Haptic perception of force

From Scholarpedia
Wouter M. Bergmann Tiest and Astrid M.L. Kappers (2015), Scholarpedia, 10(4):32732. doi:10.4249/scholarpedia.32732 revision #151740 [link to/cite this article]
Jump to: navigation, search
Post-publication activity

Curator: Wouter M. Bergmann Tiest

This article reviews research that deals with measuring the precision and/or the accuracy of haptic force perception, using psychophysical methods. Other aspects of force perception might include physiological aspects or neuronal processing, but these are beyond the scope of the present article. Furthermore, force sensation plays a role in the perception of other physical aspects, such as friction or stiffness. These aspects are reviewed separately elsewhere.

Force perception relates to two aspects of force: its magnitude and its direction. Perception of these aspects is discussed separately below. Concerning force magnitude, many early studies have focused on the perception of force in the direction of gravity, i.e. the weight of objects. This is discussed first. Then, force magnitude perception in other directions is discussed. Finally, some applications of this research are discussed.

Different psychophysical techniques have been used to study force perception. To study the relationship between physical and perceived force magnitude, the technique of magnitude estimation has been used. To measure the smallest difference in force magnitude or direction that can be perceived, discrimination experiments have been performed. Finally, to study the relationship between force magnitudes perceived in different ways, or between physical and perceived force direction, matching experiments were done. This subdivision is used to categorise the different studies.


Perception of force magnitude

An overview of perception of force magnitude is given by Jones (1986). The most important findings, as well as some more recent research, will be discussed below. First, the focus will be on force magnitude perception in the direction of gravity, and then, in other directions.

In the direction of gravity (weight perception)

Discrimination Formal investigation of force perception started with the weight discrimination experiments of E. H. Weber, published in 1834 (Weber, 1834/1996). By placing weights on the hands of subjects, he was able to measure the smallest weight difference that could be perceived. With the subjects’ hands lying on the table, he found Weber fractions (the ratio between the smallest detectable difference and the reference weight) of about 0.3. However, with the hands and weights lifted in the air, the Weber fractions were in the order of 0.09, indicating a much smaller difference. This shows that force perception is much more precise when both the cutaneous sense (skin receptors) and kinaesthetic sense (receptors in limbs and muscles) are involved, compared to just the cutaneous sense. The relative importance of the cutaneous and kinaesthetic senses probably depends on the magnitude of the force itself, with cutaneous inputs playing a larger role in the perception of weaker forces. The experiment was performed with weights of about 1.2 N and 10 N, with similar results in terms of Weber fractions. Thus, although in absolute terms the discrimination threshold depends on the force used, the relative discrimination threshold seems fairly constant. Note that for very small weights, the relative discrimination threshold is expected to go up, as there also exists a minimum discrimination threshold in absolute terms.

Weight discrimination appears to depend on object size: in experiments on weight discrimination with objects of different densities (the ratio between mass and volume), it was found that weight perception was most precise for the density that corresponded to the expected density of the object’s material (Ross & Gregory, 1970). With more or less dense (i.e. smaller or larger) objects, discrimination was poorer. This suggests that there is more to weight discrimination than just force perception. This is also illustrated by the fact that people can use inertial cues to improve their weight discrimination (Brodie & Ross, 1985; Ross & Brodie, 1987). When not only the static force of earth’s gravity on the object is available, but also the dynamic inertial force of an object that is moved about, then extra information is available to determine the object’s mass when combined with an estimate of the object’s acceleration. In fact, mass discrimination based just on inertial force is possible in the absence of gravitational force, e.g. in orbit in space (Ross & Reschke, 1982; Ross, Brodie, & Benson, 1984, 1986).

