Do exploratory arm movements contribute to maximum reach distance judgements?

Abstract

Exploratory movements provide information about agents’ action capabilities in a given environment. However, little is known about the specifics of these exploratory movements, such as which movements are necessary to perceive a given action capability. This experiment tested whether arm movements contributed to judgements of maximum reach distance. Participants made judgements about their maximum reach distance by walking to the point farthest from an object from which they still perceived the object to be reachable. Over the course of two sets of nine judgements, participants’ arms either swung naturally by their sides (Unrestricted Condition) or were held together behind their backs (Restricted Condition). Arm movement restriction increased maximum reach distance judgement error when compared with unrestricted judgements. In addition, judgement error improved over trials only when exploratory arm movements were unrestricted, and the improvements did not carry over to subsequent judgements made when exploratory arm movements were restricted. Arm movement restriction did not increase the variability of judgement error when compared with unrestricted judgements. The results indicate that exploration is necessary to generate affordance information, show that restricted exploration degrades affordance perception, and suggest that maximum reach distance exists at the global array level. In addition, they have practical implications for operational situations in which actors’ arm movements are restricted, such as when military personnel wear body armour.

Keywords

Affordance exploratory movement restricted exploration direct perception perception–action

Gibson (1979/1986) described affordances as opportunities for action made available to a given animal in a given environment. More formally, Stoffregen (2003) argued that affordances are relational properties of the actor–environment system. Implicit in this definition is the concept that neither subsystem alone can define affordances. For example, a step only affords climbing in a bipedal manner if its height is less than or equal to some critical proportion of the length of the actor’s leg (Warren, 1984).

Gibson (1979/1986) hypothesised that exploratory movements generate information about the actor–environment system’s affordances. Exploratory movements are self-generated movements of perceptual systems. Gibson (1966) argued that perceptual systems are not passive entities that receive stimulation, but instead move so as to actively structure the energy surrounding the actor (e.g., light, sound, force) in ways that are informative about the actor–environment system, including affordances.

Several studies have supported his claim (Adolph et al., 2000; Bingham et al., 1989; Cornus et al., 1999; Mantel et al., 2015; Mark et al., 1990, 1999; Solomon & Turvey, 1988; Yu et al., 2011). For example, hefting balls of varying size and weight allowed actors to determine which ball could be thrown the farthest (Bingham et al., 1989).

Perhaps more importantly, past studies have found that restricting exploratory movements increased judgement error, that is, judgements reflected participants’ actual abilities more poorly (Cornus et al., 1999; Harrison et al., 2011; Mantel et al., 2015; Mark et al., 1990, 1999; Oudejans et al., 1996; Yu et al., 2011). For example, Mark et al. (1990) had participants judge the maximum chair height on which they could sit. They found that participants accurately judged their own maximum seat height while looking at the chair and either walking between two points in the room (Experiment 1) or simply standing in place (Experiment 2). However, when participants viewed the chair through a monocular peephole (Experiment 3), while maintaining an awkward stance (Experiment 4), or while resting their head and back against a wall (Experiment 5), their maximum seat height judgements contained significantly more error than when they simply stood normally (Experiment 2). Collectively, these results show that exploratory movements, which can be as minute as subtle head and torso movements (Stoffregen et al., 2005; Yu et al., 2011), are necessary to accurately perceive affordances, even for common actions such as sitting.

Exploration about maximum reach distance

The studies described in the preceding section provide important insights about exploratory movements. However, many fundamental questions regarding such movements have yet to be answered. For example, what exploratory movements are necessary to perceive a given affordance? To begin to address that question, we chose to research what exploratory movements must be executed to perceive whether the actor can reach an object. We chose reaching because existing research allowed us to reasonably hypothesise about (some of) the associated exploratory movements.

Maximum reach distance is a property of the actor–environment system that is determined by the relationship between the distance the actor can extend their hand away from their body in a given plane and the distance separating the actor and the to-be-reached object in that plane. The actor–object system affords reaching if the actor can extend their hand away from their body to a distance that is equal to or greater than the distance separating the actor and the object.

Thus, exploration that generates information about how the distance between the actor and the object relates to the distance the actor can extend their hand away from their body would enable perception of maximum reach distance. The exact nature of that relational information is unclear, although existing research provides clues about what it might entail.

