Research in virtual reality and haptic technologies has consistently aimed to enhance immersion. While advanced head-mounted displays are now commercially available, kinesthetic haptic interfaces still face challenges such as limited workspaces, insufficient degrees of freedom, and kinematics not matching the human arm. In this paper, we present HapticGiant, a novel large-scale kinesthetic haptic interface designed to match the properties of the human arm as closely as possible and to facilitate natural user locomotion while providing full haptic feedback. The interface incorporates a novel admittance-type force control scheme, leveraging hierarchical optimization to render both arbitrary serial kinematic chains and Cartesian admittances. Notably, the proposed control scheme natively accounts for system limitations, including joint and Cartesian constraints, as well as singularities. Experimental results demonstrate the effectiveness of HapticGiant and its control scheme, paving the way for highly immersive virtual reality applications.