Virtual Environments (VE) need large workspaces. On the other hand, haptic devices are mostly grounded and typically have small workspaces compared to the VE. The main objective of this work is to extend the smaller workspace of haptic devices for Virtual Reality (VR) applications without affecting the haptic perception of the user. A position drift-based robotic approach has been proposed in which a redundant kinematic Degree of freedom (DOF) is added to the haptic device by moving its base using a mobile robot to expand the workspace of the haptic interface point (HIP) in the VE. In order to validate the proposed approach, a psychophysical study measuring stiffness Just Noticeable Difference (JND) has been conducted to compare the user perception before (Stationary Robot) and after the proposed approach (Moving Robot). Two experiments were conducted separately, one for a single axis (Experiment I) and another for a two-axis (Experiment II). The %JND for Experiment I is 21.08% and 24.59% for stationary and moving haptic devices. The %JND for Experiment II is 20.55% and 26.56% for stationary and moving haptic devices. One-way ANOVA was performed to test whether the difference in the %JND between the two cases is insignificant. With the insignificant %JND difference (p = 0.32 for Experiment I, p = 0.34 for Experiment II), the proposed method could be considered as not affecting the user haptic perception while expanding the haptic workspace for the interactions in VE. The stability of the haptic device has been analyzed, including robot dynamics. The current study implements up to two axes of workspace expansions for the 3D systems Touch haptic device; however, the algorithm is extensible to three axes and any grounded haptic devices.