Prehension synergies during nonvertical grasping, I: experimental observations

Grip-force modulation in multi-finger prehension during wrist flexion and extension

Extrinsic digit muscles contribute to both fingertip forces and wrist movements (FDP and FPL-flexion, EDC-extension). Hence, it is expected that finger forces depend on the wrist movement and position. We investigated the relation between grip force and wrist kinematics to examine whether and how the force (1) scales with wrist flexion-extension (FE) angle and (2) can be predicted from accelerations induced during FE movement. In one experiment, subjects naturally held an instrumented handle using a prismatic grasp and performed very slow FE movements. In another experiment, the same movement was performed cyclically at three prescribed frequencies. In quasistatic conditions, the grip force remained constant over the majority of the wrist range of motion. During the cyclic movements, the grip force changed. The changes were described with a linear regression model that represents the thumb and virtual finger (VF = four fingers combined) normal forces as the sum of the effects of the object's tangential and radial accelerations and an object-weight-dependent constant term. The model explained 99 % of the variability in the data. The independence of the grip force from wrist position agrees with the theory that the thumb and VF forces are controlled with two neural variables that encode referent coordinates for each digit while accounting for changes in the position dependence of muscle forces, rather than a single neural variable like referent aperture. The results of the cyclical movement study extend the principle of superposition (some complex actions can be decomposed into independently controlled elemental actions) for a motor task involving simultaneous grip-force exertion and wrist motion with significant length changes of the grip-force-producing muscles.

Multi-digit coordination during lifting a horizontally oriented object: synergies control with referent configurations

We explored digit coordination during the acceleration phase of a quick lifting movement of a hand-held horizontal object. We tested three hypotheses related to: (1) the scaling of mechanical variables produced by the hand with changes in the external load, torque, and moment of inertia; (2) changes in the safety margin for the thumb with both the loading conditions and acceleration; and (3) changes in the indices of synergies. The subjects held a horizontal handle with a prismatic grasp (the thumb acted on top of the handle) and performed series of "very quick" lifting movements to a visual target. Multi-digit synergies were quantified as co-variation indices among elemental variables (forces and moments produced by individual digits). The resultant force scaled with the external load but not torque, while the grip force scaled with the external torque but not load. The safety margin dropped with an increase in acceleration; it also showed changes with the external torque and moment of inertia. Total moment of force was primarily produced by the tangential forces (over 80 %) across all movement phases and loading conditions. The index and little fingers produced close to zero moment with their normal forces, while the middle and ring fingers produced consistent moments due to the reproducible shifts of their centers of pressure. Synergy indices at the upper level of the assumed hierarchy (the task is shared between the thumb and virtual finger--an imagined digit with the action equal to that of the four fingers combined) did not drop with acceleration for the three force vector components and one of the moment vector components. They did drop with acceleration at the lower level (virtual finger action is shared among the four fingers). There was a trade-off between synergy indices computed at the two levels for the three force vector components, but not for the moment of force components. We confirmed specialization of different fingers with respect to different task components in quick manipulation tasks. The findings have implications for hypotheses on the control of voluntary movements involving redundant sets of effectors. Within the referent configuration hypothesis, components of a referent configuration may be adjusted to task mechanical characteristics using simple scaling rules. The neural organization of multi-digit synergies in a hierarchal system is able to selectively protect synergies related to stabilization of some performance variables from detrimental effects of the rate of change of those variables. A large number of apparently redundant elemental variables are not the source of additional computational problems but may be beneficial, allowing the central nervous system to facilitate synergies at both levels of the hierarchy.

Prehension Synergy: Use of Mechanical Advantage During Multifinger Torque Production on Mechanically Fixed and Free Objects

The aim of this study was to test the mechanical advantage (MA) hypothesis in multifinger torque production tasks in humans: fingers with longer moment arms produce greater force magnitudes during torque production tasks. There were eight experimental conditions: two prehension types determined by different mechanical constraints (i.e., fixed- and free-object prehension) with two torque directions (supination and pronation) and two torque magnitudes (0.24 and 0.48 N·m). The subjects were asked to produce prescribed torques during the fixed-object prehension or to maintain constant position of the free hand-held object against external torques. The index of MA was calculated for agonist and antagonist fingers, which produce torques in the same and opposite directions to the target torques, respectively. Within agonist fingers, the fingers with longer moment arms produced greater grasping forces while within antagonist fingers, the fingers with shorter moment arms produced greater forces. The MA index was greater in the fixed-object condition as compared with the free-object condition. The MA index was greater in the pronation condition than in the supination condition. This study supports the idea that the CNS utilizes the MA of agonist fingers, but not of antagonist fingers, during torque production in both fixed- and free-object conditions.