Exploratory head movements can generate information about the body-scaled distance between the actor and the to-be-reached object (Bingham & Pagano, 1998; Bingham & Stassen, 1994; Pagano & Bingham, 1998). Specifically, the amplitude of an oscillatory head movement, the period of that movement, and the time to contact associated with the peak velocity of that oscillation combine to produce the distance between the actor and the object in units scaled to the amplitude of the oscillatory head movement (Bingham & Stassen, 1994).

Prior research has shown that exploratory head movements are necessary for accurate perception of maximum reach distance. In Mantel et al. (2015), participants wearing head-mounted displays judged whether they could reach a virtual object under three conditions: when (a) their heads moved freely and the consequences of those movements were represented in the display, (b) their heads were restrained and the virtual object remained stationary, and (c) their heads were restrained but the virtual object moved; participants were shown a playback of a recording made of the object moving in response to head movements the participant made during an earlier exploration condition trial. The absolute values of the difference between a participant’s judged and the actual maximum reach distance in the head movement, head restriction, and playback conditions were 20.3%, 114.6%, and 111.1%, respectively. The large difference in error between the head movement and other conditions indicates that exploratory head movements are necessary for accurate perception of maximum reach distance.

Furthermore, exploratory arm movements can generate information about the length of an actor’s arm (Carello & Turvey, 2000; Shibata et al., 2012; Turvey & Carello, 2011). Specifically, eigenvalues of the arm’s inertia tensor (i.e., the principal moments of inertia experienced when the arm is rotated around a given axis) are informative about arm length (Carello & Turvey, 2000).

Prior research demonstrated that manipulating those eigenvalues affects perceptions of arm length. In Shibata et al. (2012), participants judged their arm length under multiple conditions: (a) a weight was attached to their hand, (b) a weight was attached to their forearm, and (c) no weight was attached. Attaching weight to participants’ hands produced larger eigenvalues of the inertia tensor compared with attaching weight to participants’ forearms. Consequently, participants judged arm length to be greater when a weight was attached to their hand as opposed to their forearm, or when no weight was attached. Importantly, such differences were not observed in a follow-up experiment during which participants held their arms still, which suggests that exploratory arm movements are necessary to generate the inertia tensor and thus perceive arm length.

Arm length relates to an actor’s maximum reach distance, so exploratory arm movements are probably necessary to judge maximum reach distance. Consistent with that possibility, Anderson and Turvey (1998) compared maximum reach judgements when weights were attached to participants’ wrists or elbows; participants perceived their reach to be greater when weights were attached to their wrists as opposed to their elbows. However, Anderson and Turvey (1998) did not manipulate arm movement, so their results do not conclusively demonstrate that exploratory arm movements are necessary to judge maximum reach distance.

This study

We addressed this gap in the literature by evaluating whether arm movements contribute to maximum reach distance judgements. To do so, our participants judged their maximum reach distance either while holding their arms behind their backs to limit arm movements (Restricted Condition), or while their arms swung naturally at their sides (Unrestricted Condition). Judgements were made actively, by walking forwards or backwards, to allow participants to generate the exploratory movements they would normally create (with the exception of arm movements in Restricted Condition) when moving towards an object with the intention to perform a reach (Mantel et al., 2010).

Previous research concerning other affordances (e.g., sitting and gap crossing) demonstrated that restricting exploratory movements increased affordance judgement error (Mark et al., 1990, 1999). Accordingly, if arm movements contribute to the maximum reach distance judgement, then judgements in Restricted Condition should contain more error than those in Unrestricted Condition. If that is not the case, then it would suggest that arm movements are not a necessary component of the exploratory movements associated with maximum reach distance judgements.

Exploration is a key component of Gibson’s (1979/1986) theory, yet we know relatively little about the exact nature of exploratory movements. This research will thus make a significant contribution to the literature by determining whether exploratory arm movements are necessary to judge maximum reach distance. In doing so, this research will also impact our understanding about the information actors use to judge maximum reach distance. For example, if exploratory arm movements contribute to maximum reach judgements, then actors generate and use information about arm length when judging whether they can reach something.

Method

Participants

Thirty-two undergraduate Introduction to Psychology students from Texas Tech University participated in this experiment (23 female, 9 male). Their ages ranged from 18 to 23 years (M = 18.75, SD = 1.14). Their maximum reach distance ranged from 89.00 to 128.46 cm (M = 104.95, SD = 8.03). Participants reported being free of motor impairments and having normal or corrected-to-normal vision. All participants were awarded course credit in exchange for participation.

