This paper presents a method for contact-based pose estimation of workpieces using a collaborative robot. The proposed pose estimation exploits positions and surface normal vectors along an arbitrary path on an object with known geometry, where surface normal vectors are estimated based on contact forces measured by the robot. When data is only available along a single path, it is difficult to find initial correspondences between source data (recorded points and normal vectors) and target data (CAD of an object); hence, a novel weighted incremental spatial search approach for generating correspondences based on point pair features is proposed. Subsequently, robust pose estimation is employed to reduce the effect of erroneous correspondences. The proposed pose estimation is verified in simulation on three paths on two objects and with different levels of noise on the source data to quantify the robustness of the algorithm. Finally, the method is experimentally validated to provide an average pose rotation and translation accuracy of 0.55° and 0.51 mm, respectively, when using the robust estimation cost function Geman-McClure.