This paper proposes a kinematic and dynamic modelling of a differential–type mechanical transmission, in order to ensure the displacement of a powered wheelchair, for people with locomotors disabilities. The mechanical transmission is designed to allow the wheelchair displacement for four models, namely: displacement in a straight line, displacement on a curve, moving on rough terrain and spinning. For the simulations of the transmission functioning in these four cases, the authors propose the virtual prototyping of the constructive solution, for the beginning.