Abstract
Background Environmental and task modifications are powerful methods used to affect action in rehabilitation and are frequently used by therapists.
Objective The purpose of this study was to examine and quantify the relationship between hand size (person characteristics) and object size (environmental characteristics) and the effect of this relationship on the emergent reaching patterns for children and adults with typical development.
Design This was a crosssectional prospective study.
Methods Seventeen children and 20 adults participated and were required to reach and grasp 10 pairs of cubes of different sizes. The dimensionless ratios were calculated by dividing the cube size by the aperture between index finger and thumb to quantify emergent reach and grasp patterns. A critical ratio was used to establish the shift from a 1handed to an exclusive 2handed reach pattern.
Results The results demonstrated no significant difference in the mean critical ratios between the 2 groups. However, a 2handed reach was used more frequently than a 1handed reach at a significantly smaller ratio for children in comparison with adults.
Limitations The relational metrics between the cube and hand are only one contribution to the emergent reaching and grasping patterns.
Conclusions Children had more variability of reaching patterns than adults. A personal constraint, such as experience, and a task constraint of accuracy may account for the variability. The results encourage further research on bodyscaled information for individuals with different personal constraints (eg, children with cerebral palsy) and the impact of bodyscaled information on emergent actions.
Therapists are frequently challenged to identify ways to optimize action, with the goal of enhancing function and reducing disability in patients with a variety of disorders. Environmental and task modifications are powerful methods used to affect action in rehabilitation and are frequently used by therapists. However, these modifications typically are introduced using a trialanderror approach. A better understanding of how to optimize the “fit” between the patient and the environment may help therapists develop a more principled approach to manipulating environmental and task demands in order to enhance the emergent actions of patients.
This fit between an actor and the environment was termed an “affordance” by Gibson.^{1} For example, a staircase of certain dimensions may afford bipedal locomotion by an adult or quadrupedal locomotion by an infant, and a barrier to a person in a wheelchair. Different people may perceive different “affordances,” and different actions emerge due to the varying properties of the person and environment. The form of locomotion that emerges is assumed to be directly specified by the relationship between the perceived information from the stair properties and specific person characteristics and capabilities.^{2–5} This perceived information is termed “bodyscaled information.”^{6,7} Perceiving this bodyscaled information is the foundation of successful functional actions.^{2,3,8,9}
The perceptionaction framework (PAF) for action development emphasizes bodyscaled information as derived from an interactive system between the person and his or her environment. Information is considered the basis for perception, which involves an awareness of properties of environmental objects in relation to the person.^{1,10} The information perceived or picked up from the environment influences the development of action.^{10–13} By quantifying the perceived information, we can begin to understand the specific relationship between the body and an object. For example, Warren^{2} demonstrated that a critical ratio of riser height to leg length determined whether a stair was climbable bipedally. Both tall and short participants changed from walking up stairs on 2 feet to climbing the stairs on all fours when stair height exceeded 88% of their leg length. At this critical ratio (ie, 0.88), an action shift from bipedal to quadrupedal locomotion emerged. Thus, scaling the environment to a person's characteristics can affect the emergent action. The PAF offers a principled approach to understanding and measuring these modifications for our patients.^{8} Thoughtfully creating fits among the environment, task, and patient characteristics encourages the spontaneous emergence of action.
The purpose of this study was to examine the relationship between hand size (person characteristics) and object size (environmental characteristics) and the effect of this relationship on the emergent reaching patterns for children and adults with typical development. By adapting object sizes, we create an environment in which a 1 or 2handed reach emerges spontaneously. We first sought to investigate the emergence of reaching patterns in a typical sample, with the goal of then investigating the same patterns in children with cerebral palsy (CP) in the future. The bodyscaled information for a 1handed reach and a 2handed reach can be related to the environment and quantified by a dimensionless ratio created between a specific object property and a person property measured in the same units, thus canceling units. In the current study, we defined the dimensionless ratio as the ratio of the cube size to the maximal index fingerthumb aperture (using active movement) for each cube size. We hypothesized that as the cube size became larger “in relation to the size of the hand,” participants would change from a 1handed to a 2handed reaching pattern. The larger the dimensionless ratio (object size and hand size become more similar), the higher the percentage that a 2handed reach would emerge. We further hypothesized that the dimensionless ratio that specifies this change from a 1handed to a 2handed reach is the same for children and adults, even though absolute hand sizes are different in these 2 groups. The dimensionless ratio created between the hand and task properties then would generalize to a lifespan concept that might be applied regardless of anthropomorphic characteristics of the mover.
