This paper introduces a novel continuous path tracking method based on curvatures called Weingarten Maps and implementation of this method in a quadruped robot model. The path to be followed is assumed to be defined in Cartesian coordinates. The path tracking method is achieved both using open and closed loop algorithms. Quadruped gaits are generated due to instantaneous center of rotations of the sample path which are calculated using Weingarten Maps. Quadruped robot model is simulated in ADAMS cooperated with MATLAB/Simulink.