In humanoids and other redundant robots interacting with the environment, one can often choose between different configurations and control parameters to achieve a given task. A classic tool to describe specifications of the desired force/displacement behavior in such problems is the stiffness ellipsoid, whose geometry is affected by the choice of parameters in both joint control and redundancy resolution—namely, gains and angles. As is well known, impedance control techniques can regulate gains to realize any desired shape of the Cartesian stiffness ellipsoid at the end-effector, so that robot geometry selection could appear secondary. However, humans do not use this possibility: To control the stiffness of our arms, we predominantly use arm configurations. Why is that, and does it makes sense to do the same in robots? To understand this discrepancy, we provide a more complete analysis of the task-space force/deformation behavior of compliant redundant arms to illustrate why the arm geometry plays a dominant role in interaction capabilities of robots. We introduce the notion of allowable Cartesian force/displacement (“stiffness feasibility”) regions (SFR) for compliant robots with given torque boundaries. We show that different robot configurations modify such regions and explore the role of robot geometry in achieving an appropriate SFR for the task at hand. The novel concepts and definitions are first illustrated in simulations. Experimental results are then provided to verify the effectiveness of the proposed Cartesian force and stiffness control.