Modelling a contour tracking robot on unknown contours is a relatively difficult task. Therefore, a new compliant motion controller is developed in this study by applying the on-line rule-adaptive fuzzy control to have a Cartesian manipulator perform contour tracking on unknown contours. Also, the contact force is controlled here within a certain constant value and the manipulator is controlled along the tangent direction in which the manipulator is unconstrained. Experimental results verify the feasibility of our designed control strategy.