Significance When we actively explore objects by touch, the brain receives two types of signals, tactile sensory inputs and signals about the exploratory movement, which must be combined to perceive the shape and location of objects in space. Whereas these signals usually come from the same body part, we have developed a technique to separate them, directing the tactile signals to one hand and the movement signals to the other. We find that separated and synchronized signals are combined as if they arose from the same hand. Our results suggest that to solve the difficult problem of multidimensional signal combination in touch perception, the brain uses a simplified, source-independent representation of movement.