Experimental design

This experiment employed a completely within-subject design with Arm Movement (Unrestricted, Restricted) as the independent variable. Arm Movement referred to whether participants judged maximum reach distance while walking normally with their arms swinging naturally by their sides (Unrestricted), or while restricting those natural arm movements by grasping their non-dominant wrist with their dominant hand, with both arms behind their backs (Restricted). In line with previous affordance perception research, the dependent variable, Error, was computed in terms of percentage of absolute error (|[judged maximum reach/actual maximum reach] – 1| × 100) (Cornus et al., 1999; Oudejans et al., 1996). This dependent variable was chosen because past studies have used changes in affordance judgement error across conditions to determine whether movements associated with those conditions are necessary to perceive a given affordance (e.g., Cornus et al., 1999; Mantel et al., 2015; Mark et al., 1990, 1999; Yu et al., 2011).

Apparatus

Participants made their maximum reach judgements in a 4.57 m × 4.27 m room (hereafter referred to as the back room). The room’s walls were covered by black cloth to discourage participants from basing their judgements on arbitrary testing environment features (Figure 1). The object about which judgements were made was placed near the room’s rear corner, 1.83 m from each of the two connecting walls and perpendicular to each wall. It hung in the air via a thin white string and consisted of a masking-tape-wrapped cardboard cylinder (9.53 cm height, 3.18 cm diameter), hanging vertically in the air, with a retroreflective sphere (2.54 cm diameter) protruding from the top (Figure 2).

Figure 1.

Back room experimental setup.

Figure 2.

Experimental object about which reaching judgements were made.

An eight-camera passive optical motion capture system, sampling at 100 Hz, recorded participants’ movements (software: Nexus 1.8; cameras: MX T10 near-infrared; Vicon Motion Systems, Oxford, UK). Participants wore a Velcro jacket and a flat-brimmed cap, both of which were adorned in retroreflective spheres (1.70 cm diameter). The retroreflective markers were placed on the front of the jacket and on the hat in the physiologically identifiable locations specified in Vicon’s “Preparation” guidebook (Vicon, Oxford, UK), with two additional markers placed on the hat’s brim and apex to assist with orientation. MATLAB (MathWorks, 2017) programs utilising Vicon’s software development kit (SDK) produced real-time information about the participant’s position. The experimenter utilised these programs when moving each participant to the correct starting position before each trial, and when recording their perceived and actual maximum reach distances.

After completing both experimental conditions, participants filled out a questionnaire that inquired about the degree to which they followed specific instructions, their thoughts on the effect of the manipulation, and their thought processes while making judgements. Finally, a demographics questionnaire was administered that asked only for the participant’s age and sex.

Procedure

Participants completed both conditions. Participants were randomly assigned to begin in either Unrestricted or Restricted Condition, and starting condition was completely counterbalanced. Each participant was tested individually for approximately 1 hr.

Preparation

Participants entered a sitting room, read and signed the informed consent paperwork, and dressed in the Velcro jacket and cap. In line with prior research, participants were asked to remove their socks and shoes (Stoffregen et al., 2005), as such items might affect their gait. They worked with the experimenter to place markers in the correct positions. With the hanging object being removed from sight, participants were led into the back room. The participants stood in the room for 30 s as the motion capture system was calibrated, before being led back to the sitting room where they received instructions.

Instructions

Before each condition, participants were instructed that they would be making judgements of their maximum reach distance. It was explained that a maximum reach was defined as a reach occurring from as far away from the object as the participant could possibly be, while still being able to grasp the object with their dominant hand. To limit the restrictiveness of the judgement, participants were told that performance of a maximum reach would be a multi-degree-of-freedom reach defined in the following manner: they would prepare by standing up straight at their point of maximum reach with their feet parallel; they would then bend forwards at the waist towards the object, keep their dominant foot in place, move their non-dominant foot backwards from the maximum reach point to counterbalance their forward lean, and stretch their upper body outwards towards the object. That is, while maintaining the position of their dominant foot at their point of maximum reach, they could perform other actions associated with a more naturalistic multi-degree-of-freedom reach. However, such a reach would need to be performed with both feet touching the ground, without falling, without swinging the object, and without moving either foot forwards past the point of maximum reach. That is, they could move a leg backwards from their maximum reach point to counterbalance their forward leaning, but they could not step forwards from their maximum reach position (Figure 3). Participants were not told what exactly constituted a grasp; that was explained later via demonstration. Participants reported only on whether the object could be reached from the described multi-degree-of-freedom maximum reach posture. They did not report on whether the object could be reached from other postures (e.g., upright standing).