Magnitude estimation Many studies have used magnitude estimation to characterise the relationship between physical and perceived heaviness of objects, which corresponds to the magnitude of the force that gravity exerts on these objects. It has been found that this relationship can be described by a power function with an exponent of about 1.45 (S. S. Stevens & Galanter, 1957). In the papers reviewed by Jones (1986), a range of exponents of 0.8–2.0 have been reported, depending on the specific conditions of the experiments. Indeed, perceived heaviness is subject to the influence of numerous factors. For example, in a matching task between forces exerted on the left and the right wrists, grasping an object firmly in the hand made the force feel smaller, whereas anaesthetising the hand (not the muscles involved in lifting) made the force feel larger (Gandevia & McCloskey, 1976).

Furthermore, it has been found that with forces exerted on the skin of the hand palm, the area of stimulation plays a role in the perceived magnitude of the force: with a larger area of stimulation, the same force felt smaller (Bergmann Tiest, Lyklema, & Kappers, 2012). This occurred mainly with the hand lying flat on a table, so that only cutaneous force information was available. With the unsupported hand, when also proprioceptive force information was available, this effect was reduced significantly. This is in accordance with the idea that proprioception of force is unaffected by the area of stimulation on the skin.

Lastly, it has been long known that perceived heaviness is influenced by object size: a smaller object of the same weight feels heavier, an effect known as the size-weight illusion (Charpentier, 1891, as discussed in Murray, Bandomir & Ross, 1999; J. C. Stevens & Rubin, 1970). This is the topic of a large body of research, but is beyond the scope of the present article.

In other directions

Discrimination Using an electromechanical apparatus, Pang, Tan, and Durlach (1991) let subjects squeeze two plates between thumb and forefinger, which offered an adjustable resistive force. In this way, different forces could be displayed to the subjects in a horizontal direction, and force discrimination thresholds could be measured. In this dynamic scenario (involving movement of the fingers), the Weber fraction for force discrimination was found to be about 0.07 for a wide range of reference forces, initial finger spans, and squeezing distances, as long as the kinaesthetic sense was involved. A Weber fraction of about 0.1 for force magnitude discrimination was found in an experiment using a hand-held stylus to which forces were applied (Pongrac, Hinterseer, Kammerl, Steinbach, & Färber, 2006). These findings are consistent with the earlier weight discrimination experiments (Weber, 1834/1996; Brodie & Ross, 1985; Ross & Brodie, 1987), indicating that the direction of the presented force is not critical to force discrimination. However, when force magnitude had to be discriminated while the whole hand was moving, discrimination thresholds were found to be higher, with Weber fractions around 0.45 (Yang, Bischof, & Boulanger, 2008b). In this experiment, subjects moved a hand-held stylus from left to right while forces were applied at five different angles with respect to the movement direction: either in the same or opposite direction, perpendicular, or at an angle of 45° or 135°. In particular, subjects found it difficult to discriminate the magnitude of forces applied at 45°, with a Weber fraction as high as 0.6.

Such an angular dependence was not observed in an experiment where subjects had to discriminate the magnitude of a horizontally applied force (to the right) of 2.5 N from forces applied in all six cardinal directions of the 3D space (Dorjgotov, Bertoline, Arns, Pizlo, & Dunlop, 2008). Weber fractions for all directions were around 0.33. This suggests that for the stationary hand, and a relatively low magnitude, force discrimination is quite isotropic. However, it should be noted that in this experiment, the reference force was always in the same direction. This was different in the experiment by Vicentini, Galvan, Botturi, and Fiorini (2010), which used five reference force magnitudes in each of the six cardinal directions, but with the test and reference forces always in matching directions. They found differences in discrimination thresholds between the different directions, with the highest Weber fractions (~ 0.14) in the horizontal-tangential direction, and the lowest (~ 0.11) in the radial direction. These numbers are asymptotic Weber fractions for high force magnitudes; with lower forces (< 5 N), a significant increase in Weber fractions was found. Thus, we can conclude that with these higher forces, force discrimination thresholds are in accordance with the earlier weight discrimination experiments, but that there are anisotropies depending on the direction of the force.

