Mechanical analysis and hierarchies of multidigit synergies during accurate object rotation

Evidence to support the mechanical advantage hypothesis of grasping at low force levels

Grasping an object is one of the several tasks performed by human hands. Object stabilization while grasping is a fundamental aspect to consider for the safety of grasped objects. Fingertip forces re-distribute to establish equilibrium when systematic variations are introduced to objects held in hand. During torque variations to the grasped handle, the central nervous system prefers to support the mechanical advantage hypothesis. According to this hypothesis, during torque production tasks, fingers with longer moment arm for normal force produce greater normal force than the fingers with shorter moment arm. The current study was performed to examine and confirm the factor that causes the central nervous system to employ this strategy. In addition to minimising the thumb's contribution to hold the handle, thumb normal force was restricted to a minimal level. Such a restriction made the task even more challenging. Therefore, it was confirmed that the challenging task induces the central nervous system to employ the mechanical advantage principle.

Support for mechanical advantage hypothesis of grasping cannot be explained only by task mechanics

Successful object interaction during daily living involves maintaining the grasped object in static equilibrium by properly arranging the fingertip contact forces. According to the mechanical advantage hypothesis of grasping, during torque production tasks, fingers with longer moment arms would produce greater normal force than those with shorter moment arms. Previous studies have probed this hypothesis by investigating the force contributions of individual fingers through systematic variations (or perturbations) of the properties of the grasped handle. In the current study, we examined the validity of this hypothesis in a paradigm wherein the thumb tangential force was constrained to a minimal constant magnitude. This was achieved by placing the thumb on a freely movable slider platform. The total mass of the handle was systematically varied by adding external loads directly below the center of mass of the handle. Our findings suggest that the mechanical advantage hypothesis manifests only during the heaviest loading condition when a threshold difficulty is reached. We infer that the support for the mechanical advantage hypothesis depends not only on the physical parameters but also on the individual ability to manage the task.

Distinct behavior of the little finger during the vertical translation of an unsteady thumb platform while grasping

Object stabilization while grasping is a common topic of research in motor control and robotics. Forces produced by the peripheral fingers (index and little) play a crucial role in sustaining the rotational equilibrium of a handheld object. In this study, we examined the contribution of the peripheral fingers towards object stabilization when the rotational equilibrium is disturbed. For this purpose, the thumb was placed over an unsteady platform and vertically translated. The task was to trace a trapezoid or an inverted trapezoid pattern by moving the thumb platform in the vertical direction. The thumb displacement data served as visual feedback to trace the pattern displayed. Participants were instructed to maintain the handle in static equilibrium at all times. We observed that the change in the normal force of the little finger due to the downward translation of the thumb was significantly greater than the change in the normal force of the index finger due to the upward translation. We speculate that morphological correlations (between thumb and little finger) during the displacement of the thumb might be a reason for such large increases in the little finger forces.

Number of Trials Necessary to Apply Analysis Within the Framework of the Uncontrolled Manifold Hypothesis at Different Levels of Hierarchical Synergy Control

The uncontrolled manifold hypothesis is a method used to quantify motor synergies, defined as a specific central nervous system organization that maintains the task-specific stability of motor actions. The UCM allows for inter-trial variance analysis between consecutive trials. However, despite the large body of literature within this framework, there is no report on the number of movement repetitions required for reliable results. Based on the hypothetical hierarchical control of motor synergies, this study aims to determine the minimum number of trials necessary to achieve a good to excellent level of reliability. Thirteen young, healthy participants performed fifteen bilateral isometric contractions of elbow flexion when visual feedback was provided. The force and electromyography data were recorded to investigate synergies at different levels of hierarchical control. The intraclass correlation coefficient was used to determine the reliability of the variance indices. Based on the obtained results, at least twelve trials are required to analyze the inter-trial variance in both force and muscle synergies within the UCM framework.

