**3. Effects of object "size" on perceived heaviness**

Object size is the oldest, most-studied factor since Müller and Schuman (1889, as cited in Davis, 1973) and Charpentier (1891, as cited in Murray et al. 1999) reported the phenomenon of the size-weight illusion (SWI): the larger of two objects of equal weight is perceived as lighter than the smaller. The mechanism underlying the SWI has been continuously discussed with various interpretations: Expectation Theory (H.E. Ross, 1969), Information Integration Theory (Anderson, 1970; Masion & Crestoni, 1988), Density Theory (J. Ross & Di Lollo, 1970), Gain Adjustment Theory (Burgess & Jones, 1997), Inertia Tensor Theory (Amazeen, 1999), Bayesian Approach (Brayanov & Smith, 2010), and Throwing Affordance Theory (Zhu & Bingham, 2011). The reasons for these ongoing differences of opinion are that heaviness is affected by various factors (as noted in Sec. 2) and the difficulty of strictly manipulating object size as a single independent variable, uncontaminated by other object properties. As a result, object size remains a wide-open topic regarding perception of heaviness.

Computer Graphic and PHANToM Haptic Displays:

conditions.

Springer-Verlag.)

for all weight-density conditions.

Powerful Tools to Understand How Humans Perceive Heaviness 31

sets of two cubes of identical density, e.g., CP vs. CP. In addition, equal numbers of trials for each weight difference with identical combination of weights were presented for all density

Fig. 2. A Real Haptics + Real Vision environment (Left) and a Real Haptics - Real Vision environment (Right). (Reproduced by permission from Kawai, 2002a. Copyright © 2002

Figure 3A indicates, as an example, the differences between the 0.10 N-cube and the 0.20 Ncube among three different materials. By evaluating the accuracy of weight discrimination among three material conditions, it was possible to investigate whether or not haptic object size affected heaviness perception (Kawai, 2002a). As indicated in Fig. 3B, it was possible to investigate the accuracy of weight discrimination for all possible combinations by manipulating both weight (dotted arrows) and density (solid arrows) using these cubes. Surprisingly, this was the first published research attempt to study the psychological scales or discriminative abilities for weight or heaviness that covered all weight-density conditions (Kawai, 2003a). The probable reason for this is that researchers focusing on weight have concentrated on constant density conditions (D, E, and F in Fig. 3B) in which the psychological scale complemented physical weight. On the other hand, researchers focusing on the SWI have been interested primarily in equal-weight with different density conditions (B and H) believing that only in such conditions can object size affect heaviness perception. We believe that humans judge heaviness in the same manner for any combination of weight and density; our goal is to establish a heaviness model that explains heaviness perception

With these manipulations, new findings were obtained regarding the effect of haptic size on perceived heaviness: (1) Whenever we lift objects to compare heaviness, haptically perceived object size is significantly involved in heaviness perception (Kawai, 2002a), (2) The effect of haptic size is not limited to a specific situation such as Charpentier's SWI (Kawai, 2002a), (3) The effect of haptically perceived size was strong for some subjects but less for others (Kawai, 2002a), (4) Object density also contributes to perception of heaviness, with significant interaction with weight (Kawai, 2002b), (5) As no other forms of input were presented to subjects to detect object density, it is concluded that approximate, but not exact, information about density is derived possibly from the integration of haptic size information

The next sections present our research on the effect of object size on perceived heaviness. The experimental environment must be set up in accordance with the objective of the experiment: objective first and methodology second. Therefore, note that totally different experimental environments were set up, based upon the questions asked and sensory modalities examined.

## **3.1 Effects of haptically perceived object size on perceived heaviness: Use of the Real Haptics – Real vision environment: First experiments**

It is a common tendency to interpret object size to mean that which has been visually perceived rather than that which has been haptically acquired during grasping and lifting (MacKenzie & Iberall, 1994). Similarly, the majority of researchers on heaviness perception have focused specifically on the effects of visually perceived object size (Ellis & Lederman, 1993) despite the fact that object size affects heaviness perception both visually and haptically (Charpentier 1891, as cited in Murray et al. 1999). As a consequence, experimental environments have kept haptic size constant through the use of grip apparatus, a handle, or strings (Gordon et al., 1991; Mon-Williams & Murray 2000; Buckingham & Goodale, 2010). Surprisingly few studies specifically focused on the effects of haptic size on heaviness perception, in spite of the evidence that effects on heaviness were considerably stronger for haptic size than visual size (Ellis & Lederman, 1993).

