This thesis studies the reconstruction of unknown curved surfaces in 3D through contour tracking. The implementation involves a 2-axis joystick sensor and a 4-DOF Adept robot. The joystick's force sensing is combined with the Adept's high positional accuracy to yield precise contact measurements.;A surface patch in 3D can be rebuilt by tracking along three concurrent curves on the surface. These data curves lie in different planes and are acquired via planar contour tracking. The Darboux frame at the curve intersection is first estimated to reflect the local geometry. Then polynomial fitting is carried out in this frame. Minimization of the total (absolute) Gaussian curvature of the surface fit effectively prevents unnecessary folding otherwise expected to result from the use of touching data. Experiments have demonstrated high accuracy of reconstruction.