Figure 3.

Example of what a maximum reach would look like.

Participants were told that such judgements would be made by walking directly towards or away from a hanging object, and stopping when they reached their judged point of maximum reach. Participants in Restricted Condition were told that they would be walking with their dominant hand grasping their non-dominant wrist, with both arms behind their back. It was made clear that participants would not be allowed to perform any reaches during the judgement phase. Participants were instructed to keep their eyes strictly on the object, and to perform the task rapidly, without overthinking it. Heft (1993) argued that the latter two instructions reduce the risk that participants will make error-prone analytical judgements instead of more accurate perceptual judgements. In addition, participants were instructed to keep their eyes closed between trials. The experimenter would lead them to their new starting position before each trial.

The experimenter demonstrated a maximum reach (Figure 3). During the demonstration, the experimenter grasped the object between the tips of his forefinger and thumb to clarify how we defined a grasp. The experimenter then demonstrated a judgement of maximum reach via locomotion, so participants could observe the manner by which they would make their own judgements, and the action about which they would be making judgements. Participants were given the opportunity to ask clarifying questions about the nature of the task they would be performing, before beginning the experiment.

The participant then waited in the sitting area while the experimenter completed the setup procedure. During that time, the experimenter walked into the back room and adjusted the height of the object such that the retroreflective sphere on its top was situated at the height of the participant’s dominant shoulder (as marked at their acromion process and recorded in MATLAB during calibration), which was self-reported at the start of the study. Participants were then led into the back room with their eyes closed.

Data collection: Unrestricted Condition

Each participant completed one practice trial and then nine experimental trials. The number of experimental trials reflects our efforts to balance several factors: the desire to (a) vary factors such as the initial distance between the participant and the object, (b) keep the experiment as short as possible, and (c) include roughly the same number of trials as was employed in prior maximum reach distance experiments (e.g., Ramenzoni et al., 2008; Wagman, 2012).

The purpose of the practice trial was to ensure that the participants understood the task and to allow the experimenter to correct any mistakes before data collection began (i.e., “do not actually reach for the object”). Participants were not told that the first trial was a practice trial. Practice trial data were not included in the analyses.

To begin the practice trial, the participant was verbally directed to a practice location, which was the same for every participant. The experimenter utilised the Vicon motion capture system and MATLAB to visualise the participant’s current location relative to their predetermined starting location, used colloquial language regarding step size (e.g., “big step” vs. “step” vs. “little step”), and adapted the number of such steps requested from the participant based on how the participant interpreted the difference in those subjective step sizes, to quickly (approximately 4–7 s) guide the participant to their correct starting location. Upon arriving at the practice location, the participant was verbally asked to “open their eyes and begin.” Participants then walked forwards and/or backwards until they were positioned at their judged point of maximum reach. Once satisfied, the participant said “here” to indicate their judgement. The motion capture system then recorded the distance between the retroreflective marker placed on the participant’s clavicle and the hanging object. Given that participants made their maximum reach distance judgements about an object that was located in line with their clavicle, we felt it was appropriate to use their clavicle to denote their position in space when recording their judgements.

After their judgements, participants closed their eyes. Any procedural mistakes made by participants during the practice trial were corrected at this time.

The participant then completed their nine experimental trials. The participants’ starting positions for those trials consisted of various angle–distance combinations relative to the object. For each condition, three starting distances (integers) were randomly selected from each of the following three ranges: 2.54–60.96 cm, 63.50–121.92 cm, and 124.46–182.88 cm. For each condition, three starting angles (integers) were randomly selected from each of the following three ranges: 0°–29°, 30°–59°, and 60°–89°. Rays representing the 0° and 89° angles mirrored each other in terms of their distance from the left and right rear walls, such that a participant starting 2.54 cm from the object at 0° would be the same distance from the left wall that a participant starting 2.54 cm from the object at 89° would be from the right wall. These angles and distances were randomly combined and ordered such that no participant ever started at the same angle or distance in any trial across both conditions. The purpose of this was to limit the participants’ ability to memorise (a) their position relative to environment cues observed from a given distance/angle and (b) the number of steps required to make a given judgement. Otherwise, the experimental trials were identical to the practice trial. After completing the nine experimental trials in this condition, participants were led back to the sitting area.

