs hydraulic fluid consumption balance equations with account for its volumetric compression providing one first-order differential equation for each engine cavity. The paper demonstrates results of numeric realization of the proposed description for a flat three-link mechanism driven by three hydraulic engines with program control.