This paper presents a kinematic and force analysis of a mobile robot built on the principle of parallel mechanisms. The robot consists of an upper plate connected to 3 legs, each equipped with an asynchronous driving unit. A kinematic model for the robot provides data for accurate position estimate, even in rough and slippery terrains where conventional odometry fails. The paper presents an analysis of the forces acting on the robot under various surface conditions and robot configurations. This analysis provides useful data to determine whether a specific motion can be completed given the limitations on stability, the geometry and friction of the surface, and the required motion direction. The paper presents simulation results that are verified by experiments using our prototype model.