An adaptive controller that achieves a pure tracking force objective for n-link robot manipulators is presented in this paper. The main features of the proposed algorithm are: (i) the dynamic parameters of the robot are assumed to be unknown, (ii) object stiffness is unknown, (iii) only position, velocity and interaction force measurements are required. Under the practical assumption of a constant inertia matrix, the scheme is shown to be globally convergent to zero-force tracking error. This assumption can be removed for single link devices, thus providing the first proof of the global convergence of an adaptive force controller that includes estimation of both manipulator and environment dynamics