Determining where the fingers of a multi-fingered robot hand touch an object of unknown shape plays an important role in achieving a stable grasp. This paper focuses on a scheme for identifying such contact points. Instead of mounting a distributed tactile sensor all over the finger links, we propose an active sensing approach using joint compliance. The proposed scheme is composed of two phases. In the first phase, the approach phase, each finger is extended to its most distal position as it approaches the object. This phase continues until any part of a finger link contacts the object. During the second phase, the detection phase, each finger's posture is strategically changed by sliding the finger over the object while maintaining contact between the object and the finger. Using two selected postures during the detection phase, we can compute an intersecting point that gives an approximate contact point. This paper develops the algorithm and provides results from an experimental implementation of the scheme on a two-fingered robot hand running a joint level compliance controller. The process of changing the posture of the finger while maintaining object-finger contact is called self posture changeability (SPC). It also develops sufficient conditions to demonstrate the robustness of the SPC technique to variations in the coefficient of friction.< >