Magnitude estimation Forces on the fingers can be applied either normal or tangential to the skin. In the former case, the skin is indented, whereas in the latter case, the skin is stretched sideways. In a magnitude estimation experiment by Paré, Carnahan, and Smith (2002), both methods were used with a range of low forces (0.15–0.70 N). For both methods, a linear relationship between physical and perceived force was found, with correlation coefficients ranging from 0.48–0.96, and 0.70–0.97 for the tangential and normal force conditions, respectively. There was no significant difference in slope between the two conditions. This suggests that, at least for these small forces, the human sensitivity for tangential force is comparable to that for normal force. However, an anisotropy in perceived force magnitude was found for forces applied to the hand, both for relatively high forces (5–30 N; Tanaka & Tsuji, 2008) and for medium forces (2–6 N; Van Beek, Bergmann Tiest, & Kappers, 2013). In both these experiments, forces in different directions in the horizontal plane were applied to a handle held in the subject’s hand. The perceived magnitude was found to be the greatest in the directions of the line connecting the shoulder to the hand and vice versa, and smallest in the perpendicular directions. Thus, when applied to the whole hand, the same force might feel different, depending on the direction.

Matching If forces from different directions on the same body part feel different, how do forces applied to different body parts compare? This was investigated in a force matching experiment where subjects had to produce a force with one body part, based on a visual display of the required force, and then reproduce that force with another body part, without visual feedback (Jones, 2003). The results showed that forces were reproduced as larger by the elbow than by the hand, and as larger by the hand than by the finger. Thus, the perceived magnitude of a force varies as a function of the muscle group generating the force. When the reproduced forces were expressed as a percentage of the maximum force that can be generated by each body part, they showed a much better correspondence. It seems that the forces are matched based on their relative magnitude with respect to the maximum.

Furthermore, the perceived magnitude of a force has been found to depend on whether it is passively perceived or actively generated. In an experiment where pairs of subjects were asked to reproduce a force to the other person that this other person just applied to their index finger, the magnitude of the force going back and forth quickly escalated (Shergill, Bays, Frith, & Wolpert, 2003). On average, subjects generated a force 38 % higher than was applied to them. The authors concluded that the perceived magnitude of self-generated forces is attenuated as a result of a mechanism that removes some of the predictable sensory consequences of a movement, in order for externally generated sensations to become relatively more salient. This might also explain an effect observed by Bergmann Tiest and Kappers (2010), in an experiment where mass perceived through gravitational force (weight) and inertial force (resistance to acceleration or deceleration) had to be matched. When subjects accelerated a mass by pushing it, it had to be twice as heavy as a mass resting on the hand in order to feel equal. However, when subjects decelerated a moving mass by stopping it, it was matched veridically to a mass resting on the hand. Thus, the force used to actively push a mass is perceived as smaller than the force necessary to passively stop it. Taken together, this illustrates that the perceived magnitude of a force depends on many factors, such as the direction, the body part involved, and whether or not the force is self-generated.

Perception of force direction

Let us now turn our attention from force magnitude to force direction perception. The precision of this can be assessed using discrimination experiments, which will be discussed first. Afterwards, matching experiments will be discussed, which are used to measure the accuracy of force direction perception.

Discrimination Using a force-feedback joystick, Elhajj, Weerasinghe, Dika, and Hansen (2006) determined that a 83 % correct force direction discrimination level was attained for an angle difference of 15°. This can be interpreted as the discrimination threshold for direction of force applied to the whole hand. However, the research does not tell us how this threshold depends on the magnitude or direction of the force. The latter question was investigated by Tan, Barbagli, Salisbury, Ho, and Spence (2006) for five directions in the frontoparallel plane and a 2 N force applied to the finger tip. They found an average discrimination threshold of 33°, but no effect of direction. It is unknown whether the considerably higher threshold compared to Elhajj et al. (2006) should be ascribed to a difference in force magnitude or to whether the force is applied to the whole hand or just the index finger. It should be noted that these thresholds might be quite variable: using the same setup and paradigm, the authors found a threshold of 26° in another experiment (Barbagli, Salisbury, Ho, Spence, & Tan, 2006). In that experiment, they also included conditions in which (congruent or incongruent) visual information was present. This led to a decrease or increase, respectively, of the discrimination threshold, even though the subjects were instructed to base their judgements on the haptic information only. This prompted the authors to conclude that visual information can modulate haptic force perception (Ho, Tan, Barbagli, Salisbury, & Spence, 2006).

