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Exoskeleton systems in recent years has become a prime choice technology due to the various possibilities it can deliver. These possibilities comprise the assisting and rehabilitative techniques designed for disabled and elderly people, so that they can regain control of their limbs and in addition to this also to augment and boost the abilities of able-bodied persons during heavy work-load conditions. Many works are reported on the modeling and control of a exoskeleton robot, but very few paper discuss the complete derivation of the model of the system. Here, first the dynamic model of a physical system used as lower limb exoskeleton robot is obtained. Secondly the analysis of the system done that is derived through dynamic modelling of a 3-link robotic manipulator using Euler-Lagrange approach and validation of the corresponding model in simulation. Further, design of a finite-time SMC for desired trajectory tracking of the system is implemented. The dynamic model of the 3-link system and its control using finite-time sliding mode control are validated in MATLAB simulation environment.