This paper presents a novel design for a mobile robot based on the kinematics of parallel mechanisms. The robot consists of 3 legs, each equipped with an asynchronous driving unit. The legs are connected to the driving units with spherical joints and to the upper plate with a revolute joint. Three additional encoders, attached to the upper revolute joints provide redundant data. This data is used by a kinematic model for accurate estimation of the robot's configuration and position in space, even in rough terrains, where conventional odometry fails. Simulation results show the advantages of the design, and suggest a method for detection of irregularities of surfaces in unknown environments.