Nowadays, engineering is working side by side with medical sciences to design and create devices which could help to improve medical processes. Physiotherapy is one of the areas of medicine in which engineering is working. There, several devices aimed to enhance and assist therapies are being studied and developed. Mechanics and electronics engineering together with physiotherapy are developing exoskeletons, which are electromechanical devices attached to limbs which could help the user to move or correct the movement of the given limbs, providing automatic therapies with flexible and configurable programs to improve the autonomy and fit the needs of each patient. Exoskeletons can enhance the effectiveness of physiotherapy and reduce patient rehabilitation time. As a contribution, this paper proposes a dynamic model for two degrees of freedom (2 DOF) leg exoskeleton acting over the knee and ankle to treat people with partial disability in lower limbs. This model has the advantage that it can be adapted for any person using the variables of mass and height, converting it into a flexible alternative for calculating the exoskeleton dynamics very quickly and adapting them easily for a child’s or young adult’s body. In addition, this paper includes the linearization of the model and an analysis of its respective observability and controllability, as preliminary study for control strategies applications.