Comparable behaviour of ring and little fingers due to an artificial reduction in thumb contribution to hold objects

Background

The human hand plays a crucial role in accomplishing activities of daily living. The contribution of each finger in the human hand is remarkably unique in establishing object stabilization. According to the mechanical advantage hypothesis, the little finger tends to exert a greater normal force than the ring finger during a supination moment production task to stabilize the object. Similarly, during pronation, the index finger produces more normal force when compared with the middle finger. Hence, the central nervous system employs the peripheral fingers for torque generation to establish the equilibrium as they have a mechanical advantage of longer moment arms for normal force. In our study, we tested whether the mechanical advantage hypothesis is supported in a task in which the contribution of thumb was artificially reduced. We also computed the safety margin of the individual fingers and thumb.

Methodology

Fifteen participants used five-finger prismatic precision grip to hold a custom-built handle with a vertical railing on the thumb side. A slider platform was placed on the railing such that the thumb sensor could move either up or down. There were two experimental conditions. In the “Fixed” condition, the slider was mechanically fixed, and hence the thumb sensor could not move. In the “Free” condition, the slider platform on which the thumb sensor was placed could freely move. In both conditions, the instruction was to grasp and hold the handle (and the platform) in static equilibrium. We recorded tangential and normal forces of all the fingers.

Results

The distribution of fingertip forces and moments changed depending on whether the thumb platform was movable (or not). In the free condition, the drop in the tangential force of thumb was counteracted by an increase in the normal force of the ring and little finger. Critically, the normal forces of the ring and little finger were statistically equivalent. The safety margin of the index and middle finger did not show a significant drop in the free condition when compared to fixed condition.

Conclusion

We conclude that our results does not support the mechanical advantage hypothesis at least for the specific mechanical task considered in our study. In the free condition, the normal force of little finger was comparable to the normal force of the ring finger. Also, the safety margin of the thumb and ring finger increased to prevent slipping of the thumb platform and to maintain the handle in static equilibrium during the free condition. However, the rise in the safety margin of the ring finger was not compensated by a drop in the safety margin of the index and middle finger.

Does practicing a wide range of joint angle configurations lead to higher flexibility in a manual obstacle-avoidance target-pointing task?

Flexibility in motor actions can be defined as variability in the use of degrees of freedom (e.g., joint angles in the arm) over repetitions while keeping performance (e.g., fingertip position) stabilized. We examined whether flexibility can be increased through enlarging the joint angle range during practice in a manual obstacle-avoidance target-pointing task. To establish differences in flexibility we partitioned the variability in joint angles over repetitions in variability within (GEV) and variability outside the solution space (NGEV). More GEV than NGEV reflects flexibility; when the ratio of the GEV and NGEV is higher, flexibility is higher. The pretest and posttest consisted of 30 repetitions of manual pointing to a target while moving over a 10 cm high obstacle. To enlarge the joint angle range during practice participants performed 600 target-pointing movements while moving over obstacles of different heights (5-9 cm, 11-15 cm). The results indicated that practicing movements over obstacles of different heights led participants to use enlarged range of joint angles compared to the range of joint angles used in movements over the 10 cm obstacle in the pretest. However, for each individual obstacle neither joint angle variance nor flexibility were higher during practice. We also did not find more flexibility after practice. In the posttest, joint angle variance was in fact smaller than before practice, primarily in GEV. The potential influences of learning effects and the task used that could underlie the results obtained are discussed. We conclude that with this specific type of practice in this specific task, enlarging the range of joint angles does not lead to more flexibility.

Temporary Nerve Block at Selected Digits Revealed Hand Motor Deficits in Grasping Tasks

Peripheral sensory feedback plays a crucial role in ensuring correct motor execution throughout hand grasp control. Previous studies utilized local anesthesia to deprive somatosensory feedback in the digits or hand, observations included sensorimotor deficits at both corticospinal and peripheral levels. However, the questions of how the disturbed and intact sensory input integrate and interact with each other to assist the motor program execution, and whether the motor coordination based on motor output variability between affected and non-affected elements (e.g., digits) becomes interfered by the local sensory deficiency, have not been answered. The current study aims to investigate the effect of peripheral deafferentation through digital nerve blocks at selective digits on motor performance and motor coordination in grasp control. Our results suggested that the absence of somatosensory information induced motor deficits in hand grasp control, as evidenced by reduced maximal force production ability in both local and non-local digits, impairment of force and moment control during object lift and hold, and attenuated motor synergies in stabilizing task performance variables, namely the tangential force and moment of force. These findings implied that individual sensory input is shared across all the digits and the disturbed signal from local sensory channel(s) has a more comprehensive impact on the process of the motor output execution in the sensorimotor integration process. Additionally, a feedback control mechanism with a sensation-based component resides in the formation process for the motor covariation structure.

