Decoupled Control of Grasp and Rotation Constraints During Prehension of Weightless Objects

Dayuan Xu; Jiwon Park; Jiseop Lee; Sungjune Lee; Jaebum Park

doi:10.1123/mc.2022-0074

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Decoupled Control of Grasp and Rotation Constraints During Prehension of Weightless Objects

in Motor Control

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Dayuan Xu

Dayuan XuDepartment of Physical Education, Seoul National University, Seoul, South Korea

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Jiwon Park

Jiwon ParkDepartment of Physical Education, Seoul National University, Seoul, South Korea

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Jiseop Lee

Jiseop LeeDepartment of Physical Education, Seoul National University, Seoul, South Korea

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Sungjune Lee

Sungjune LeeDepartment of Physical Education, Seoul National University, Seoul, South Korea

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Jaebum Park

Jaebum ParkDepartment of Physical Education, Seoul National University, Seoul, South Korea
Institute of Sport Science, Seoul National University, Seoul, South Korea
Advanced Institute of Convergence Technology, Seoul National University, Seoul, South Korea

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DOI:: https://doi.org/10.1123/mc.2022-0074

Keywords:: principle of superposition; chain-effect; object lifting; digit forces

First Published Online:: 17 Oct 2022

In Print:: Volume 27: Issue 1

Page Range:: 35–53

Open access

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Gravity provides critical information for the adjustment of body movement or manipulation of the handheld object. Indeed, the changes in gravity modify the mechanical constraints of prehensile actions, which may be accompanied by the changes in control strategies. The current study examined the effect of the gravitational force of a handheld object on the control strategies for subactions of multidigit prehension. A total of eight subjects performed prehensile tasks while grasping and lifting the handle by about 250 mm along the vertical direction. The experiment consisted of two conditions: lifting gravity-induced (1g) and weightless (0g) handheld objects. The weightless object condition was implemented utilizing a robot arm that produced a constant antigravitational force of the handle. The current analysis was limited to the two-dimensional grasping plane, and the notion of the virtual finger was employed to formulate the cause–effect chain of elemental variables during the prehensile action. The results of correlation analyses confirmed that decoupled organization of two subsets of mechanical variables was observed in both 1g and 0g conditions. While lifting the handle, the two subsets of variables were assumed to contribute to the grasping and rotational equilibrium, respectively. Notably, the normal forces of the thumb and virtual finger had strong positive correlations. In contrast, the normal forces had no significant relationship with the variables as to the moment of force. We conclude that the gravitational force had no detrimental effect on adjustments of the mechanical variables for the rotational action and its decoupling from the grasping equilibrium.

Gravity is one of the most significant examples of forces as it enables us to be aware of the properties of body mechanics (Lackner & DiZio, 1996) and provides critical cues for the regulation of body posture, such as adjusting body orientation (Benson et al., 1997; Lackner & DiZio, 2003). In addition, gravity affects the mechanical outcomes of manipulated objects that can be accompanied by the actions of body segments such as grasping, rotating, and lifting an object (Momiyama et al., 2006; Verheij et al., 2013; Zatsiorsky et al., 2005), whereby the interaction strategies between the adaptive behavioral response and the physical environment considerably depend on gravity. Most researchers have focused on adaptive posture control and ambulatory function in humans with changes in gravity (Bloomberg & Mulavara, 2003; Bloomberg et al., 1997; Clement & Lestienne, 1988; Clement et al., 1984; Lackner & DiZio, 1996, 2003; Madansingh & Bloomberg, 2015; Mulavara et al., 2010). Although a few experiments have been conducted on the force control (Opsomer et al., 2018, 2020; White, 2015) and arm kinematics (Crevecoeur et al., 2009, 2014) during precision grip, less attention has been paid to the adaptive control strategies in a more ecologically relevant tasks such as multidigit prehension using all five hand digits.