The question whether the force direction discrimination threshold depends on the magnitude of the force was investigated by Pongrac et al. (2006). They applied forces to a hand-held stylus, either straight or with a perturbation in the magnitude or direction. When the perturbation was perpendicular to the reference force, the test force differed only in direction from the reference force. In those cases, they found discrimination thresholds corresponding to a perpendicular force magnitude of 25 % and 20 % of the reference force for 1 and 2 N, respectively. Using the arctangent, this corresponds to angle differences of 14° and 11°, respectively. This difference was statistically significant, so it seems that with a higher force magnitude, the force direction is perceived with better precision, at least for forces in this range.

Furthermore, the force direction discrimination threshold has been investigated in the case of a moving hand, using a hand-held stylus and a 1.5 N force (Yang, Bischof, & Boulanger, 2008a). Averaged over five different reference directions and two speeds, the discrimination threshold was found to be 32°. However, no effect was found of reference direction or movement speed. To sum up, it seems that the precision of haptic force perception is fairly isotropic, with a discrimination threshold of around 30° for low forces applied to the fingers or during movement, and about 10–15° for higher forces or forces applied to the whole hand.

Finally, a discrimination experiment has been used to determine the smallest magnitude of force necessary to differentiate between two diametrically opposing directions (Baud-Bovy & Gatti, 2010). Subjects had hold the handle of a robotic device, to which either a left- or rightward force was applied, and then select the correct direction. When they had to keep their hand still, the minimum required force magnitude was 0.1 N, but when they were allowed to move their hand left and right, this was only 0.05 N, suggesting that movement can actually help in determining the direction of a force.

Matching In this last paragraph, we look at the accuracy of force direction perception; that is, how well does the perceived force direction correspond to the physical one? This type of question is usually investigated using matching experiments, in which the subject has to adjust some parameter until it matches his/her perception. In one such task, subjects had to hold a joystick and resist a 5 N force that was applied in a certain direction (Toffin, McIntyre, Droulez, Kemeny, & Berthoz, 2003). Then, they had to reproduce it, that is, apply a force to the joystick in the exact opposite direction. The difference between the presented force direction and the reproduced one is the bias. The magnitude and the sign of this bias were found to depend on the force direction, indicating an anisotropy in either the perception or the reproduction of force direction. However, since every trial consisted of both a perception and a reproduction phase, it was unclear from which phase the anisotropy originates. This problem was circumvented in the experiment by Van Beek et al. (2013), in which only a perception phase was present, and the perceived direction had to be matched by turning a visual arrow in the correct direction. Subjects showed substantial biases, up to 30° in both directions. Within subjects, repeated measurements (using different force levels (2–6 N), different hands, and on different days) showed consistent bias patterns, but these differed between subjects. These intra-subject similarities and inter-subject differences were further explored in a follow-up study (Van Beek et al., 2014). In one experiment, subjects performed the same task three or four times on different days, with a month between the third and the fourth session. Six out of eight subjects showed high correlations between the first three sessions, and three of the five subjects that completed a fourth session showed high correlations between the first three and the fourth session. The second experiment revealed that only 7 % of the bias patterns showed a high correlation with patterns of other subjects. These findings indicate that the bias pattern of a particular subject is not random, but a unique feature of that person. This knowledge could be used to compensate for biases in force direction perception on a person-by-person basis, after a simple characterisation procedure.