Independent digit contributions to rotational manipulation in a three-digit pouring task requiring dynamic stability

Many activities of daily living involve multi-digit, voluntary rotational manipulations of grasped objects. Yet, only a few studies have focused on coordination of individual fingertip forces during such tasks. The objective of this study was to investigate individual digit contributions to a three-digit task in which an object was rotationally manipulated against gravity. Center of mass was varied through the use of containers shaped like a water bottle, pint glass, and cocktail glass, from which subjects poured fluid carefully into a nearby receptacle. The center of mass of the grasped object changed continuously as fluid was poured out. Self-selected digit placement and contributions of fingertip forces to rotational manipulation were dependent upon anticipated center of mass location associated with container shape. The thumb resisted the rotation of the top-heavy, cocktail glass container until 79 % of the pouring phase had elapsed, but actively assisted the rotation of the less challenging containers. More directly opposing the thumb, the index finger contributed more to grasp stability. The middle finger contributed more to rotation of the container for pouring. It was found that the thumb, index, and middle fingers acted in unison temporally, but contributed independently to the grip forces and stabilizing moments throughout the dynamic, rotational manipulation task.

Effects of aging on force coordination in bimanual task performance

We investigated within- and between-hands grip-load force coordination in both healthy young and older adult participants during bimanual tasks involving realistic actions. Age-related changes in manual behaviors such as grip force production and safety margins were expected in older adults. Within-hand grip-load coordination was expected to decrease with aging during the performance of dynamic actions, but not static actions. The effects of task and hand dominance on task performance were also evaluated. Grip force production increased with age; however, changes in fingertip frictional properties with aging increased the risk of object slip. Indices of within-hand grip-load coordination did not alter with age, but such indices were affected by task goals. The action of connecting two independent objects, particularly with rotational action, was associated with declines in all indices of within- and between-hands force coordination, independent of age. Evidence of task-specific differences in within-hand grip-load coordination in the current data set suggests that individual hand specification emerges and persists with age in everyday bimanual prehension tasks, independent of the action role assigned to the dominant and non-dominant hands.

Force coordination during bimanual task performance in Parkinson's disease

We investigated within- and between-hand grip-load force coordination in medically managed Parkinson's disease (PD) patients during bimanual tasks involving realistic actions. Increased grip force production and evidence of bradykinesia were expected in PD patients. Force coordination indices were also expected to be reduced in PD, due to impaired anticipatory force control. Increased grip force, bradykinesia, and abnormal load force production were exhibited in PD patients as compared to healthy controls. Indices of between-hand load force coordination, but not between-hand grip force coordination, were reduced in PD patients. Discrepancies in the strength of within-hand force coordination with respect to hand action were also noted in PD patients. Increased grip force production, in conjunction with abnormal load force production, may result in reduced fine motor control in PD patients during daily activities. Integrating quantitative analyses of realistic motor function in clinic may assist clinicians in evaluating the effectiveness of medical intervention in PD patients.

Effects of task complexity on grip-to-load coordination in bimanual actions

We investigated within- and between-hand grip and load force coordination in healthy young subjects during bimanual tasks involving realistic manual actions. Actions involving disparate actions of the two hands (bimanual asymmetry) were expected to result in lower overall measures of within- and between-hand measures of grip and load force coordination. As dissociation between two hands performing disparate actions may be expected, it was also hypothesized that increased task asymmetry would result in a shift toward higher within-hand force coordination. Features such as object rotation were found to reduce some, but not all indices of both within- and between-hand force coordination. The action of connecting two independent objects was associated with declines in all indices of within- and between-hand force coordination. Evidence of task-specific differences in force application timing and a trend toward within-hand grip-load coordination differences in the current data set suggest that individual hand specification emerges naturally in everyday bimanual prehension tasks, independent of the action role of the assigned to the dominant and non-dominant hands.

