Continuous formulation of the layout of a hydromechanical transmission

In this paper, an analytical formulation of the layouts of three-shaft hydromechanical transmissions is presented. The formulation was obtained starting from the Willis equation for the planetary gears. Its graphical representation results in a polar plot dependent only on the angular coordinate: by varying the latter between 0 and 2 π, all the transmission layouts can be continuously described. In this way, the layout, together with the transmis- sion ratios of the gears and the displacements of the hydraulic machines, can enter as a degree of freedom in the problem of mathematical optimization of the hydromechanical transmissions. The potential of this analytical formulation will be shown by studying the case of a transmission for a forklift of 75 kW.