Reproducibility and variability of the cost functions reconstructed from experimental recordings in multifinger prehension

The study examines whether the cost functions reconstructed from experimental recordings are reproducible over time. Participants repeated the trials on three days. By following Analytical Inverse Optimization procedures, the cost functions of finger forces were reconstructed for each day. The cost functions were found to be reproducible over time: application of a cost function C(i) to the data of Day j (i≠j) resulted in smaller deviations from the experimental observations than using other commonly used cost functions. Other findings are: (a) the 2nd order coefficients of the cost function showed negative linear relations with finger force magnitudes; (b) the finger forces were distributed on a 2-dimensional plane in the 4-dimensional finger force space for all subjects and all testing sessions; (c) the data agreed well with the principle of superposition, i.e. the action of object prehension can be decoupled into the control of rotational equilibrium and slipping prevention.

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.

Reconstruction of the unknown optimization cost functions from experimental recordings during static multi-finger prehension

The goal of the research is to reconstruct the unknown cost (objective) function(s) presumably used by the neural controller for sharing the total force among individual fingers in multifinger prehension. The cost function was determined from experimental data by applying the recently developed Analytical Inverse Optimization (ANIO) method (Terekhov et al. 2010). The core of the ANIO method is the Theorem of Uniqueness that specifies conditions for unique (with some restrictions) estimation of the objective functions. In the experiment, subjects (n = 8) grasped an instrumented handle and maintained it at rest in the air with various external torques, loads, and target grasping forces applied to the object. The experimental data recorded from 80 trials showed a tendency to lie on a 2-dimensional hyperplane in the 4-dimensional finger-force space. Because the constraints in each trial were different, such a propensity is a manifestation of a neural mechanism (not the task mechanics). In agreement with the Lagrange principle for the inverse optimization, the plane of experimental observations was close to the plane resulting from the direct optimization. The latter plane was determined using the ANIO method. The unknown cost function was reconstructed successfully for each performer, as well as for the group data. The cost functions were found to be quadratic with nonzero linear terms. The cost functions obtained with the ANIO method yielded more accurate results than other optimization methods. The ANIO method has an evident potential for addressing the problem of optimization in motor control.

Static prehension of a horizontally oriented object in three dimensions

We studied static prehension of a horizontally oriented object. Specific hypotheses were explored addressing such issues as the sharing patterns of the total moment of force across the digits, presence of mechanically unnecessary digit forces, and trade-off between multi-digit synergies at the two levels of the assumed control hierarchy. Within the assumed hierarchy, at the upper level, the task is shared between the thumb and virtual finger (an imagined finger producing a wrench equal to the sum of the wrenches of individual fingers). At the lower level, action of the virtual finger is shared among the four actual fingers. The subjects held statically a horizontally oriented handle instrumented with six-component force/torque sensors with different loads and torques acting about the long axis of the handle. The thumb acted from above while the four fingers supported the weight of the object. When the external torque was zero, the thumb produced mechanically unnecessary force of about 2.8 N, which did not depend on the external load magnitude. When the external torque was not zero, tangential forces produced over 80% of the total moment of force. The normal forces by the middle and ring fingers produced consistent moments against the external torque, while the normal forces of the index and little fingers did not. Force and moment variables at both hierarchical levels were stabilized by covaried across trials adjustments of forces/moments produced by individual digits with the exception of the normal force analyzed at the lower level of the hierarchy. There was a trade-off between synergy indices computed at the two levels of the hierarchy for the three components of the total force vector, but not for the moment of force components. Overall, the results have shown that task mechanics are only one factor that defines forces produced by individual digits. Other factors, such as loading sensory receptors may lead to mechanically unnecessary forces. There seems to be no single rule (for example, ensuring similar safety margin values) that would describe sharing of the normal and tangential forces and be valid across tasks. Fingers that are traditionally viewed as less accurate (e.g., the ring finger) may perform more consistently in certain tasks. The observations of the trade-off between the synergy indices computed at two levels for the force variables but not for the moment of force variables suggest that the degree of redundancy (the number of excessive elemental variables) at the higher level is an important factor.