In this study, we investigated the effect of the gravitational force of a handheld object on the control strategies for subactions (e.g., grasp and rotation) of multidigit prehension. Grasping behavior are assumed to be governed by the central nervous system, such that the forces exerted by individual digits are organized to satisfy the mechanical constraints in a particular force field. For instance, the mechanical constraints in a static grasping task require that the sum of the digit contact forces in the vertical direction (i.e., tangential forces) be equal in magnitude and opposite in direction to the weight of the handheld object (i.e., vertical translational constraint) in the Earth’s gravitational force field (Shim & Park, 2007; Shim et al., 2003, 2005, 2006; Zatsiorsky et al., 2002, 2004). While satisfying the vertical translational constraints, the digit tangential forces contribute to the moment of force about the sagittal axis in the object–reference perpendicular to the plane spanned by the digit contact forces (Shim et al., 2003, 2005; Zatsiorsky et al., 2004). Therefore, changes in gravity, for example, zero gravity condition, modify the mechanical constraints of prehensile actions accordingly, such that the role of the tangential forces is limited to the generation of torque and inertia. Furthermore, the modification of the vertical translational constraint may cause a sequential chain effect on other variables, such as the contributions of digit normal and tangential forces to the rotational effect. Therefore, it is highly probable that the change in gravity induces conjoint adjustments in the chains of variables.

Specifically, lifting an object free from gravity, that is, a weightless object, is not influenced by the gravitational force, in contrast to lifting a weighted object. Hence, we expect, first, the magnitude of grasp force (normal force) would be smaller during lifting a weightless object compared to the weighted object lifting due to the changes in the minimal grip force preventing a slip (Hypothesis 1), and second, a stronger correlation between the tangential forces of the thumb and fingers, as well as between the tangential force and moment of force, will be observed in the weightless object lifting as compared to the weighted object lifting because of the modified roles of the tangential forces (Hypothesis 2). Again, there is no requirement of weight bearing by tangential forces in the weightless object lifting, possibly resulting in a stronger relationship between the tangential force and moment of force.

Numerous studies have provided clear evidence of decoupled organization of grasping and rotational equilibrium during the prehensile action by the opposition of the thumb and fingers (Latash & Zatsiorsky, 2006; Shim & Park, 2007; Shim et al., 2005, 2013; Zatsiorsky et al., 2004), as well as during finger pressing (Danion et al., 2003; Zatsiorsky, 2004; Zhang et al., 2008). In particular, Zatsiorsky first introduced and provided experimental evidence for the decoupled organization of grasping and rotational equilibrium during static prehensile tasks (Danion et al., 2003; Zatsiorsky, 2004). Zatsiorsky found that fine-tuning the normal forces over a series of data has no significant correlation with the torque produced by the normal forces, whereas the torque produced by the normal force has a strong correlation with the tangential force. In other words, tuning the moment of force is associated with adjusting the tangential force and not with the normal force. This is not a trivial result because both the normal and tangential forces contribute to torque production. The organization of the digit tangential force in prehension is critical to torque stabilization of the object, and a few studies have examined the active control of tangential forces (Niu et al., 2009; Pataky et al., 2004; Shim & Park, 2007; Shim et al., 2003; Slota et al., 2012). Furthermore, the role of the tangential force on a handheld object in weightless conditions should be modified. Here, we raise the following question: Is decoupled control of grasp and rotational equilibrium valid during the weightless object prehension? Specifically, we hypothesized that the trial-to-trial tuning of the torque would have a strong correlation with that of the tangential force but not with the normal force during the prehension of a weightless object to preserve equilibrium. In addition, the relations between the tuning of the normal and tangential forces will not be significant, as demonstrated by the experimental findings of the weighted object prehension (Hypothesis 3).

Prehensile tasks with five hand digits were employed in the present study, and the condition of the weightless object was implemented using a robot arm that produced a constant antigravitational force of the object. We measured the digit forces in both normal and tangential directions to test the formulated hypotheses.

Methods

Subjects

A total of eight young right-handed male subjects (age 28 ± 3.24 years; height 176 ± 4.54 m; weight 72 ± 3.49 kg) with no diagnosed neurological disorder or arthritis in their upper extremities volunteered for the experiment. A priory sample size computation using G*Power (Faul et al., 2007), suggested recruiting at least eight participants to achieve an effect size (d) greater than 0.9 with at least 70% power and α = .05 to detect significant differences between the current experimental conditions. The Seoul National University institutional review board approved the use of a customized experimental protocol, and all experimental procedures were performed in accordance with relevant guidelines and regulations.