Method
Participants
This was a crosssectional prospective study. Participants were 17 children (mean age=3 years 11 months; range=3–5) and 20 adults (mean age=29 years 2 months; range=18–46) with typical development. None of the participants had injuries or illnesses that would have influenced the results of the experiment. Parental permission forms and informed consents for all participants were obtained before participation.
Apparatus and Procedure
Testing was conducted by the first author in the Development of Infant Motor Performance Lab, Division of Biokinesiology and Physical Therapy, University of Southern California, or at the child's house. All participants were seated on a chair that was adjusted to each participant's popliteal height with the knee flexed to 90 degrees. The following anthropometric measurements were collected without additional pressure being provided from the experimenter while doing the measurement: maximal index fingerthumb aperture (tip of thumb to tip of index finger), hand length (wrist joint to tip of middle finger), and maximal hand width (tip of the thumb to tip of the little finger) when positioning the forearm in the neutral position and the palm facing down on the table while extending all of the fingers to the limit.
Ten pairs of cubes of different sizes were presented by the experimenter seated opposite the participant. Cubes were made of foam board, and thus were very lightweight, and had one side open. The widths and weights (in parentheses) of the cubes were 0.8 cm (<2.8 g), 2.2 cm (2.8 g), 4.2 cm (5.6 g), 6.2 cm (11.2 g), 8.2 cm (19.6 g), 10.2 cm (30.8 g), 14.2 cm (61.6 g), 16.2 cm (78.4 g), 20.2 cm (123.2 g), 24.2 cm (173.6 g), and 26.2 cm (201.6 g). Each cube was paired, in turn, with the next larger cube. The additional cube of width 26.2 cm was created for the 24.2cm cube such that there were 10 cube pairs. After collecting the anthropometric data, the cube pairs were presented in front of the participants. The smaller cube was placed on the table directly in front of the seated participant, on a line extending from the body midline. It was placed at a distance that each participant could reach comfortably without excessive shoulder and trunk movements. The larger cube also was placed on the body midline, but 3 cm behind the smaller cube to be grasped. Each participant initiated his or her reach movements from a standard starting “home” position, with palms face down on hand shapes made of foam board that were glued onto the table, elbows flexed about 90 degrees, and the upper arm relaxed at the side of the upper body.
Participants were allowed one practice trial. No instructions were given as to how the task was to be performed or by which hand or hands. The instructions were: “I need a helper to put the small boxes into the bigger boxes. Please help me put the small box into the big box.” Children earned a prize of small toy cars or small stuffed toy animals when they completed the task. After each trial, participants were instructed to place both hands on the home position. The 10 cube pairs were presented in a random order 3 times per pair. The random order was determined by using a random numbers table. To prevent the participant from seeing the experimenter grasp the cube, the cube pairs were initially hidden behind a screen. Participants were instructed to begin the trial when the screen was removed. A total of 30 trials were collected during the experiment for each participant. Parents were with their children at all times during testing. All trials were videotaped using 2 video cameras with zoom lenses (Canon HG 10 [Canon USA Inc, One Canon Plaza, Lake Success, New York], Sony DCRTRV33 [Sony Corporation of America, New York, New York]) located on the right and left sides of the participant.
Data Reduction and Analysis
All videotapes were coded by 2 independent coders who were graduate students at the University of Southern California. Prior to making their ratings, the coders were instructed as to coding procedures, but they were not informed about the purpose of the experiments. They rated 4 pilot study participants for a total of 120 trials: 2 children (60 trials) and 2 adults (60 trials). The kappa coefficient between the 2 coders was .93 for children and .96 for adults for reaching variables, which is categorized as almost perfect (.81–1.00) agreement between 2 raters.^{14}
The number of hands used to reach (1 or 2) was coded from videotape. The frequency of 1handed or 2handed reach was recorded, divided by the total number of trials (ie, 3) for each cube size, and multiplied by 100 to express the percentage of the movement pattern.