Tangential Finger Forces Use Mechanical Advantage During Static Grasping

When grasping and manipulating objects, the central controller utilizes the mechanical advantage of the normal forces of the fingers for torque production. Whether the same is valid for tangential forces is unknown. The main purpose of this study was to determine the patterns of finger tangential forces and the use of mechanical advantage as a control mechanism when dealing with objects of nonuniform finger positioning. A complementary goal was to explore the interaction of mechanical advantage (moment arm) and the role a finger has as a torque agonist/antagonist with respect to external torques (±0.4 N m). Five 6-dfforce/torque transducers measured finger forces while subjects held a prism handle (6 cm width × 9 cm height) with and without a single finger displaced 2 cm (handle width). The effect of increasing the tangential moment arm was significant (p< .01) for increasing tangential forces (in >70% of trials) and hence creating greater moments. Thus, the data provides evidence that the grasping system as a rule utilizes mechanical advantage for generating tangential forces. The increase in tangential force was independent of whether the finger was acting as a torque agonist or antagonist, revealing their effects to be additive.

Age effects on rotational hand action

We investigated age-related differences in finger coordination during rotational hand actions. Two hypotheses based on earlier studies were tested: higher safety margins and lower synergy indices were expected in the elderly. Young and elderly subjects held a handle instrumented with five six-component force sensors and performed discrete accurate pronation and supination movements. The weight of the system was counterbalanced with another load. Indices of synergies stabilizing salient performance variables, such as total normal force, total tangential force, moments produced by these forces, and total moment of force were computed at two levels of a hypothetical control hierarchy, at the virtual finger-thumb level and at the individual finger level. At each level, synergy indices reflected the normalized difference between the sum of the variances of elemental variables and variance of their combined output, both computed at comparable phases over repetitive trials. The elderly group performed the task slower and showed lower safety margins for the thumb during the rotation phase. Overall, the synergy indices were not lower in the elderly group. In several cases, these indices were significantly higher in the elderly than in the younger participants. Hence, both main hypotheses have been falsified. We interpret the unexpectedly low safety margins in the elderly as resulting from several factors such as increased force variability, impaired feed-forward control, and the fact that there was no danger of dropping the object. Our results suggest that in some natural tasks, such as the one used in this study, healthy elderly persons show no impairment, as compared to younger persons, in their ability to organize digits into synergies stabilizing salient performance variables.

Effects of carpal tunnel syndrome on adaptation of multi-digit forces to object weight for whole-hand manipulation

The delicate tuning of digit forces to object properties can be disrupted by a number of neurological and musculoskeletal diseases. One such condition is Carpal Tunnel Syndrome (CTS), a compression neuropathy of the median nerve that causes sensory and motor deficits in a subset of digits in the hand. Whereas the effects of CTS on median nerve physiology are well understood, the extent to which it affects whole-hand manipulation remains to be addressed. CTS affects only the lateral three and a half digits, which raises the question of how the central nervous system integrates sensory feedback from affected and unaffected digits to plan and execute whole-hand object manipulation. We addressed this question by asking CTS patients and healthy controls to grasp, lift, and hold a grip device (445, 545, or 745 g) for several consecutive trials. We found that CTS patients were able to successfully adapt grip force to object weight. However, multi-digit force coordination in patients was characterized by lower discrimination of force modulation to lighter object weights, higher across-trial digit force variability, the consistent use of excessively large digit forces across consecutive trials, and a lower ability to minimize net moments on the object. Importantly, the mechanical requirement of attaining equilibrium of forces and torques caused CTS patients to exert excessive forces at both CTS-affected digits and digits with intact sensorimotor capabilities. These findings suggest that CTS-induced deficits in tactile sensitivity interfere with the formation of accurate sensorimotor memories of previous manipulations. Consequently, CTS patients use compensatory strategies to maximize grasp stability at the expense of exerting consistently larger multi-digit forces than controls. These behavioral deficits might be particularly detrimental for tasks that require fine regulation of fingertip forces for manipulating light or fragile objects.