Apparatus

A total five six-component force/moment transducers (Nano-17s, ATI Industrial Automation) were used to measure the individual digit forces and moments (Figure 1a and 1b). The total mass of the experimental handle, including the transducers, was 500 g. The sampling frequency of the digit force data was set to 400 Hz. A motion capture system (Qualisys AB) with five infrared cameras was used to measure the position and orientation of the handheld object. Furthermore, a vertical reference bar and two markers were attached to the bar to indicate the initial and terminal positions where the handle was supposed to be fixed by holding and lifting along the y-axis (Figure 1b). The sampling frequency of the motion capture data was set to 120 Hz.

A three degree of freedom robot arm (HapticMaster, Moog) was used to generate a constant antigravitational force on the weight of the handle (Figure 1a). The experimental handle was firmly attached to the end of the robot arm using a three degree of freedom joint, which allowed the translation and rotation of the handle in all directions (i.e., constraints free). A pilot experiment and analysis confirmed that both static and dynamic (kinetic) frictions of the robot-arm movement were minimal (<0.01 N·m); therefore, we assumed that the task mechanics with the robot arm were not significantly affected by the frictional forces of the device.

Experimental Procedure

The subjects sat in a height-adjustable chair and held the experimental handle with their dominant hand. The main tasks for the subjects were to grasp the handle with five digits and to align the handle vertically at the initial position. Thereafter, they were required to lift the handle by approximately 250 mm and hold it statically at the terminal position for approximately 2–3 s (Figure 1a).

The experiment consisted of two conditions: lifting (a) gravity-induced (1g) and (b) weightless (0g) handheld objects using all five digits. Note that the programmed force via the robot arm produces an antigravitational force to compensate for the weight of the handle for the 0g condition, and the handle could be translated or rotated by unbalanced force or torque for both the 1g and 0g conditions. The subjects were instructed to lift the handle along the straight line to the marked position on the reference bar at moderate to high speed and then hold the handle statically at the terminal position. An additional instruction was to maintain its orientation constant during lifting to minimize rotation and horizontal translation of the handle. A practice session was provided for approximately 30 min to 1 hr. For the actual data acquisition, each subject performed 20–25 trials for each of the two conditions. Each trial lasted approximately 10 s. A 30 s break was provided between every two trials. The experimental conditions were given in a random order, and the total duration of the experiment for each subject was approximately 2 hr, including the practice and data acquisition sessions.

Data Processing

Customized analysis codes (MATLAB) were used to analyze both the kinematic and kinetic data (e.g., force data). The raw data were digitally low-pass filtered at a 10 Hz cutoff for the kinetic data and a 15 Hz cutoff for the kinematic data using a zero-lag fourth-order Butterworth filter (Augurelle et al., 2003; Park & Xu, 2017). The variables in the mechanical model were computed to test the hypotheses formulated in the introduction. Note that the task constraints in the analysis were limited to a two-dimensional grasping plane (i.e., the y–z plane in Figure 1a). In addition, the notion of a virtual finger (VF) was used to describe the current task mechanics of multidigit prehensile actions (Baud-Bovy & Soechting, 2001; Latash & Zatsiorsky, 2009). The VF forces and moments were calculated as the vector sum of the individual finger forces and moments, resulting in the same mechanical effects produced by a set of four fingers.

Time Events

We identified six time events by observing the time profile of the resultant tangential forces (F_T) within a single trial. E1 was the initiation time of lifting, which is defined as the time when the first derivative of the resultant tangential force (dF_T/dt) reaches 5% of its peak value. E2 was the time at which the magnitude of the resultant tangential force was the largest (i.e., positive peak). E3 was the time at which the magnitude of the resultant tangential force was equal to the weight of the handle (m·g) for the 1g condition or equal to zero for the 0g condition after E2. E4 was the time at which the magnitude of the resultant tangential force was the smallest (i.e., negative peak). E5 was the time at which the magnitude of the resultant tangential force is equal to the weight of the handle (m·g) for the 1g condition or equal to zero for the 0g condition after E4 (i.e., the highest vertical position of the handle). E6 corresponded to the end of a trial after completing steady state holding for approximately 1 s. Actual time duration was measured, and the interval time between two adjacent time events were computed as the percentages of the entire duration. Furthermore, the data set between two adjacent time events were resampled to 100 data points using cubic spline interpolation.