Selecting an experimental environment to focus solely on the haptically perceived object size was quite simple. Where we normally interact with an object in the real world through both haptics and vision (left of Fig. 2), we had only to enclose the subject's working space with screens (right of Fig. 2), to remove the real world visual input. The next step was to determine the type of objects to be used. Since heaviness is affected by an object's physical properties as described in Fig. 1, it was decided to use cubes given the properties of distribution of mass, center of gravity, density, and inertia tensor. When grasping cubes it is possible to constantly maintain the center of gravity between the thumb and index finger. This keeps the points of action on the object surface where normal forces are applied along an opposition vector between the thumb and index finger pads, with the center of gravity on the same line. Spherical objects were also considered (Charpentier 1891, as cited in Murray et al. 1999; Zhu & Bingham, 2011), but it proved difficult to consistently grasp the exact center of gravity between the thumb and index finger in a precision grip, especially when visual input was not available.

The next experimental design decision was whether or not haptically perceived size should be treated as a single independent factor. Objects of equal size can vary in weight depending on their specific density (Harper & Stevens, 1948; Zhu & Bingham, 2011). On the other hand, objects of equal density can vary in weight depending on their specific size (J. Ross & Di Lollo, 1970; Zhu & Bingham, 2011). Logically then, objects of equal weight can vary in both size and density. Thus, all three factors of weight, size and density were considered. This led to the decision to use three sets of cubes with different densities, one set each of: copper (CP; 8.93 g/cm3), aluminum (AL; 2.69 g/cm3), and plastic (PL; 1.18 g/cm3), with 10 cubes in each set having progressively varying weights ranging from 0.05 N to 0.98 N. The surfaces of all cubes were covered with smooth, black vinyl to standardize input related to texture, thermal conductivity, friction, compliance, and colour. As a result, subjects received no cues as to the underlying materials. Each subject performed weight discrimination trials between

The next sections present our research on the effect of object size on perceived heaviness. The experimental environment must be set up in accordance with the objective of the experiment: objective first and methodology second. Therefore, note that totally different experimental environments were set up, based upon the questions asked and sensory

**3.1 Effects of haptically perceived object size on perceived heaviness: Use of the Real** 

It is a common tendency to interpret object size to mean that which has been visually perceived rather than that which has been haptically acquired during grasping and lifting (MacKenzie & Iberall, 1994). Similarly, the majority of researchers on heaviness perception have focused specifically on the effects of visually perceived object size (Ellis & Lederman, 1993) despite the fact that object size affects heaviness perception both visually and haptically (Charpentier 1891, as cited in Murray et al. 1999). As a consequence, experimental environments have kept haptic size constant through the use of grip apparatus, a handle, or strings (Gordon et al., 1991; Mon-Williams & Murray 2000; Buckingham & Goodale, 2010). Surprisingly few studies specifically focused on the effects of haptic size on heaviness perception, in spite of the evidence that effects on heaviness were considerably stronger for

Selecting an experimental environment to focus solely on the haptically perceived object size was quite simple. Where we normally interact with an object in the real world through both haptics and vision (left of Fig. 2), we had only to enclose the subject's working space with screens (right of Fig. 2), to remove the real world visual input. The next step was to determine the type of objects to be used. Since heaviness is affected by an object's physical properties as described in Fig. 1, it was decided to use cubes given the properties of distribution of mass, center of gravity, density, and inertia tensor. When grasping cubes it is possible to constantly maintain the center of gravity between the thumb and index finger. This keeps the points of action on the object surface where normal forces are applied along an opposition vector between the thumb and index finger pads, with the center of gravity on the same line. Spherical objects were also considered (Charpentier 1891, as cited in Murray et al. 1999; Zhu & Bingham, 2011), but it proved difficult to consistently grasp the exact center of gravity between the thumb and index finger in a precision grip, especially when

The next experimental design decision was whether or not haptically perceived size should be treated as a single independent factor. Objects of equal size can vary in weight depending on their specific density (Harper & Stevens, 1948; Zhu & Bingham, 2011). On the other hand, objects of equal density can vary in weight depending on their specific size (J. Ross & Di Lollo, 1970; Zhu & Bingham, 2011). Logically then, objects of equal weight can vary in both size and density. Thus, all three factors of weight, size and density were considered. This led to the decision to use three sets of cubes with different densities, one set each of: copper (CP; 8.93 g/cm3), aluminum (AL; 2.69 g/cm3), and plastic (PL; 1.18 g/cm3), with 10 cubes in each set having progressively varying weights ranging from 0.05 N to 0.98 N. The surfaces of all cubes were covered with smooth, black vinyl to standardize input related to texture, thermal conductivity, friction, compliance, and colour. As a result, subjects received no cues as to the underlying materials. Each subject performed weight discrimination trials between

**Haptics – Real vision environment: First experiments** 

haptic size than visual size (Ellis & Lederman, 1993).

visual input was not available.

modalities examined.

sets of two cubes of identical density, e.g., CP vs. CP. In addition, equal numbers of trials for each weight difference with identical combination of weights were presented for all density conditions.