Prehension synergies during smooth changes of the external torque

We studied characteristics of digit action and their co-variation patterns across trials (prehension synergies) during static holding of an object while the external torque could change slowly and smoothly. The subjects held in the air an instrumented handle with an attachment that allowed a smooth change in the external torque over about 12 s; the load was always kept constant. Series of trials were performed under three conditions: The torque could be zero throughout the trial, or it could change slowly requiring a smooth change of the effort from a non-zero pronation value to zero (PR-0) or from a non-zero supination value to zero (SU-0). The handle was kept vertical at all times. Indices of variance and co-variation of elemental variables (forces and moments of force produced by individual digits) stabilizing such performance variables as total normal force, total tangential force, and total moment of force were computed at two levels of an assumed control hierarchy. At the upper level, the task is shared between the thumb and virtual finger (an imagined digit with the mechanical action equal to that of the four fingers), while at the lower level, the action of the virtual finger is shared among the actual four fingers. We analyzed the total moment of force as the sum of the moments of force produced by the thumb and virtual finger and also as the sum of the moments of force produced by the normal forces and tangential forces. The results showed that the adjustments in the total moment of force were produced primarily with changes in the moment produced by the virtual finger and by changes in the moment produced by the normal forces. The normal force of the thumb at the final state (which was the same across conditions) was larger in the two conditions with changes in the external torque. The safety margin was significantly higher in the PR-0 condition, and it dropped with the decrease in the external torque. A co-contraction index was computed to reflect the moment of force production by the fingers acting against the total moment produced by the virtual finger. It was higher for the SU-0 condition. Most variance indices dropped with a decrease in the external torque. The co-variation indices, however, remained unchanged over the trial duration. They showed signs of a trade-off between the two levels of the assumed hierarchy: larger indices at the higher level corresponded to smaller indices at the lower level. This study and the previous one (Sun et al. in Exp Brain Res 209:571-585, 2011) document several previously unknown features of prehensile tasks. The results show that characteristics of digit action and interaction in such tasks depend not only on the magnitudes of external constraints but also on a variety of other factors including time changes in the constraints and their history.

Manipulation of a fragile object by elderly individuals

We investigated strategies of healthy elderly participants (74-84 years old) during prehension and transport of an object with varying degrees of fragility. Fragility was specified as the maximal normal force that the object could withstand without collapsing. Specifically, kinetic and kinematic variables as well as and force covariation indices were quantified and compared to those shown by young healthy persons (19-28 years old). We tested three hypotheses related to age-related changes in two safety margins (slip safety margin and crush safety margin) and indices of force covariation. Compared to young controls, elderly individuals exhibited a decrease in object acceleration and an increase in movement time, an increase in grip force production, a decrease in the correlation between grip and load forces, an overall decrease in indices of multi-digit synergies, and lower safety margin indices computed with respect to both dropping and crushing the object. Elderly participants preferred to be at a relatively lower risk of crushing the object even if this led to a higher risk of dropping it. Both groups showed an increase in the index of synergy stabilizing total normal force produced by the four fingers with increased fragility of the object. Age-related changes are viewed as a direct result of physiological changes due to aging, not adaptation to object fragility. Such changes in overall characteristics of prehension likely reflect diminished synergic control by the central nervous system of finger forces with aging. The findings corroborate an earlier hypothesis on an age-related shift from synergic to element-based control.

