Generalized impedance control is a method for specifying multiple impedances (for joints, links, and the end effector) in order to achieve primary and secondary control objectives (besides just end effector control) and is particularly relevant to the control of n degree of freedom (DOF) serial link manipulators with emphasis on the kinematically redundant case. By introducing impedance interpolation, we have generalized the impedance control concept in order to resolve the multiple and likely conflicting impedance specifications. To verify the above method, a constrained motion experiment was performed: 'crank turning' in the presence of obstacles. A fictitious (or 'virtual') stiffness is associated with the obstacle and serves to 'push' the manipulator away from the obstacle (secondary control objective) while simultaneously allowing the end effector to turn the crank (primary control objective). In order to examine the control issues associated with the redundant manipulator case, we focused our attention on the simplest case of such a manipulator - the 3 DOFs, with parallel axes of rotation, of the PUMA operating in a plane and using a multi-DOF force sensor at the wrist. Furthermore, our experiments demonstrated that the eigenvectors of a Jacobian-stiffness matrix expression, closely related to manipulability, play an important role in the functionality of the impedance controlled machine for the case of unconstrained motion. Our experiments demonstrated that impedance controlled robots can achieve specified motion in the unconstrained case without requiring the computation of the inverse kinematic equations (an interesting additional result of using our approach).