Dimensionless ratios.
For each participant, the ratio of the cube size to the maximal index fingerthumb aperture was calculated for each cube size.
Critical ratio.
The ratio at which the frequency of the 2handed pattern was 100% and remained so at increasing ratios was defined as the critical ratio and determined for each participant. By definition, if the 2handed reach was 100%, the 1handed reach was zero. If a participant never achieved 100% of the 2handed pattern, the critical ratio was defined as that ratio at which the highest percentage of 2handed reaches was achieved and did not decrease at subsequent increases in ratios. At the critical ratio, participants exclusively used 2 hands to reach the cube. The mean and standard deviation of the critical ratios for both groups were calculated.
Crossover point.
We also determined the ratio at the crossover point when participants' reaches were 50% for each reach strategy (ie, 1 handed and 2 handed). The crossover point at 50% referred to the point when there was equal use of a 1handed reach and a 2handed reach. When the dimensionless ratio was larger than the crossover point, it referred to the point when there was greater use of a 2handed reach than a 1handed reach. This crossover point was used to determine whether both groups would have equal use of 1 or 2 hands at a similar ratio. The mean and standard deviation of the ratios at the crossover points in both groups were calculated. This crossover point often was calculated in the motor control or psychology literature,^{15,16} whereas the 100% point has been used in other research using the PAF.^{17,18}
In addition to using index fingerthumb aperture in the critical ratio calculation, we calculated the mean critical ratios using different anthropometric measures relating to hand size, including middle fingerthumb aperture, and hand width. However, the different measures provided similar results. Therefore, we report only the ratio of cube size in relation to index fingerthumb aperture in this article.
Normality of the data was tested with the KolmogorovSmirnov and ShapiroWilk tests.^{19} Significant results indicated a nonnormal distribution. Thus, the MannWhitney U Test was used to compare the means of critical ratios, whereas the t test was used to compare the means of the ratios at crossover points (ie, at 50%) due to a normal distribution of the data. An alpha level of .05 determined significance in 2sided hypothesis testing. All analyses were performed using SPSS version 15.0 (SPSS Inc, Chicago, Illinois).
Results
The demographic characteristics, anthropometric measurements, and mean frequencies of 1handed and 2handed reaches for adults and children are provided in the Table and in Figure 1.
Reach
There was no statistically significant difference of the mean critical ratios between adults (X̅=1.00, SD=0.37) and children (X̅=1.15, SD=0.77) (z=−.06; 95% confidence interval [CI]=−0.54, 0.24; P=.95). On average, both children and adults made the transition from a 1handed reach to an exclusive 2handed reach when the cube was approximately the size of the index fingerthumb aperture regardless of the absolute value of this aperture.
However, there was a significant difference in the mean ratios at crossover points (ie, crossover points at which 50% of the reaches were 1handed and 50% were 2handed) between adults (X̅=0.76, SD=0.22) and children (X̅=0.43, SD=0.25) (t_{35}=4.23; 95% CI=0.17, 0.49; P=.00). Children transitioned to a 2handed strategy at a significantly smaller ratio (ie, the cube size was slightly smaller than half of the maximal aperture between index finger and thumb) in comparison with adults.
We depict the above data with plots of the mean percentages of the frequencies of 1handed and 2handed reaches at each ratio of cube size to maximal index fingerthumb aperture for both children and adults (Fig. 1). The frequency of 1handed reach approached 100% at the smallest ratio and decreased to 0% at the largest ratio for both groups. However, the mean frequency of 1handed reach for children had a steep decline at the second smallest ratio in comparison with adults. The mean frequency of 2handed reach demonstrated the reverse and had a steep incline at the second smallest ratio in comparison with adults. The standard deviations demonstrate children tended to have more variability of reach patterns at the smallest 2 ratios compared with the adults (Fig. 2). Both groups had increased variability while transitioning from a 1handed to a 2handed reach pattern. Then, the variability decreased when an exclusive 2handed pattern emerged.
