We present the design and development of a fully immersive virtual reality (VR) system that can provide prop-based haptic feedback in an infinite virtual environment. It is conceived as a research tool for studying topics related to haptics in VR and based on off-the-shelf components. A robotic arm moves physical props, dynamically matching pose and location of an object in the virtual world. When the user reaches for the virtual object, his or her hands also encounter it in the real physical space. The interaction is not limited to specific body parts and does not rely on an external structure like an exoskeleton. In combination with a locomotion platform for close-to-natural walking, this allows unrestricted haptic interaction in a natural way in virtual environments of unlimited size. We describe the concept, the hardware and software architecture in detail. We establish safety design guidelines for human-robot interaction in VR. Our technical evaluation shows good response times and accuracy. We report on a user study conducted with 34 participants indicating promising results, and discuss the potential of our system.