This study quantitatively investigates the actual movements that observers make when exploring a shape. It addresses the question of how the kinematics of these movements relate to and may affect perceived shape. It is one of the first studies to do so for real stimuli and for relatively unconstrained exploration. Observers discriminated the curvature of circularly shaped strips. We identify a kinematic cue for a single finger stroking across circular strips under conditions of slip. This cue consists of two terms that are related to the shift of the skin contact surface across the fingertip and the rotation angle of the finger. The rotation angle of the finger is found to increase linearly with the curvature of the stimulus. Observers rotated their finger less on a concave curvature by a constant amount, while at the same time they overestimated the radius of the concave strips compared to the convex ones. We show that responses were related to kinematic properties of the actual movements and we consider several mechanisms that could explain this finding.