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This article presents a novel, model-free, Cartesian sliding PID control scheme for obtaining transparency in teleoperation systems with parametric uncertainties and hard nonlinearities. A condition has been found, which establishes that it is equivalent to get transparency in dynamically similar teleoperation systems by simply implementing the same proposed controller at the master and the slave sites. In this manner, fast exponential convergence of position and velocity tracking errors, and an acceptable force tracking are attained, without acceleration measurements, nor any knowledge of the master/slave robot dynamics, nor estimating the impedance of human and environment. Moreover, computation of inverse kinematics and/or Cartesian robot dynamics are not necessary. Simulation results validate the proposed teleoperation scheme.