Data collection: Restricted Condition

Data collection in Restricted Condition was equivalent to that in Unrestricted Condition with two exceptions. First, once at the trial’s starting location, participants grasped their non-dominant wrist with their dominant hand, with both arms behind their back, before opening their eyes and beginning the trial. Second, after saying “here,” participants in Restricted Condition were asked to “close their eyes and relax their arms,” so that locomotion between trials was equivalent across conditions.

Maximum reach measurement

When both conditions had been completed, the participant’s actual maximum reach distance was measured. To do so, the participant attempted to reach the object from various distances in a stepwise fashion, until the difference between their longest successful reaching attempt and their shortest unsuccessful reaching attempt was 12.5 mm (half of an inch). Their maximum reach distance was recorded as the average of their maximum successful reach and minimum unsuccessful reach, each measured from the participant’s clavicle from a normal standing position before leaning in to attempt the reach.

Reserving measurement of actual maximum performance until the end of the judgement phase is standard practice for affordance perception research (cf. Carello et al., 1989; Mantel et al., 2010; Pepping & Li, 2005; Stoffregen et al., 2005; Wagman, 2012; Wagman et al., 2014). It ensures that participants’ judgements are not affected by prior feedback from the actual maximum performance measurement.

Questionnaires and debriefing

Finally, participants were led back to the sitting room where they completed the questionnaires described earlier. Participants were then debriefed.

Results

Analytic approach

Analyses are organised by the research question they answer. A cumulative alpha level of .05 was employed for each individual research question. Research questions requiring multiple analyses were Bonferroni corrected such that the sum of the per-comparison alpha levels was .05 (Tabachnick & Fidell, 2007). Research questions requiring a single analysis were not Bonferroni corrected.

Did arm restriction increase judgement error?

Error scores for Unrestricted and Restricted Conditions were separately averaged across trials for each participant. This produced one average percentage of absolute error score per Arm Movement condition for each participant. Those scores were subjected to an outlier analysis, which followed Stevens’ (2009) recommendations. Two outliers were identified. Each was replaced by the next largest non-outlier, which reduced their impact without greatly reducing variance (Tabachnick & Fidell, 2007). These Error scores were used for the analyses in the current and immediately following sections. Conclusions drawn from original and outlier-adjusted data were identical.

A repeated-measures t test compared the average Error scores from Unrestricted and Restricted Conditions. This test was performed to determine whether restriction of exploratory arm movements increased judgement error. There was a significant difference in average Error between the Unrestricted (M = 8.48%, SD = 3.38) and Restricted (M = 10.84%, SD = 5.86) conditions, t(31) = –2.27, p = .031, d = 0.40 (Figure 4). Average Error scores of 8.48% and 10.84% are equivalent to average absolute deviations of 8.90 and 11.38 cm, respectively. This outcome suggests that when exploratory arm movements are restricted, participants’ judgements of maximum reach contained more error than when such exploration was unrestricted.

Figure 4.

Comparison of error (average percentage of absolute error) at each level of arm movement (unrestricted, restricted). Error bars represent ±1 standard error.

Were judgements free from error?

Two one-sample t tests compared the average Error in each condition to zero. Both tests revealed that the average Error significantly differed from zero, Unrestricted: M = 8.48%, SD = 3.38, t(31) = 14.20, p < .001, d = 2.51; Restricted: M = 10.84%, SD = 5.86, t(31) = 10.46, p < .001, d = 1.85. These outcomes suggest that participants’ maximum reach judgements were not free from error in either condition.

Did judgements improve over trials?

Error scores for each trial within Unrestricted and Restricted Conditions were computed for each participant. Those scores were subjected to an outlier analysis. Fourteen outliers (out of 576 scores) were identified and replaced by the next largest non-outlier. Conclusions drawn from original and outlier-adjusted data were identical.

Two linear regressions determined whether Error, square root transformed to correct positive skew, improved over trials in Unrestricted and Restricted Conditions. The linear regression for Unrestricted Condition was significant, F(1, 286) = 6.29, p = .013, residual SE = 1.02, R² = .022 (Figure 5), which indicates that the judgement error improved over trials when exploratory arm movements were unrestricted, despite the absence of feedback. The linear equation was as follows: Error = 10.06 – 0.34 × Trial (this equation is based on non-transformed data, for the sake of interpretation, and the associated residual SE = 5.58). In contrast, the linear regression for Restricted Condition was not significant, F(1, 286) = 0.41, p = .52, residual SE = 1.21, R² = .001 (Figure 5), which indicates that the judgement error did not improve over trials when exploratory arm movements were restricted. The linear equation was as follows: Error = 11.35 – 0.11 × Trial (this equation is based on non-transformed data, for the sake of interpretation, and the associated residual SE = 7.68).