Fig. 2. A Real Haptics + Real Vision environment (Left) and a Real Haptics - Real Vision environment (Right). (Reproduced by permission from Kawai, 2002a. Copyright © 2002 Springer-Verlag.)

Figure 3A indicates, as an example, the differences between the 0.10 N-cube and the 0.20 Ncube among three different materials. By evaluating the accuracy of weight discrimination among three material conditions, it was possible to investigate whether or not haptic object size affected heaviness perception (Kawai, 2002a). As indicated in Fig. 3B, it was possible to investigate the accuracy of weight discrimination for all possible combinations by manipulating both weight (dotted arrows) and density (solid arrows) using these cubes. Surprisingly, this was the first published research attempt to study the psychological scales or discriminative abilities for weight or heaviness that covered all weight-density conditions (Kawai, 2003a). The probable reason for this is that researchers focusing on weight have concentrated on constant density conditions (D, E, and F in Fig. 3B) in which the psychological scale complemented physical weight. On the other hand, researchers focusing on the SWI have been interested primarily in equal-weight with different density conditions (B and H) believing that only in such conditions can object size affect heaviness perception. We believe that humans judge heaviness in the same manner for any combination of weight and density; our goal is to establish a heaviness model that explains heaviness perception for all weight-density conditions.

With these manipulations, new findings were obtained regarding the effect of haptic size on perceived heaviness: (1) Whenever we lift objects to compare heaviness, haptically perceived object size is significantly involved in heaviness perception (Kawai, 2002a), (2) The effect of haptic size is not limited to a specific situation such as Charpentier's SWI (Kawai, 2002a), (3) The effect of haptically perceived size was strong for some subjects but less for others (Kawai, 2002a), (4) Object density also contributes to perception of heaviness, with significant interaction with weight (Kawai, 2002b), (5) As no other forms of input were presented to subjects to detect object density, it is concluded that approximate, but not exact, information about density is derived possibly from the integration of haptic size information

Computer Graphic and PHANToM Haptic Displays:

stereo images (dotted line) on a monitor.

limitation of the real physical world for experimental control.

Powerful Tools to Understand How Humans Perceive Heaviness 33

differences in visual size or inertia tensor, when we adhere to the conventional methodology of the Real Haptic + Real Vision environment (left in Fig.4A and Fig.4B). This is the

We decided, therefore, that the only way to separate the factor of visual size cues completely from other factors such as inertial tensor was to use a combination of 3D motion analysis and 3D computer graphics techniques to create virtual objects for the SWI paradigm. This type of augmented environment was developed as the Virtual Hand Laboratory at Simon Fraser University in Burnaby, Canada, in which 3D graphics (and other displays) were driven by 3D motion and forces. Computer graphics were developed to ensure completely independent manipulation of visual size information by superimposing computer-created graphics of different sizes on a single object (Fig. 4A, top) or two physically identical objects (Fig.4B, bottom); thus, haptic information was kept constant. As seen in Fig. 4, two different experimental set-ups were designed: a single physical grip apparatus was used specifically to record grip and load forces applied on the grip handle (top in Fig 4A), while two physical cubes with identical physical properties were used to investigate the effects of visual size on heaviness (bottom in Fig. 4B). In both environments, visual size varied as a single independent parameter without changing the inertia tensor. As shown in the right of Fig. 4B, each subject wore Crystal Eyes goggles and viewed through a semi-silvered mirror the

Fig. 4. From Real Haptics + Real Vision (left) to Real Haptics + Virtual Vision (right) environments. (A) a single stimulus presentation and (B) two stimuli presentation

(Reproduced with permission from Kawai et al., 2007. Copyright © 2007 Springer-Verlag.)

with weight (Kawai, 2002b), (6) The Weight/Aperture, the finger span formed during thumb-index finger grasp (the opposition vector), or the width of cube itself, can be derived as a heaviness model as it reflects subjective responses in any weight-density conditions (Kawai, 2003a, 2003b).

While it is clear that haptic object size is systematically involved in heaviness perception, the results of this study offer no neurological evidence about how, where and when in the nervous system this occurs (Flanagan et al., 2008; Chouinard et al., 2009).

Fig. 3. A. Treatment of object size as a single independent factor. B. Weight-density conditions presented to the subjects (A: Reproduced with permission from Kawai, 2002a. Copyright © 2002 Springer-Verlag.)
