—We study the problem of robot interaction with mechanisms that afford one degree of freedom motion, e.g. doors and drawers. We propose a methodology for simultaneous compliant interaction and estimation of constraints imposed by the joint. Our method requires no prior knowledge of the mechanisms’ kinematics, including the type of joint — prismatic or revolute. The method consists of a velocity controller which relies on force/torque measurements and estimation of the motion direction, the distance and the orientation of the rotational axis. It is suitable for velocity controlled manipulators with force/torque sensor capabilities at the end-effector. Forces and torques are regulated within given constraints, while the velocity controller ensures that the end-effector of the robot moves with a taskrelated desired velocity. We give proof that the estimates converge to the true values under valid assumptions on the grasp, and error bounds for setups with inaccuracies in control, mea...