Figure 5.

Comparison of error (average percentage of absolute error) across trials. Scores are averaged by trial for the sake of interpretability. Error bars represent ±1 standard error. Trend lines represent lines of best fit.

Did judgement improvements carry over?

Two tests determined whether the observed improvements during Unrestricted Condition carried over to Restricted Condition. The first test compared Error from the final trial of Unrestricted Condition (Trial 9) to the first trial of Restricted Condition (Trial 1), for participants who started the experiment in Unrestricted Condition and finished in Restricted Condition (n = 16). Separate outlier analyses were performed for each set of scores. One outlier was identified, in Unrestricted Trial 9, and replaced by the next largest non-outlier. A repeated-measures t test revealed a significant difference between those trials, Unrestricted Trial 9 (M = 6.98%, SD = 5.92), Restricted Trial 1 (M = 12.53%, SD = 7.30), t(15) = –2.95, p = .010, d = 0.74. Error scores of 6.98% and 12.53% are equivalent to average absolute deviations of 7.33 and 13.15 cm, respectively. Please note that a comparable t test of the original data, which included the outlier, resulted in a marginally significant difference, t(15) = –2.37, p = .032, d = 0.59. The second test compared the average Error scores from the first trial of Restricted Condition (Trial 1) between participants who started in Unrestricted Condition and those who started in Restricted Condition. Separate outlier analyses were performed for each set of scores. One outlier was identified and replaced by the next largest non-outlier. Conclusions drawn from the original and outlier-adjusted data were identical. An independent-samples t test did not reveal a significant difference between those trials, Restricted Trial 1 for participants who began the experiment in Unrestricted Condition (M = 12.23%, SD = 10.00) and Restricted Trial 1 for those who began in Restricted Condition (M = 12.53%, SD = 7.30), t(30) = 0.097, p = .92, d = 0.034. Error scores of 12.23% and 12.53% are equivalent to average absolute deviations of 12.84 and 13.15 cm, respectively. Collectively, these outcomes suggest that participants cannot take advantage of whatever caused the improvement during Unrestricted Condition when their exploratory arm movements are restricted.

Did arm restriction increase variability of judgement error?

A standard deviation of error scores was computed per Arm Movement condition for each participant. Those standard deviations were subjected to an outlier analysis. Two outliers were identified and replaced by the next largest non-outlier. Conclusions drawn from original and outlier-adjusted data were identical.

A repeated-measures t test compared the average standard deviations from Unrestricted and Restricted Conditions. There was not a significant difference between Unrestricted (M = 4.74%, SD = 2.09) and Restricted (M = 5.06%, SD = 2.07) conditions, t(31) = –0.91, p = .37, d = –0.16. Thus, restricting exploratory arm movements did not increase the variability of judgement error scores.

Discussion

Maximum reach distance judgements contained more error when arm movements were restricted compared with when they were unrestricted. This aligns with previous findings on the increase in affordance judgement error resulting from the restriction of exploratory movements (Cornus et al., 1999; Harrison et al., 2011; Mantel et al., 2015; Mark et al., 1990, 1999; Oudejans et al., 1996; Yu et al., 2011) and supports that exploratory arm movements contribute to the maximum reach distance judgement.

That suggests the perceptual system for maximum reach distance has at least two components: exploratory arm movements and exploratory head movements (Mantel et al., 2015). When executed simultaneously, those exploratory movements would collectively provide information about how the distance between the actor and the to-be-reached object relates to the length of the actor’s arm. That relational information would exist at the level of the global array (Stoffregen & Bardy, 2001). Such information would be sufficient when an actor only extends their hand away from their body via arm movement, that is, what Carello et al. (1989) referred to as a 1-degree-of-freedom reach. However, it would likely be insufficient for multi-degree-of-freedom reaches, such as when an actor extends their hand away from their body via arm movement and bending at the hips. In such cases, it is likely that the perceptual system for maximum reach distance would also include other exploratory movements.

