In this paper a new method for the hydrodynamic analysis of a sliding cylinder in a lubricated parallel track is presented. The method is an extension of Booker’s “Mobility Method” (developed for cylindrical journal bearings) for the case of a non‐rotating sliding cylinder in a parallel track. In this application, the clearance between the track and the cylinder, the viscosity of the lubricant, the radius and length of the pin, the sliding velocity and the applied transverse load determine the hydrodynamic behavior of the slider cylinder. An axial positive displacement vane device is used to illustrate the applicability of the hydrodynamic mobility approach for a lubrication analysis. A rotor and a stationary cylindrical cam with cycloidal tracks drive the axicycloidal motion of vanes. A case analysis is presented for a device running at constant speed, in which the inertia forces, friction forces and direct vane loads are taken into account to determine the hydrodynamic behavior of the sliding pins. The following results are produced: pin eccentricity paths, minimum lubricant film thickness history, peak film pressure history and pressure distributions on the cylindrical at any point of the motion. Results show small departures from the purely cycloidal lift‐dwell‐return‐dwell motion of the vanes due to the hydrodynamic performance of the pins.