Age-related changes in optimality and motor variability: an example of multifinger redundant tasks

We used two methods, analytical inverse optimization (ANIO) and uncontrolled manifold (UCM) analysis of synergies, to explore age-related changes in finger coordination during accurate force and moment of force production tasks. The two methods address two aspects of the control of redundant systems: Finding an optimal solution (an optimal sharing pattern) and using variable solutions across trials (covarying finger forces) that are equally able to solve the task. Young and elderly subjects produced accurate combinations of total force and moment by pressing with the four fingers of the dominant hand on individual force sensors. In session-1, single trials covered a broad range of force-moment combinations. Principal component (PC) analysis showed that the first two PCs explained about 90% and 75% of finger force variance for the young and elderly groups, respectively. The magnitudes of the loading coefficients in the PCs suggested that the young subjects used mechanical advantage to produce moment while elderly subjects did not (confirmed by analysis of moments produced by individual digits). A co-contraction index was computed reflecting the magnitude of moment produced by fingers acting against the required direction of the total moment. This index was significantly higher in the young group. The ANIO approach yielded a quadratic cost function with linear terms. In the elderly group, the contribution of the forces produced by the middle and ring fingers to the cost function value was much smaller than in the young group. The angle between the plane of experimental observations and the plane of optimal solutions (D-angle), was very small (about 1.5°) in the young group and significantly larger (about 5°) in the elderly group. In session-2, four force-moment combinations were used with multiple trials at each. Covariation among finger forces (multifinger synergies) stabilizing total force, total moment, and both was seen in both groups with larger synergy indices in the young group. Multiple regression analysis has shown that, at higher force magnitudes, the synergy indices defined with the UCM method were significantly related to the percent of variance accounted by the first two PCs and to the D-angle computed using the ANIO method. We interpret the results as pointing at a transition with age from synergic control to element-based control (back-to-elements hypothesis). Optimization and analysis of synergies are complementary approaches that focus on two aspects of multidigit coordination, sharing and covariation, respectively.

Joint angle variability and co-variation in a reaching with a rod task

The problem at the heart of motor control is how the myriad units of the neuromotor system are coordinated to perform goal-directed movements. Although for long these numerous degrees of freedom (DOFs) were considered redundant, recent views emphasize more that the DOFs should be considered abundant, allowing flexible performance. We studied how variability in arm joints was employed to stabilize the displaced end-effector in tool use to examine how the neuromotor system flexibly exploits DOFs in the upper extremity. Participants made pointing movements with the index finger and with the index finger extended by rods of 10, 20, and 30 cm. Using the uncontrolled manifold (UCM) method, the total joint angle variance was decomposed into two parts, the joint angle variance that did not affect the position of the end-effector (V_UCM) and the variance that results in a deviation of the position of the end-effector from its mean (V_ORT). Analyses showed that some angles depended on length of the rod in use. For all rod lengths, V_UCM was larger than V_ORT, and this did not differ over rod lengths, demonstrating that the arm was organized into a synergy. Finally, the variation in the joint angles in the arm as well as the degree of co-variation between these angles did not differ for the rod’s tip and the hand. We concluded that synergies are formed in the arm during reaching with an extended end-effector and those synergies stabilize different parts of the arm+rod system equally.

Motor synergies and the equilibrium-point hypothesis

The article offers a way to unite three recent developments in the field of motor control and coordination: (1) The notion of synergies is introduced based on the principle of motor abundance; (2) The uncontrolled manifold hypothesis is described as offering a computational framework to identify and quantify synergies; and (3) The equilibrium-point hypothesis is described for a single muscle, single joint, and multijoint systems. Merging these concepts into a single coherent scheme requires focusing on control variables rather than performance variables. The principle of minimal final action is formulated as the guiding principle within the referent configuration hypothesis. Motor actions are associated with setting two types of variables by a controller, those that ultimately define average performance patterns and those that define associated synergies. Predictions of the suggested scheme are reviewed, such as the phenomenon of anticipatory synergy adjustments, quick actions without changes in synergies, atypical synergies, and changes in synergies with practice. A few models are briefly reviewed.

