The success of space missions like capture-and-deorbit or capture-and-service relies on the ability of the capturing satellite to establish a stable mechanical connection by its gripping tool with the object being intercepted. Most of the potential objects of capture missions are not equipped with dedicated docking ports; hence, the satellite robot intercepting them will have to provide the mechanical compliance necessary for the safe establishment of contact between the two structures. Articulated robotic arms with controlled mechanical impedance are one set of promising solutions for this challenge. In this study, the authors discuss how the mechanical impedance realized only along a single axis can be useful for facilitating the contact between the manipulator arm’s end effector of a free-floating robot and an uncooperative object in microgravity. By distinguishing a dominant direction in the final approach and contact establishment maneuver, the need for impedance control of six degrees of freedom may be relaxed, and a single prismatic joint with controlled impedance can be used at the end effector. Such architecture is simulated and compared with the full model-based six-degree-of-freedom Cartesian impedance control of a free-floating manipulator. Authors then discuss the limitations and possibilities of such architecture in a potential practical setting.