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The problem of dissimilar kinematic teleoperator systems is discussed. Three major problems are associated with this controller design: orientation representation, accurate force reflection, and redundancy resolution. It is shown how to incorporate Euler parameters (which are related to quaternions) into the controller design. To achieve accurate force reflection, a type of stiffness controller is designed for both master and slave. Using both the master and slave Jacobians allows accurate force reflection for kinematically dissimilar manipulators. Differences in the application of a stiffness controller for robotic mode and teleoperation are pointed out. When the slave has more than six DOFs (degrees-of-freedom). redundancy resolution must be addressed. With dissimilar kinematic designs, simple joint positional differences are no longer adequate for a force-reflecting manipulator. The master manipulator is the primary focus of this work. A brief discussion is given concerning the slave controller, but details are deferred until a later paper. The results are applied to the six-DOF Kraft master manipulator and the seven-DOF Center for Engineering Systems Advanced Research Manipulator slave manipulator at Oak Ridge National Laboratory [ABSTRACT FROM PUBLISHER]