Citation: Kim, G.; Okatomo, S.;
Maruyama, H. Weight Illusion
Caused by Sinusoidal Vibration
Correlates with Grip Force
Adjustment. Appl. Sci. 2023, 13, 2717.
https://doi.org/10.3390/
app13042717
Academic Editors: Zhihan Lv, Kai Xu
and Zhigeng Pan
Received: 29 January 2023
Revised: 11 February 2023
Accepted: 16 February 2023
Published: 20 February 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Article
Weight Illusion Caused by Sinusoidal Vibration Correlates
with Grip Force Adjustment
Giryeon Kim
1,2,
*, Shogo Okamoto
1,2
and Hisataka Maruyama
3
1
Department of Mechanical Systems Engineering, Nagoya University, Nagoya 464-8601, Japan
2
Department of Computer Science, Tokyo Metropolitan University, Tokyo 191-0065, Japan
3
Department of Micro-Nano Systems Engineering, Nagoya University, Nagoya 464-8601, Japan
* Correspondence: kim.giryeon.y2@s.mail.nagoya-u.ac.jp
Abstract:
Our research team previously identified a weight illusion in which a lifted object feels heavy
when it continuously presents a sinusoidal vibration to the fingertips. However, the mechanism
underlying this illusion remains unknown. We thus hypothesized that the autonomous grip force
adjustment against a vibrating object would be one of the factors underlying the weight illusion.
The autonomous grip force adjustment increases the motor outputs of a human hand system, subse-
quently raising the sense of effort to keep holding the lifted object. The grip forces and perceived
heaviness were evaluated using vibratory stimuli with five different frequencies (30 Hz, 60 Hz, 100 Hz,
200 Hz, and 300 Hz) and three different amplitudes (156
µ
m, 177
µ
m, and 203
µ
m). The results
showed that the stimuli at lower frequencies or large amplitudes increased the grip forces more and
felt heavier than the stimuli at higher frequencies or small amplitudes. Specifically, the 30 Hz stimuli
felt the heaviest and increased the grip force the most. An increase in the grip force was positively
correlated with the perceived heaviness. These results indicate that vibratory stimuli influence both
the grip force and weight perception. Our findings can contribute to developing haptic displays to
present virtual heaviness.
Keywords:
weight illusion; vibration; grasp force; grip force adjustment; heaviness; mechanoreceptor
1. Introduction
The weight of an object is defined as the product of its mass and gravitational ac-
celeration. However, humans do not always perceive weight according to its physical
definition. Instead, weight is often estimated based on generated motor commands and
sensations during motions [
1
–
4
] and various types of physical quantities, such as density
and inertia [
5
–
7
]. By controlling specific factors that affect weight perception, an object can
feel heavier or lighter than its actual weight. These phenomena are referred to as weight
illusions. Investigating weight illusions leads to an understanding of weight perception
mechanisms.
The size-weight illusion is a representative example of weight illusions, in which an
object with a smaller volume is perceived as heavier than an object with a larger volume,
despite weighing the same [
8
]. The underlying principle behind this illusion however is
still under debate. Nevertheless, a gap between the perceived weight of the lifted object and
its expected weight before lifting is considered to be part of the reason for the illusion [
1
,
9
].
Furthermore, the material, color, and brightness also cause weight illusions, in which an
object that is expected to be heavy from its appearance is perceived as being light [
10
–
12
].
As evident from the above examples, the appearance of an object is one of the factors
underlying the weight illusion.
The presentation of tactile stimuli to the hand also leads to the weight illusion. Deep
sensations primarily influence weight perception, but cutaneous sensations are also influ-
ential, especially for light objects [
13
–
16
]. When lifting an object, the skin deforms in the
Appl. Sci. 2023, 13, 2717. https://doi.org/10.3390/app13042717 https://www.mdpi.com/journal/applsci