In many situations in which an operator remotely controls a vehicle or robotic arm, force feedback can be used to provide the operator with information about the task or the situation. Especially when visual feedback is limited (for example under water), haptic force feedback becomes more important and is relied upon more. In order to be able to correctly provide this force feedback, it is important to know how forces are perceived by humans. Using the thresholds reported above, the minimum resolution can be calculated that a system needs to have so that no perceptible degradation occurs. Furthermore, the discussed research illustrates that there are systematic deviations in force perception that should be taken into account when designing such a system for a situation with reduced or absent visual information.

It should be noted that most studies discussed above deal with perception of forces that are constant in time, or do not change when the subject moves. However, these are rare in everyday interactions with the world around us. We can assume that the knowledge about perception of these constant forces generalises to the perception of dynamic forces, but future research should confirm whether this assumption is justified.


  • Barbagli, F; Salisbury, K; Ho, C; Spence, C and Tan, H Z (2006). Haptic discrimination of force direction and the influence of visual information. ACM Transactions on Applied Perception 3: 125-135.
  • Baud-Bovy, G and Gatti, E (2010). Hand-held object force direction identification thresholds at rest and during movement. In: A M L Kappers, J B F van Erp, W M Bergmann Tiest and F C T van der Helm (Eds.), Haptics: Generating and perceiving tangible sensations. Part II, Vol. 6192 of Lecture Notes in Computer Science (pp. 231-236). Berlin/Heidelberg: Springer-Verlag.
  • Bergmann Tiest, W M and Kappers, A M L (2010). Haptic perception of gravitational and inertial mass. Attention, Perception & Psychophysics 72(4): 1144-1154.
  • Bergmann Tiest, W M; Lyklema, C and Kappers, A M L (2012). Investigating the effect of area of stimulation on cutaneous and proprioceptive weight perception. In: P Isokoski and J Springare (Eds.), Haptics: Perception, devices, mobility, and communication. Part II, Vol. 7283 of Lecture Notes in Computer Science (pp. 7-12). Berlin/Heidelberg: Springer-Verlag.
  • Brodie, E E and Ross, H E (1985). Jiggling a lifted weight does aid discrimination. American Journal of Psychology 98(3): 469-471.
  • Dorjgotov, E; Bertoline, G R; Arns, L; Pizlo, Z and Dunlop, S R (2008). Force amplitude perception in six orthogonal directions. In: Proc. Symposium on Haptic Interfaces for Virtual Environments and Teleoperator Systems (pp. 121-127). Reno, Nevada, USA: IEEE.
  • Elhajj, I; Weerasinghe, H; Dika, A and Hansen, R (2006). Human perception of haptic force direction. In: Proc. IEEE/RSJ International Conference on Intelligent Robots and Systems (pp. 989–993).
  • Gandevia, S C and McCloskey, D I (1976). Perceived heaviness of lifted objects and effects of sensory inputs from related, non-lifting parts. Brain Research 109: 399-401.
  • Ho, C; Tan, H Z; Barbagli, F; Salisbury, K and Spence, C (2006). Isotropy and visual modulation of haptic force direction discrimination on the human finger. In: Proceedings of EuroHaptics (pp. 483-486).
  • Jones, L A (1986). Perception of force and weight: Theory and research. Psychological Bulletin 100(1): 29-42.
  • Jones, L A (2003). Perceptual constancy and the perceived magnitude of muscle forces. Experimental Brain Research 151(2): 197-203.
  • Murray, D; Ellis, R; Bandomir, C and Ross, H (1999). Charpentier (1891) on the size-weight illusion. Perception & Psychophysics 61: 1681-1685.
