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?, all the transmission layouts can be continuously described. In this way, the layout, together with the transmission 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.