Mechanical Constraints

The following three mechanical constraints were formulated for digit forces and moments in a two-dimensional grasping plane.

Normal Force Constraint

The thumb normal force (i.e., the z-axis force,

F_{N}^{th}

) should be equal in magnitude and opposite in direction to the VF normal forces (

F_{N}^{vf}

) for all experimental conditions (Equation 1).

| F_{N}^{th} (t) | - | \sum_{j} F_{N}^{j} (t) | = | F_{N}^{th} (t) | - | F_{N}^{vf} (t) | = 0,

(1)

where F represents the digit force; N refers to the normal force component; superscript j represents the individual fingers (e.g., j = {index, middle, ring, and little}); and th and vf represent the thumb and VF, respectively.

Tangential Force Constraint

The sum of the tangential forces of all five digits (i.e., inertial load, F_T) and the gravitational force of the object is proportional to the acceleration of the handle about the y-axis (Equation 2).

\sum_{k} F_{T}^{k} (t) - (m \cdot g) = (F_{T}^{th} [t] + F_{T}^{vf} [t]) - (m·g) = m \cdot a (t),

(2)

where T refers to the tangential component, and superscript k stands for the individual digits (e.g., k = {thumb, index, middle, ring, and little}). m represents the mass of the handle, and a and g are the acceleration of the handle and gravitational constant, respectively.

Moment of Force Constraint

The sum of the moments of the digit normal and tangential forces should be close to zero (Equation 3a). The moment arms of the tangential forces (D_T in Equation 3c) were constant in magnitude (i.e., half of the width of the handle, Figure 1b), whereas the moment arms of the normal forces (D_N in Equation 3b) varied owing to the tolerance for rolling of the digit tip on the contact surfaces of the transducers.

\sum_{k} M_{N}^{k} (t) + \sum_{k} M_{T}^{k} (t) = 0,

(3a)

\sum_{k} M_{N}^{k} (t) = D_{N}^{th} (t) \cdot F_{N}^{th} (t) + D_{N}^{vf} (t) \cdot F_{N}^{vf} (t), and

(3b)

\sum_{k} M_{T}^{k} (t) = - (D_{T}^{th} [t] \cdot F_{T}^{th} [t] + D_{T}^{vf} [t] \cdot F_{T}^{vf} [t]),

(3c)

where M, F, and D represent the moment of the force, force, and moment arm, respectively. The subscripts N and T indicate the normal and tangential components, respectively.

Model of the Cause–Effect Chain and Correlation Analysis

The model of the cause–effect chains was formulated using a set of VF-level variables (for details, see “Results” section). For each pair of selected variables, the Pearson correlation coefficients across repeated trials were calculated for each event and subject (Figure 2).

PC Analysis at the Level of VF and Thumb

The corrected correlations among sets of variables at the VF level (thumb and VF normal and tangential forces and moment arm of VF normal force) were computed to construct correlation matrices for six time events. These matrices were used to perform principal component (PC) analysis with variance-maximizing rotation. The Kaiser criterion (i.e., the extracted PC should be eigenvectors whose eigenvalues are larger than 1) was used to extract PCs (Kaiser, 1960). Thereafter, significant PCs with a 0.4 cutoff loading coefficient, which accounted for more than 95% of the total variance, were counted (Krishnamoorthy et al., 2003; Shim & Park, 2007).

Statistics

First, repeated-measures analysis of variances (ANOVAs) were performed to test how the entire duration and the interval times between two adjacent time events were affected by the two gravity conditions.

One-dimensional statistical parametric mappings (SPMs) with repeated-measures ANOVAs (SPM{F}) were applied to the resultant normal force, tangential forces, and moment to test the effect of simulated gravity on the time-series kinetic variables (Pataky et al., 2016). A critical threshold for SPM analyses was computed based on random field theory (Worsley et al., 2004), which was set at α = .05.

Linear regression was used to characterize the relationships between VF-level variables formulating the cause–effect chains. Pearson coefficients of correlation (r) were computed and corrected for noise and error propagation (Taylor, 1997). We further tested whether the two regression lines were statistically different based on the significant relations for 1g and 0g conditions (Neter et al., 1996).

