The primary objective of this study was to establish the coordinate frame for force control by observing how parameters of force that are not explicitly specified by a motor task vary across the workspace. We asked subjects to apply a force of a specific magnitude with their hand. Subjects could complete the task by applying forces in any direction of their choice in the transverse plane. They were tested with the arm in seven different configurations. To estimate whether contact forces are represented in extrinsic or intrinsic coordinates, we applied the parallel transport method of differential geometry to the net joint torques applied during the task. This approach allowed us to compare the force variability observed at different arm configurations with the force variability that would be expected if the control system were applying an invariant pattern of joint torques at the tested configurations. The results indicate that for the majority of the subjects, the predominant pattern was consistent with an invariant representation in joint coordinates. However, two out of eleven subjects also demonstrated a preference for extrinsic representation. These findings suggest that the central nervous system can represent contact forces in both coordinate frames, with a prevalence toward intrinsic representations.