Although judgements in Unrestricted Condition contained less error than those in Restricted Condition, maximum reach distance judgements, in general, were not free of error. Such inaccuracy has been observed previously (for a review, see Heft, 1993) and could stem from several factors. In general, it could reflect that actors may not typically execute maximum reaches and thus have little experience making judgements about such reaches (Day et al., 2015), or actors may not need to judge maximum reach distance in an error-free manner to successfully execute maximum reaches, for example, actors may fine-tune their reaches in real time as they reach (Carello et al., 1989). In the present context, it is also possible that inaccuracy was due to the focal nature of the reaching task (Heft, 1993). When the perceptual–motor judgement of interest is the participants’ primary task, participants are more likely to allow analytical reflections to influence judgements. Such reflection reduces the accuracy of judgements that are typically perceptual in nature (Heft, 1993).

In addition, an improvement over trials was only observed when arm movements were unrestricted. This finding suggests that exploratory arm movements are necessary to improve judgements of maximum reach distance, and that this improvement can occur even without verbal or performance feedback. This finding is in line with prior work on the necessity of exploratory movements for the improvement of perceptual judgements (Mark et al., 1990; Ramenzoni et al., 2010; Stoffregen et al., 2005). To elaborate on an earlier example, participants’ maximum sitting height judgements contained more error and did not improve over time when participants observed a chair while their head and torso movements were restricted (by resting their heads and backs against a wall), as compared with when their movements were unrestricted (Mark et al., 1990).

The present results do not make clear why restricting arm movements prevented participants from improving their judgements. One possibility is that those improvements directly concerned use of the information generated by the exploratory arm movements, and, without that information, its use could not be improved. Another possibility is that those improvements may concern something on the perceptual system level, and disrupting any aspect of the perceptual system may prevent participants from improving their maximum reach distance judgements. Future research should investigate such possibilities.

Finally, when participants experienced Unrestricted Condition prior to Restricted Condition, improvements observed in Unrestricted Condition did not carry over to Restricted Condition. This suggests that participants were not able to leverage such improvements when exploratory arm movements were restricted. That is, whatever drives the improvements could not be carried over from Unrestricted to Restricted Condition. Adolph et al. (1997) observed a somewhat similar effect. Specifically, they found that children improved their judgements about whether a slope could be descended via crawling, but those improvements did not carry over to later judgements about whether a slope could be descended via walking, which suggests that how one perceives whether a slope can be crawled down is different than how one perceives whether a slope can be walked down. In the present experiment, it is possible that how participants judged maximum reach distance in Unrestricted Condition was different than how they judged maximum reach distance in Restricted Condition, which prevented improvements in Unrestricted Condition from carrying over to Restricted Condition. Future research should investigate that possibility.

A potential limitation of our experimental design is that participants’ arms may have been visible to participants during Unrestricted Condition. Participants were not prevented from seeing their arms. However, we do not think that participants saw their arms because they kept their eyes on the object and did not swing their arms to the degree necessary to bring their arms into view while looking at an object at shoulder height in front of them.

The present results have important theoretical implications. First, our results provide further evidence in support of Gibson’s (1979/1986) argument that exploratory movements are necessary to generate information about affordances and contribute to the body of literature that has shown that restriction of exploration degrades affordance perception (Cornus et al., 1999; Harrison et al., 2011; Mantel et al., 2015; Mark et al., 1990, 1999; Oudejans et al., 1996; Yu et al., 2011). Second, our findings extend the current literature regarding maximum reach distance by providing evidence that exploratory movements other than head movements contribute to maximum reach distance judgements. Third, our results support that the perceptual system for maximum reach distance includes components that influence both visual and haptic arrays, which suggests that information about maximum reach distance exists at the level of the global array (Stoffregen & Bardy, 2001).

The present results also have important practical implications. Stoffregen and Mantel (2015) suggest that exploratory movements required to perceive affordances should be considered when designing products. Our results suggest that manufacturers of products that might be used in situations where reaching is required, for example, body armour, should account for the actor’s need to make unrestricted exploratory arm movements, to avoid inadvertently degrading maximum reach distance judgements when using their product. It is important to note that body armour might not need to completely restrict arm movements, as was the case in our experiment, to have this effect. Sitting judgements were degraded when participants stood in an awkward, Charlie Chaplin-esque stance, which still afforded exploratory movements, albeit atypical ones (Mark et al., 1990). Thus, affordance judgements can be degraded when exploratory movements are disrupted, so body armour that disrupts exploratory movements could degrade maximum reach distance judgements.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Benjamin P Widlus

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