Results

Timing Indices

On average, the entire duration of lifting was 4.43 ± 0.80 s (mean ± SD) for the 1g condition, which was statistically smaller than that for the 0g condition, 5.53 ± 0.97 s (p < .05). In addition, the significant effects of factor gravity on the time intervals were observed only in the first and second intervals (i.e., E1–E2 and E2–E3 in Table 1; p < .05), showing a larger time interval of “E1-E2” for the 1g condition (32% and 18% for the 1g and 0g, respectively) and “E2-E3” for the 0g condition (10% and 21% for the 1g and 0g, respectively).

Table 1

Mean and SD of Interval Time in Percentage Across the Subjects (Unit: %); E1 ∼ E6 Represent Six Time Events

Time event
1g	Mean	32.43	10.31	11.98	13.41	31.86
1g	SD	8.15	1.84	1.73	1.85	6.60
0g	Mean	18.05	21.06	15.25	17.68	27.96
0g	SD	7.69	4.13	3.80	2.70	4.61

Digit Force/Moment Production

On average, the difference between the magnitudes of the normal forces exerted by the thumb ( $F_{N}^{th}$ ) and the VF ( $F_{N}^{vf}$ ) was less than 2 N at any instant during lifting a handheld object for all the subjects and gravitational conditions, which was smaller than 10% of the averaged $F_{N}^{th}$ or $F_{N}^{vf}$ in the 1g or 0g conditions (Figure 3a). These results imply minimal horizontal translation during the given task. The patterns of the digit resultant normal force ( $F_{N}^{res}$ ) exhibited a single bump and double bumps for the 1g and 0g conditions, respectively, over time (Figure 3a). However, these differences were not statistically significant in the entire lifting duration, which was confirmed by the SPM analysis with repeated-measures ANOVA (Figure 3d).

The patterns of the digit resultant tangential force ( $F_{T}^{res}$ ) were consistent in the two gravitational conditions, which exhibited sinusoidal behavior from E1 to E5 (Figure 3b). In particular, $F_{T}^{res}$ was larger (p < .05) in the 1g condition than in the 0g condition in the entire lifting duration, except around E2, when the peak tangential forces were observed (Figure 3e). The difference between $F_{T}^{res}$ in two conditions was approximately 5 N at the initiation and termination phases, which was consistent with the magnitude of the handle weight (Figure 3b). Under both gravitational conditions, the magnitudes of the resultant moments (M^res) were less than 5 N·m in the entire lifting duration (Figure 3c). SPM analysis with repeated-measures ANOVA demonstrated the significant effect of simulated gravity on M^res for a short duration between E4 and E5 (Figure 3f).

Correlation Coefficients in Chains of Prehension

There were two groups of “cause–effect” chains based on the continuous alliance of significant correlations, and the compositions of the variables in the two groups were similar under the two gravitational conditions. The first group comprised the horizontal translational constraint, which demonstrated a strong positive correlation between the thumb and VF normal forces (first chain, r > .7, Figures 4 and 5a).

The second group comprised a set of chains from the third to seventh chain, where the variables of moment production were significantly correlated. In particular, the moment of the normal force ( $M_{N}^{vf}$ ), which was obtained using the cross product of the normal force ( $F_{N}^{vf}$ ) and its moment arm ( $D_{N}^{vf}$ ), exhibited a strong positive correlation with $D_{N}^{vf}$ (third chain, r > .7) but not with $F_{N}^{vf}$ (second chain, |r| < .7), wherein the two groups of chains were separated across all time events (Figures 4 and 5b and 5c). In addition, the correlations between the normal and tangential forces that comprised the eighth and ninth chains were not statistically significant (Figure 4). Significant |r| value differences were observed between the 1g and 0g conditions in the seventh chain at E2 and E4 (six out of eight subjects), which confirmed that the |r| values were larger (p < .05) in the 1g condition than in the 0g condition (Figures 4 and 5d).

PC Analysis

The PC analysis was performed on the VF variables, including the thumb and VF normal and tangential forces and moment arm of the VF normal force ( $F_{N}^{th}$ , $F_{N}^{vf}$ , $F_{T}^{th}$ , $F_{T}^{vf}$ , and $D_{N}^{vf}$ ). The first two PCs accounted for more than 95% of the total variance in the five-dimensional space (averaged across subjects ± SD, 98.87% ± 0.70% for 1g condition; 98.19% ± 0.63% for 0g condition). In PC1, the normal forces of the thumb and VF had large loadings with the same sign for all the time events. In PC2, the loadings of the thumb and VF tangential forces were larger than those of the normal forces (Table 2). Furthermore, the signs of loadings of the two tangential forces in the PC2 were opposite.

