The rubber hand illusion is a well-known multisensory illusion. In brief, watching a rubber hand being stroked by a paintbrush while one's own unseen hand is synchronously stroked causes the rubber hand to be attributed to one's own body and to "feel like it's my hand." The rubber hand illusion is thought to be triggered by the synchronized tactile stimulation of both the subject's hand and the fake hand. To extend the conventional rubber hand illusion, we introduce robotic technology in the form of a master-slave telemanipulator. The developed one degree-of-freedom master-slave system consists of an exoskeleton master equipped with an optical encoder that is worn on the subject's index finger and a motor-actuated index finger on the rubber hand, which allows the subject to perform unilateral telemanipulation. The moving rubber hand illusion has been studied by several researchers in the past with mechanically connected rigs between the subject's body and the fake limb. The robotic instruments let us investigate the moving rubber hand illusion with less constraints, thus behaving closer to the classic rubber hand illusion. In addition, the temporal delay between the body and the fake limb can be precisely manipulated. The experimental results revealed that the robotic instruments significantly enhance the rubber hand illusion. The time delay is significantly correlated with the effect of the multisensory illusion, and the effect significantly decreased at time delays over 100 ms. These findings can potentially contribute to the investigations of neural mechanisms in the field of neuroscience and of master-slave systems in the field of robotics.