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.

Grip forces during object manipulation: experiment, mathematical model, and validation

When people transport handheld objects, they change the grip force with the object movement. Circular movement patterns were tested within three planes at two different rates (1.0, 1.5 Hz) and two diameters (20, 40 cm). Subjects performed the task reasonably well, matching frequencies and dynamic ranges of accelerations within expectations. A mathematical model was designed to predict the applied normal forces from kinematic data. The model is based on two hypotheses: (a) the grip force changes during movements along complex trajectories can be represented as the sum of effects of two basic commands associated with the parallel and orthogonal manipulation, respectively; (b) different central commands are sent to the thumb and virtual finger (Vf-four fingers combined). The model predicted the actual normal forces with a total variance accounted for of better than 98%. The effects of the two components of acceleration-along the normal axis and the resultant acceleration within the shear plane-on the digit normal forces are additive.

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.

Coordination of Contact Forces During Multifinger Static Prehension

This study investigated the effects of modifying contact finger forces in one direction—normal or tangential—on the entire set of the contact forces, while statically holding an object. Subjects grasped a handle instrumented with finger force-moment sensors, maintained it at rest in the air, and then slowly: (1) increased the grasping force, (2) tried to spread fingers apart, and (3) tried to squeeze fingers together. Analysis was mostly performed at the virtual finger (VF) level (the VF is an imaginable finger that generates the same force and moment as the four fingers combined). For all three tasks there were statistically significant changes in the VF normal and tangential forces. For finger spreading/squeezing the tangential force neutral point was located between the index and middle fingers. We conclude that the internal forces are regulated as a whole, including adjustments in both normal and tangential force, instead of only a subset of forces (normal or tangential). The effects of such factors as EFFORT and TORQUE were additive; their interaction was not statistically significant, thus supporting the principle of superposition in human prehension.

Prehension of half-full and half-empty glasses: time and history effects on multi-digit coordination

We explored how digit forces and indices of digit coordination depend on the history of getting to a particular set of task parameters during static prehension tasks. The participants held in the right hand an instrumented handle with a light-weight container attached on top of the handle. At the beginning of each trial, the container could be empty, filled to the half with water (0.4 l), or filled to the top (0.8 l). The water was pumped in/out of the container at a constant, slow rate over 10 s. At the end of each trial, the participants always held a half-filled container that has just been filled (Empty-Half), emptied (Full-Half) or stayed half-filled throughout the trial (Half-Only). Indices of covariation (synergy indices) 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. Filling or emptying the container led to a drop in the safety margin (proportion of grip force over the slipping threshold) below the values observed in the Half-Only condition. Synergy indices at both levels of the hierarchy showed changes over the Full-Half and Empty-Half condition. These changes could be monotonic (typical of moment of force and normal force) or non-monotonic (typical of tangential force). For both normal and tangential forces, higher synergy indices at the higher level of the hierarchy corresponded to lower indices at the lower level. Significant differences in synergy indices across conditions were seen at the final steady state showing that digit coordination during steady holding an object is history dependent. The observations support an earlier hypothesis on a trade-off between synergies at the two levels of a hierarchy. They also suggest that, when a change in task parameters is expected, the neural strategy may involve producing less stable (easier to change) actions. The results suggest that synergy indices may be highly sensitive to changes in a task variable and that effects of such changes persist after the changes are over.

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.