Table 2

Loadings of PC1 and PC2 of Variables at the VF Level

		1g		0g
Time events	Variables	PC1	PC2	PC1	PC2
E1	$F_{N}^{th}$	0.71	0.12	0.70	−0.07
	$F_{N}^{vf}$	0.70	0.03	0.71	−0.09
	$F_{T}^{th}$	0.09	−0.66	0.08	0.70
	$F_{T}^{vf}$	−0.05	0.73	−0.08	−0.69
	$D_{N}^{vf}$	−0.01	0.12	0.00	−0.12
E2	$F_{N}^{th}$	0.70	0.13	0.72	−0.09
	$F_{N}^{vf}$	0.70	0.01	0.69	−0.06
	$F_{T}^{th}$	0.13	−0.61	0.08	0.75
	$F_{T}^{vf}$	−0.01	0.77	−0.07	−0.65
	$D_{N}^{vf}$	−0.01	0.11	0.00	−0.09
E3	$F_{N}^{th}$	0.71	−0.10	0.69	−0.10
	$F_{N}^{vf}$	0.71	0.03	0.70	−0.15
	$F_{T}^{th}$	0.03	0.70	0.13	0.70
	$F_{T}^{vf}$	−0.04	−0.69	−0.12	−0.68
	$D_{N}^{vf}$	0.00	−0.13	−0.01	−0.12
E4	$F_{N}^{th}$	0.71	0.08	0.69	−0.10
	$F_{N}^{vf}$	0.70	0.00	0.71	−0.05
	$F_{T}^{th}$	0.01	−0.69	0.05	0.85
	$F_{T}^{vf}$	−0.07	0.71	−0.12	−0.50
	$D_{N}^{vf}$	0.00	0.15	0.00	−0.11
E5	$F_{N}^{th}$	0.70	0.06	0.70	−0.14
	$F_{N}^{vf}$	0.70	0.13	0.70	−0.08
	$F_{T}^{th}$	0.09	−0.61	0.11	0.72
	$F_{T}^{vf}$	−0.11	0.75	−0.11	−0.66
	$D_{N}^{vf}$	−0.01	0.20	0.00	−0.16
E6	$F_{N}^{th}$	0.69	0.15	0.70	0.11
	$F_{N}^{vf}$	0.70	0.14	0.69	0.13
	$F_{T}^{th}$	0.13	−0.63	0.13	−0.65
	$F_{T}^{vf}$	−0.15	0.70	−0.12	0.71
	$D_{N}^{vf}$	−0.03	0.25	−0.01	0.23

Note. 1g and 0g stand for two gravitational conditions. E1−E6 stand for six time events. The bold black numbers represent the loadings of significant (p < .01) and large (|r| > .6) correlations. Data are from a representative subject. PC = principal component; VF = virtual finger; th = thumb.

Discussion

The current results seemed to contradict the dramatic modification in the control strategies in which the strategies of decoupled organization of two subsets of variables were also observed during the weightless object prehension, as similarly demonstrated by the results of weighted object lifting. That is, the control strategies for organizing multiple variables (i.e., motor redundancy, Latash & Zatsiorsky, 2009; Li et al., 1998) were not affected by the gravitational force of the object. Note that the current results explicitly demonstrated that the production of mechanical variables was in accordance with the mechanics of the presence and absence of gravitational load. The decoupled organization is possibly a choice of the controller for fine-tuning a set of variables for the control, not mechanics, of grasping and rotating the handheld object.