Handwriting: hand-pen contact force synergies in circle drawing tasks

This study investigated synergistic actions of hand-pen contact forces during circle drawing tasks in three-dimensional (3D) space. Twenty-four right-handed participants drew thirty concentric circles in the counterclockwise (CCW) and clockwise (CW) directions. Three-dimensional forces acting on an instrumented pen as well as 3D linear and angular positions of the pen were recorded. These contact forces were then transformed into the 3D radial, tangential, and normal force components specific to circle drawing. Uncontrolled manifold (UCM) analysis was employed to calculate the magnitude of the hand-pen contact force synergy. Three hypotheses were tested. First, hand-pen contact force synergies during circle drawing are dependent on the angular position of the pen tip. Second, hand-pen contact force synergies are dependent on force components in circle drawing. Third, hand-pen contact force synergies are greater in CCW direction than CW direction. The results showed that the strength of the hand-pen contact force synergy increased during the initial phase of circle drawing and decreased during the final phase. The synergy strength was greater for the radial and tangential components as compared to the normal component. Also, the circle drawing in CW direction was associated with greater hand-pen contact force synergy than the CCW direction. The results of this study suggest that the central nervous system (CNS) prioritizes hand-pen contact force synergies for the force components (i.e., radial and tangential) that are critical for circle drawing. The CNS modulates hand-pen contact force synergies for preparation and conclusion of circle drawing, respectively.

Manipulation of a fragile object

We investigated strategies of adjustments in kinetic and kinematic patterns, and in multi-digit synergies during quick vertical transport of an instrumented handle that collapsed when the grasping force exceeded a certain magnitude (quantified with a fragility index). The collapse threshold of the object was set using a novel electromagnetic device. Moving a fragile object is viewed as a task with two constraints on the grip force defined by the slipping and crushing thresholds. When moving more fragile objects, subjects decreased object peak acceleration, increased movement time, showed a drop in the safety margin (SM) (extra force over the slipping threshold), and showed a tendency toward violating the minimum-jerk criterion. Linear regression analysis of grip force against load force has shown tight coupling between the two with a decline in the coefficient of determination with increased fragility index. The SM was lower in bimanual tasks, compared to unimanual tasks, for both fragile and non-fragile objects. Two novel indices have been introduced and studied, the SM due to fragility and the drop-crush index. Both indices showed a decrease with increased object fragility. Changes in the drop-crush index showed that the subjects would rather crush the fragile objects as opposed to dropping them, possibly reflecting the particular experimental procedure. We did not find differences between the performance indices of the dominant and non-dominant hand thus failing to support the recently formulated dominance hypothesis. The synergies stabilizing grip force were quantified at two levels of an assumed two-level control hierarchy using co-variation indices between elemental variables across trials. There were strong synergies at the upper level of the hierarchy (the task is shared between the opposing groups of digits) that weakened with an increase in object fragility. At the lower level (action of an effector is shared among the four fingers), higher fragility led to higher synergy indices. Analysis of force variance showed that an increase in object fragility was accompanied by exploring a smaller range of equivalent combinations of elemental variables. The additional constraint imposed by high fragility facilitated synergies at the lower level of the hierarchy, while there was evidence for a trade-off between synergies at the two levels.

Prehension synergies and control with referent hand configurations

We used the framework of the equilibrium-point hypothesis (in its updated form based on the notion of referent configuration) to investigate the multi-digit synergies at two levels of a hypothetical hierarchy involved in prehensile actions. Synergies were analyzed at the thumb-virtual finger (VF) level (VF is an imaginary digit with the mechanical action equivalent to that of the four actual fingers) and at the individual finger level. The subjects performed very quick vertical movements of a handle into a target. A load could be attached off-center to provide a pronation or supination torque. In a few trials, the handle was unexpectedly fixed to the table and the digits slipped off the sensors. In such trials, the hand stopped at a higher vertical position and rotated into pronation or supination depending on the expected torque. The aperture showed non-monotonic changes with a large, fast decrease and further increase, ending up with a smaller distance between the thumb and the fingers as compared to unperturbed trials. Multi-digit synergies were quantified using indices of co-variation between digit forces and moments of force across unperturbed trials. Prior to the lifting action, high synergy indices were observed at the individual finger level while modest indices were observed at the thumb-VF level. During the lifting action, the synergies at the individual finger level disappeared while the synergy indices became higher at the thumb-VF level. The results support the basic premise that, within a given task, setting a referent configuration may be described with a few referent values of variables that influence the equilibrium state, to which the system is attracted. Moreover, the referent configuration hypothesis can help interpret the data related to the trade-off between synergies at different hierarchical levels.