To further examine the variability of reach and grasp patterns within each group and to compare the variability between groups, the mean and error bars of the frequency counts of each reach type at each ratio were calculated and are presented for both adults and children in Figure 3. Adults used an exclusive 1handed reach at the smallest 2 ratios and an exclusive 2handed reach at the largest ratio. Although children did not use an exclusive 1handed reach at the smallest 2 ratios, they used an exclusive 2handed reach at the largest ratio. Children interchanged more frequently between 1handed and 2handed patterns in comparison with adults at the smallest 2 ratios, indicating more variability for children than adults.
To provide more insight into the individual variation within both groups, data from one representative adult and one representative child are graphed in Figure 4. Most adults (75%) had similar patterns, as shown in the graph for the representative adult in Figure 4A. They exclusively used a 1handed pattern before the critical ratio. Adults did not switch between 1handed and 2handed patterns before the critical ratio. Once they switched to a 2handed pattern, they did not return to a 1handed pattern. However, only 2 children (12%) had a pattern similar to that of the adults (Fig. 4A). They did not vary between 1handed and 2handed patterns before the critical ratio. The other 15 children (88%) had a variable pattern, as shown in the graph for the representative child in Figure 4B. They switched between 1handed and 2handed patterns before the critical ratio.
Discussion
The study provides support that bodyscaled information of object size in relation to hand size influences the emergent reaching patterns for both children and adults. The results demonstrate that bodyscaled information, expressed by dimensionless ratios, guides similar emergent reaching patterns regardless of the differences in body dimensions.^{7,20,21} We also assume that changing physical metrics do not affect the specific critical ratio, which is related to the perception of bodyscaled information, but a longitudinal study is needed to test this assumption.
Our results indicate that a specific critical ratio can be used to predict the transition between 1 hand and 2 hands used to reach an object, regardless of age and body size. The critical ratios were similar for reaching patterns for both age groups (children: 1.15; adults: 1.00). Both groups of participants used 2 hands exclusively to reach the cube when the cube size was equal to or slightly larger than the index finger–thumb aperture. However, children had more variability than adults at the critical ratio (ie, a larger standard deviation) (children: 0.77; adults: 0.37). Children demonstrate more variability during exploration in the environment and gain updated information for the successful movements.^{22} Unlike adults, perceiving affordances for children is complex due, in part, to developmental changes to their bodies, skills, and environments. Children learn to perceive affordances over time and through their exploratory variability. Adolph and colleagues^{23–26} demonstrated that even experienced walkers use various action patterns to descend different slopes or pass a bridge, depending on their current constraints (eg, the steepness of the slope, a backpack loaded with different weights, different handrails provided on the bridge).^{10,27,28} They continually update information about the current status of their own motor abilities relative to environmental conditions.
Newell et al^{6} also demonstrated that a dimensionless ratio comprising the cube size and the fingerthumb aperture specified a 1handed or 2handed reach in preschoolers and adults. Both groups perceived the invariant bodyscaled information for the emergent reach pattern. However, Newell and colleagues^{6} did not report the exact value of the critical ratio in the study. They reported only mean values of dimensionless ratios and percentages of reach patterns for both groups, with no variability data and no statistical analysis. Other studies suggest only that the transition from a 1handed reach to a 2handed reach (ie, the critical ratio) emerges at the dimensionless ratio of 0.68 for 5yearolds^{7} and 0.66 for 4 to 5yearolds.^{20} However, the definition of the critical ratios varies across studies.^{6,7,20} Each of these definitions used the relation of the cube size to a dimension of the hand, but the specific calculation of the critical ratio differed across studies. Therefore, the reported critical ratios were not comparable to our data.
