Contact-rich robotic manipulation requires an accurate model of the kinematic relationship between a robot's joints and the task features it senses. This relationship is rarely known exactly: it changes with each tool the robot picks up and shifts, sometimes almost instantaneously, as contact modes change --- especially for multi-fingered hands that make and break contact at points that are not exactly prescribed, as in full-hand grasping. This paper develops an adaptive scheme that estimates that relationship online, using only joint-angle sensing and a wrist-mounted force/torque sensor, with no exteroceptive measurement of the tool tip. We derive a provably stable kinematic update law that identifies the kinematics of an unknown tool from force/torque feedback alone, and prove stability of both the rigid case and the case with a compliance controller as an inner loop. We show that identification is confined to the directions the motion excites --- so that, for example, a tool's length is unobservable under a rigid insertion push, while a compliant loop's passive yielding partially excites it; and that with a second-order admittance the compliant certificate holds unconditionally in continuous time. We also pose the combined control and estimation problem as a Quadratic Program (QP): the formulation yields the prediction term of the update law exactly but, instructively, cannot reproduce the tracking adaptation term. We validate the scheme in simulation on a peg-in-hole insertion. This work is the first step in a research program aimed at factoring manipulation learning into a task policy which can be learned in isolation of the robot, for instance by reinforcement learning, and an adaptive kinematic component that adapts online to the particular robot, hand, or tool in use.

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