A new theory for the simultaneous control of force and displacement for a partially constrained end-effector is established based upon the general spatial stiffness of the manipulator. In general, the spatial stiffness of a compliant coupling that connects a pair of rigid bodies is used to map a small twist between the bodies into the corresponding interactive wrench. This mapping is based upon a firm geometrical foundation and establishes a positive-definite inner product (elliptic metric) that decomposes a general twist into a twist of freedom and a twist of compliance. A study of the invariant properties of this mapping leads to the discovery of what are defined as the eigen-screws of stiffness. Further, the spatial stiffness of a compliant coupling is modeled by theoretically replacing the coupling with a passive Stewart Platform-type parallel mechanism. It is important to recognize that this model does not depend upon the existence of a center-of-compliance. In fact, it describes a general state of spatial stiffness between any two rigid bodies. The culmination of these finding yields a practical and meaningful theory of Kinestatic Control, viz., the simultaneous regulation of force and displacement solely via the control of displacement.