The experimental setup is illustrated in Fig. 1A. The contact surface consisted of a three-dimensional (3D)–printed circular plate, having a diameter of 15 cm. The plate had a textured surface with regularly spaced ridges. The size and the spacing of the ridges were the same as in (16) (ridge height and width, 1 mm; space between ridges, 10 mm). The plate was placed over a load cell (0 to 780 g; Micro Load Cell, CZL616C from Phidgets, Calgary, AB, Canada) to record normal contact forces. A servo motor (Ultra Torque HS-7950TH, Hitec) under the plate rotated it at the required orientation. For hand tracking, a Leap Motion device (Leap Motion Inc., San Francisco, USA) was attached to a handle placed above the plate. The current study focused on translational motion; therefore, we only tracked a single point on the tip of the finger. The sampling frequency of the Leap Motion device is equal to 40 Hz, and its accuracy in dynamic conditions is equal to 1.2 mm, allowing reliable tracking of hand and finger motion (37).

The procedure in experiment 1 was as follows. Blindfolded participants sat on an office chair in front of the setup, with the center of the plate roughly aligned with their body midline. Headphones playing pink noise masked occasional ambient sounds. Before each trial, the experimenter placed the right index fingertip of the participant in contact with the plate on the ridge closest to the nearer edge of the plate. Thereafter, participants were required to slide the hand away from them along a straight path, for approximately 10 cm (Fig. 1B). Participants were instructed to contact the plate with a light touch. Before each trial, the plate was rotated by the motor to one of the following angular positions: −60°, −30°, 0°, 30°, and 60°. As illustrated in Fig. 1D, a zero-degree angle means that the ridges of the plate were parallel to the frontal plane of the participant, whereas negative (positive) angles mean that the ridges were rotated clockwise (counterclockwise). Each stimulus orientation was presented 15 times in pseudo-random order. Participants received no feedback about their performance during the experiment. At the end of each trial, the experimenter lifted the hand of the participant to place it back to the starting position. Before the experimental session, participants underwent a training phase, where the experimenter instructed them to produce the right amount of force and hand displacement. During training, participants received feedback whenever the actual force exceeded the threshold value of 2 N. All participants replicated the task with a smooth plate without ridges. The order of the ridged- and the smooth-plate conditions was counterbalanced across participants. This aimed at correcting our results for possible biases in perceived direction introduced by extracutaneous signals [see, e.g., (38, 39)]. In addition, to address the role of frictional force, a subset of participants (n = 4) replicated the task with a lubricated surface (experiment 1b). This time, before each experimental session, the plate was lubricated using oil (ridged-plate condition only).

In experiment 2, participants performed the same task of experiment 1, either with their bare finger or while wearing a rubber glove reducing the reliability of the tactile stimulus. The two conditions, with and without glove, were tested in two experimental sessions counterbalanced across participants. In each session, each of the five orientations of the plate was presented 10 times in pseudo-random order. Before each experimental session, we verified that participants were able to feel the ridges while wearing the glove.

In experiment 3, the ridged plate was aligned with the right shoulder of the participant to reduce the offset due to extracutaneous signals. Participants wore an HMD (Oculus Rift, Oculus VR LLC) to present the visual stimuli. The virtual scene consisted of a circular plate having the same size and position as the real plate without ridges (Fig. 3A). Before the experiment, the virtual plate has been aligned in space with the real one by combining signals of the Leap Motion and the virtual scene rendered through the Oculus Rift. At the trial onset, the experimenter placed the finger of the participant on the real plate on the starting point. Thereafter, a visual target consisting of a green sphere (radius, 1 cm) briefly flashed on the virtual plate. The visual target was placed on the arc of an ideal circumference with a radius of 5 cm in one of the following angular positions: −15°, 0°, and 15° (Fig. 3A). Participants were instructed to slide the hand over the textured plate to reach the target. Before each trial, the plate was rotated by the motor to one of the following angular positions: −60°, 0°, and 60°, with respect to the virtual target. A zero-degree angle means that the ridges of the plate were orthogonal to the line joining the starting point and the target, whereas negative (positive) angles mean that the ridges were rotated clockwise (counterclockwise). Ridges were not displayed on the virtual disk, which had a uniform color. Participants did not receive any feedback whether or not they reached the target. A “beep” sound alerted the participants when they reached a distance from the origin equal to 10 cm. Whenever the contact force exceeded the threshold value of 2 N, a different sound alerted the participant to decrease the applied force. Before the experiment, a short training session allowed participants to familiarize themselves with the apparatus and to reproduce the required motion speed and contact force. During the training session, the smooth plate was used.

In none of the experiments did we provide feedback on the motion speed. Participants were simply required to move along the goal direction with a slow self-paced hand movement. Before the experiment, however, the experimenter performed the movement once to show the participants the approximate range of speed and displacement.

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