Newell et al^{6} also did not report and compare the values of ratios at the crossover point when participants' reaches were 50% for each reach strategy. The crossover point at 50% referred to the point when there was equal use of a 1handed or 2handed reach. This was an important data point in our study. Children started to use a 2handed reach more frequently than a 1handed reach at a significantly smaller ratio than adults. We expected high variability in children with typical development because their hand function does not approximate that of adults until 6 to 8 years of age.^{29–31} The children in our study demonstrated greater variability in their patterns by interchanging between 1handed and 2handed reaches. Experience and the accuracy demands of the task may have contributed to the greater variability and earlier transition phase observed in children in comparison with adults. Children may not have complete perceptual information of environmental, personal, and task constraints as they first learn a task. They require taskrelated and objectoriented experiences to gather more relevant information of the object and their own body characteristics.^{32,33} In order to achieve the task goal (ie, place the smaller cube into the larger cube), children appear to use more variable action patterns to explore the relevant information from the different constraints. Varying action patterns may help to refine their perceptual information pickup, which, in turn, assists children in rapidly determining the most successful strategy.^{32,34,35}
Of note is that the relational metrics between the cube and hand are only one contribution to the emergent reaching and grasping patterns. Other object properties, such as texture, mass, and shape, and a person's capabilities also contribute to emergent patterns. In the current study, the mass of the cube was relatively small and within the comfortable force range for reaching and grasping for the participants. Future studies could systematically add environmental or personal constraints in order to examine the effects on the relationship between bodyscaled information and emergent action patterns. Our study provides evidence and is consistent with previous results demonstrating that children's and adults' reaching patterns are consistent with a bodyscaled hypothesis. Participants relate the object properties to their constraints, and action patterns emerge from this relationship. Moreover, children have greater variability of reaching patterns compared with adults. Children demonstrate variability during exploration and gain relevant information regarding the environment and their personal constraints.^{22,36} The results of this study encourage further research examining the bodyscaled information on individuals with different personal constraints (eg, children with CP). This research may provide us with insight into the variability of reach patterns in children with different personal constraints.
Identifying the fit between reachable objects and constraints of the reaching hand in children with hemiplegic CP, for example, may provide us with a principled approach to enhancing movement and not merely a trialanderror sequence during therapy. If children with CP use the same relative information as children with typical development (ie, the ratio of the index finger–thumb aperture in relation to the object size) for 1handed versus 2handed reach, this ratio could be incorporated into therapy. A 2handed reach should emerge automatically if the object size in relation to the hand size exceeds a specific ratio. Switching between a 1handed reach and a 2handed reach during therapy may emerge as the therapist changes object sizes. This switching behavior could be practiced intensely at the boundaries of this ratio. In addition, children with mild to severe CP may have different levels of impairments and show different reaching preferences based on their perceptions and motor capabilities. Children with mild CP may switch more frequently between 2 strategies in comparison with children with moderate or severe CP, who may use 2handed reach for most of the trials due to their limited motor capabilities. Investigating the relationship between perceived affordances and the emergent reaching patterns for individuals with different personal constraints may provide us with a more explicit understanding of the specific factors that influence reaching actions. A more principled understanding of this relationship may guide therapists in their approach to modifying the environment and the task to enhance function and reduce disability among patients with a variety of personal constraints.
The Bottom Line
What do we already know about this topic?
An individual's actions are related to his or her own capabilities and environment. Actions emerge from perceived perceptual information of object properties and the individual's capabilities.
What new information does this study offer?
The purpose of this study was to examine and quantify the relationship between hand size (person characteristics) and object size (environmental characteristics) and the effect of this relationship on the emergent reaching patterns for children and adults with typical development. This study quantified a value that represents the relationship between individuals (hand size) and environment (object size) that allows clinicians to examine adults' and children's perception and action during reaching tasks.
If you're a patient or a caregiver, what might these findings mean for you?
These findings indicate that it may be possible to quantify the relationship between patient and environment, which may help the caregiver set up the environment to enhance emerging functional actions.
Footnotes

All authors provided concept/idea/research design and writing. Dr Huang provided data collection. Dr Huang, Dr Fetters, and Dr Wagenaar provided data analysis. Dr Huang and Dr Fetters provided project management and facilities/equipment. Dr Fetter provided fund procurement and institutional liaisons. Dr Wagenaar provided consultation (including review of manuscript before submission).

This study was approved by the institutional review boards of Boston University and the University of Southern California.
 Received December 16, 2011.
 Accepted September 4, 2012.
 © 2013 American Physical Therapy Association