The principle of superposition, which was originally suggested in the field of robotics (Arimoto et al., 2000, 2001, 2002), describes the decoupled organization of skilled actions. They found that the overall control inputs were designed using linear superposition, and the net results were generated based on two or more independent phenomena. Further, it has been reported that the principle of superposition is valid in the human hand grasp task, demonstrating the decoupled organization for grasp and rotational equilibrium (Latash & Zatsiorsky, 2006; Robertson & Johnston, 2012; Shim et al., 2005; Zatsiorsky et al., 2004). Specifically, fine-tuning the moment of normal forces or tangential forces significantly correlated with tuning at the point of force application (i.e., moment arm) rather than tuning of the normal force itself (Shim et al., 2003; Song et al., 2021; Zatsiorsky et al., 2004), which agrees with the findings of the present study. An evident difference between the present and previous experiments is that most existing studies used static torque production tasks involving external torques, whereas the experiment in the present study had no external torque to be compensated for and used the dynamics of the lifting action in the absence of gravitational force. Although the experiments in the present study were free from the demand for a significant amount of torque production, the constraint equation for the torque (i.e., close to zero net torque) was the same as that in previous experiments. By combining the findings from the present and existing studies, we conclude that, first, the gravitational force had no detrimental effect on conjoint adjustment that is fine-tuning of the variables for the rotational action and its decoupling from the grasping equilibrium. Second, fine-tuning of the subset for rotational actions could be a (torque) magnitude-independent phenomenon. Therefore, the decoupled organization of grasp and rotational actions could probably be a more general phenomenon, which is not limited to specific experimental conditions concerning human grasp with the thumb and fingers. Here, we would like to emphasize the following points. A coupling between the normal and tangential forces has been widely reported (Crevecoeur et al., 2009; Johansson & Westling, 1984; Westling & Johansson, 1984), seemingly contradicting the current results. The coupling of two forces components is responsible for the precise scaling of the normal force to the tangential force (i.e., changes in the magnitude of forces). The “fine-tuning” across multiple trials (i.e., trial-to-trial variation), however, refers to the relation of infinitesimal changes in a set of variables to maintain the equilibrium. In other words, a group of the tuned variables comprised subset which is responsible for the stabilization of particular action such as grasping or rotation. A new finding of the current experiments is that the decoupled control by the trial-to-trial tuning of normal and tangential forces is valid even when dynamics tangential force is produced.

A key variable that distinguished the two experimental conditions was the tangential force. A small but statistically significant difference between the 1g and 0g conditions was observed in the strength of the linear relationship between the thumb and VF tangential forces. The r values of the correlation between two tangential forces (seventh chain) were statistically larger in the 1g condition than in the 0g condition, particularly at the peak acceleration phase (cf. E2 in Figures 4 and 5d), which was in part contrary to our expectation (Hypothesis 2). Indeed, a positive correlation between the two tangential forces can be beneficial for moving the object upward, while the changes in the opposite directions of two tangential forces limit the acceleration or deceleration of the handheld object. In the meantime, the subjects were supposed to hold the handle statically at the terminal position by decreasing the net tangential forces (i.e., deceleration); therefore, a negative correlation between two tangential forces may be helpful to prevent an overshoot or undershoot of the referent target position. Then, the question remains on why the strength of the correlation of the two tangential forces in the 0g condition was smaller than that in the 1g condition? A possible explanation is that the variables to be correlated are not the two force components but the control variables such as the referent angular displacements and angular stiffnesses of the thumb and VF (Latash et al., 2010; Singh et al., 2014; Wu et al., 2012, 2013).

The cause–effect chains in the current study comprised nine pairs of variables at the VF level. The individual chains reflect the direct task constraints or the connection to variables that could be options for significant relations. For instance, strong positive correlations (i.e., synchronous increment or decrement) between two normal forces (1st chain) were commonly observed for both the 1g and 0g conditions, which were mechanically necessitated by the specific task mechanics to prevent slipping and horizontal translation. The other two constraints had a few options to satisfy the particular conditions and to gauge the strength (i.e., absolute r or r² value) and direction (i.e., negative or positive sign of r value) of correlation. A few studies have claimed that the organization of the tangential forces is constrained by the organization of the normal force, whereas the experimental results in a particular circumstance demonstrated the possibility of active control of tangential forces (Singh & Ambike, 2017; Shim & Park, 2007; Song et al., 2021). If gravity is close to zero, the role of the tangential forces should be changed such that the role of the resistant force to compensate for the weight of the handheld object is eliminated, whereas the contribution to the rotational equilibrium is still valid. However, these changes in tangential forces did not seem to cause any chain reaction to other components of the forces and their role in grasping and rotational equilibrium. One of the effects of zero-gravity objects could be the decrease in the tangential force and its torque owing to the absence of weight resistance.