  • Pang, X D; Tan, H Z and Durlach, N I (1991). Manual discrimination of force using active finger motion. Perception & Psychophysics 49(6): 531-540.
  • Paré, M; Carnahan, H and Smith, A M (2002). Magnitude estimation of tangential force applied to the fingerpad. Experimental Brain Research 142(3): 342-348.
  • Pongrac, H; Hinterseer, P; Kammerl, J; Steinbach, E and Färber, B (2006). Limitations of human 3d-force discrimination. In: Proc. Second International Workshop on Human-Centered Robotics Systems (pp. 109-114).
  • Ross, H E and Brodie, E E (1987). Weber fractions for weight and mass as a function of stimulus intensity. Quarterly Journal of Experimental Psychology 39A: 77-88.
  • Ross, H E; Brodie, E E and Benson, A J (1984). Mass discrimination during prolonged weightlessness. Science 225: 219-221.
  • Ross, H E; Brodie, E E and Benson, A J (1986). Mass-discrimination in weightlessness and readaptation to earth’s gravity. Experimental Brain Research 64(2): 358-366.
  • Ross, H E and Gregory, R L (1970). Weight illusions and weight discrimination—a revised hypothesis. Quarterly Journal of Experimental Psychology 22(2): 318-328.
  • Ross, H E and Reschke, M F (1982). Mass estimation and discrimination during brief periods of zero gravity. Perception & Psychophysics 31(5): 429-436.
  • Shergill, S S; Bays, P H; Frith, C D and Wolpert, D M (2003). Two eyes for an eye: The neuroscience of force escalation. Science 301(5630): 187.
  • Stevens, J C and Rubin, L L (1970). Psychophysical scales of apparent heaviness and the size-weight illusion. Perception & Psychophysics 8(4): 225-230.
  • Stevens, S S and Galanter, E H (1957). Ratio scales and category scales for a dozen perceptual continua. Journal of Experimental Psychology 54(6): 377-411.
  • Tan, H Z; Barbagli, F; Salisbury, K; Ho, C and Spence, C (2006). Force direction discrimination is not influenced by reference force direction. Haptics-e 4: 1-6.
  • Tanaka, Y and Tsuji, T (2008). Directional properties of human hand force perception in the maintenance of arm posture. In: M Ishikawa et al. (Eds.), Proc. International Conference on Neural Information Processing. Part I, Vol. 4984 of Lecture Notes in Computer Science (pp. 933-942). Berlin/Heidelberg: Springer-Verlag.
  • Toffin, D; McIntyre, J; Droulez, J; Kemeny, A and Berthoz, A (2003). Perception and reproduction of force direction in the horizontal plane. Journal of Neurophysiology 90(5): 3040-3053.
  • Van Beek, F E et al. (2014). Subject-specific distortions in haptic perception of force direction. In: M Auvray and C Duriez (Eds.), Haptics: Neuroscience, Devices, Modeling, and Applications. Part I, Vol. 8618 of Lecture Notes in Computer Science (pp. 48-54). Berlin/Heidelberg: Springer-Verlag.
  • Van Beek, F E; Bergmann Tiest, W M and Kappers, A M L (2013). Anisotropy in the haptic perception of force direction and magnitude. IEEE Transactions on Haptics 6(4): 399-407.
  • Vicentini, M; Galvan, S; Botturi, D and Fiorini, P (2010). Evaluation of force and torque magnitude discrimination thresholds on the human hand-arm system. ACM Transactions on Applied Perception 8(1): article 1.
  • Weber, E H (1834/1996). De tactu. In: H E Ross & D J Murray (Eds.), E. H. Weber on the Tactile Senses. Hove: Erlbaum (UK) Taylor & Francis.
  • Yang, X-D; Bischof, W F and Boulanger, P (2008a). The effects of hand motion on haptic perception of force direction. In: M Ferre (Ed.), Haptics: Perception, devices and scenarios, Vol. 5024 of Lecture Notes in Computer Science (pp. 355-360). Berlin/Heidelberg: Springer-Verlag.
  • Yang, X-D; Bischof, W F and Boulanger, P (2008b). Perception of haptic force magnitude during hand movements. In: Proc. IEEE International Conference on Robotics and Automation (pp. 2061-2066). Pasadena, CA, USA.

Internal References

Personal tools

Focal areas