Although there are several significant implications of the present experimental results, the present study also has some limitations. The relatively small sample size and uncontrolled lifting speed make the current conclusions tentative. In addition, considering the two extreme gravity conditions and fixed geometry of the handheld object in this study, the current claims cannot be generalized. Therefore, future studies should investigate whether the current claims are valid under conditions where the gravitational forces are between 0g and 1g while holding other geometric shapes of the handle at constrained lifting speeds.

Acknowledgments

This research was supported in part by the Basic Research Program through the National Research Foundation of Korea funded by the MSIT (2022R1A4A503404611) and the Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education (2021R1I1A4A01041781).

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Xu https://orcid.org/0000-0002-2625-299X

J. Lee https://orcid.org/0000-0003-4384-5145

S. Lee https://orcid.org/0000-0002-4963-6419

Jiwon Park https://orcid.org/0000-0001-6933-7005

^*Jaebum Park (parkpe95@snu.ac.kr) is corresponding author, https://orcid.org/0000-0003-0156-5591

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Figure 1

—Illustration of the experimental setup (a) and the customized handle (b). Note. Subjects sat and held the handle with five digits of their dominant hand, and then they lifted the handle by approximately 250 mm. Five force/moment transducers were attached to the handle, and the transducers were firmly attached to a customized aluminum handle using screws. Pieces of 120-grit sandpapers were attached to the contact surfaces of the transducers to provide constrained static friction between the digit tips and contact surfaces. The initial arm configuration was constrained such that the elbow was flexed at approximately 90° in the sagittal plane. The arm configuration was not strictly constrained during the lifting actions. Three markers were attached to the top plane of the handle to define the local coordinate of the handle. Another two markers were attached to the reference bar to indicate the initial and terminal positions. The robot arm was attached to the center of the handle to generate a constant antigravitational force.

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Figure 2

—Illustration of nine cause–effect chains among a set of mechanical variables. The first (&onecirc;), seventh (&sevencirc;), and fourth (&fourcirc;) chains represent the mechanical constraints (i.e., task constraints) of normal force, tangential force, and moment of force, respectively.

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Figure 3

—The time profiles of resultant normal force (a), tangential force (b), and moment (c) averaged across subjects are presented with standard SDs for 1g (solid lines) and 0g ( dotted lines) conditions, respectively. SPM{F} trajectories are presented for resultant normal force (d), tangential force (e), and moment (f) with repeated-measures analysis of variance. The horizontal dashed line indicates the threshold of critical random field theory at 0.05. SPM = statistical parametric mapping.

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Figure 4

—The absolute values of correlation coefficients (|r|) between mechanical variables in nine cause–effect chains (&onecirc;∼&ninecirc;). The |r| values in the 1g (thick solid lines) and 0g (thick dashed lines) conditions are presented for the individual chains over time event (i.e., E1–E6). The boxplots describe the distributions of |r| values across subjects for the 1g (open boxes with thin outlines) and 0g (filled boxes with thin outlines). The black dotted line indicates the threshold of significant correlation level (|r| > .7). *Statistical difference in the r values between the 1g and 0g conditions (p < .05).

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Figure 5

—The scatterplots of the pair variables in cause–effect chains, including the first (a), second (b), third (c), and seventh (d) chains. Data are from repetitive trials performed by a representative subject. The data for the 1g condition are shown with the open circles; the data for the 0g are shown with plus (+) signs. 95% confidence ellipses surrounding the data points are drawn for the 1g (solid lines) and 0g (dotted lines) conditions separately. The scatterplots for six time events are horizontally aligned, including E1–E6.

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Decoupled Control of Grasp and Rotation Constraints During Prehension of Weightless Objects

Methods

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Apparatus

Experimental Procedure

Data Processing

Time Events

Mechanical Constraints

Normal Force Constraint

Tangential Force Constraint

Moment of Force Constraint

Model of the Cause–Effect Chain and Correlation Analysis

PC Analysis at the Level of VF and Thumb

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Timing Indices

Digit Force/Moment Production

Correlation Coefficients in Chains of Prehension

PC Analysis

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