Mechanical analysis and hierarchies of multidigit synergies during accurate object rotation

We studied the mechanical variables (the grip force and the total moment of force) and multidigit synergies at two levels (the virtual finger-thumb level, VF-TH, and the individual finger level, IMRL) of a hypothetical control hierarchy during accurate rotation of a hand-held instrumented handle. Synergies were defined as covaried changes in elemental variables (forces and moments of force) that stabilize the output at a particular level. Indices of multidigit synergies showed higher values at the hierarchically higher level (VF-TH) for both normal and tangential forces. The moment of force was stabilized at both hierarchical levels during the steady-state phases but not during the movement. The results support the principles of superposition and of mechanical advantage. They also support an earlier hypothesis on an inherent tradeoff between synergies at the two hierarchical levels, although the controller showed more subtle and versatile synergic control than the one hypothesized earlier.

Effects of grasping force magnitude on the coordination of digit forces in multi-finger prehension

The study addresses three main questions: (1) Does the magnitude of the grasping force affect the prehension synergies, i.e., conjoint changes of finger forces and moments? (2) Do individual finger forces scale with the total grasping forces ('scale-invariance hypothesis')? (3) How specification of the grasping force magnitude affects the inverse optimization of digit forces. Subjects (n = 7) grasped with minimal force an instrumented handle and maintained it at rest in the air. Then, the subjects doubled the initial grasping force. The forces and moments exerted by individual digits were recorded with six-component sensors. External torques that the subjects should resist (9 in total) varied among the trials from 0 to 0.46 Nm both in clockwise and counterclockwise directions. After the force doubling, the moments of the normal forces (M (n)) increased in the pronation effort tasks (PR-tasks) and decreased in the supination effort tasks (SU-tasks). The changes in the moments of the tangential forces (M (t)) were opposite to the M (n) changes; the moments increased in the SU-tasks and decreased in the PR-tasks. The opposite effects of force doubling on the M (t)s in the SU-tasks and PR-tasks were a consequence of the unidirectional changes of the thumb tangential forces: in all the tasks the contribution of the thumb tangential force to the total tangential force increased after the grasping force doubling (and the total contribution of the four fingers decreased). The decrease of the virtual finger (VF) tangential force was mainly due to the decrease of the index finger force (VF is an imagined finger that exerts the same force and moment as all the fingers together). In the non-zero torque tasks the individual finger forces did not scale proportionally with the grasping force, the sharing percentage of the individual finger forces in the VF normal force changed with the grasping force increase. The root mean square differences between the actual finger sharing percentages in the VF force and the sharing percentages predicted from optimization procedures in which different cost functions were used were in all cases smaller after the doubling than before the doubling. Hence the answers to the three questions formulated above are: (1) the alteration of the grasping force magnitude induces complex coordinated changes of all digit forces and moments; (2) the scale invariance hypothesis is confirmed only for the zero-torque tasks and rejected for the non-zero tasks, and (3) the specification of the grasping force magnitude at the level of twice the initial grasping force-which essentially restricts the control task to the object tilt prevention-improves the accuracy of the employed optimization procedures.

Hierarchical control of static prehension: I. Biomechanics

We explored the action of digits during static prehension tasks involving one hand or two hands of one or two persons. Three hypotheses were tested: to prevent slippage of the object, grip force and safety margin (SM) would be largest in bimanual conditions, particularly involving two persons; the distribution of tangential forces would not differ among tested conditions, thus preserving the vertical orientation of the object in a stereotypical way; and the mechanical advantage of fingers would be used to maintain rotational equilibrium. The multi-digit synergies are discussed in the companion paper (Gorniak et al. 2009, in review). The subjects held vertical one of the two handles, a narrow one and a wide one. They used the four fingers of the right hand opposed by either the right hand thumb, the left hand thumb, the left hand index finger, the thumb of an experimenter, the index finger of an experimenter, or an inanimate object. Forces and moments of force produced by each digit were recorded. The first two hypotheses were falsified. Both grip force and SM were the largest in the one-hand task, and they were the lowest for the tasks involving two persons. The distribution of tangential forces among fingers was significantly different in the one-hand task. The mechanical advantage hypothesis was supported across all the tested conditions. The results suggest that the neural controller uses a different strategy in the one-hand task as compared to other tasks, while bimanual prehension involving two persons differs from one-person two-hand tasks. The findings do not support a hypothesis that normal (grip) forces are adjusted to ensure a particular value of the SM. Maintaining rotational equilibrium was achieved differently in different tasks. In particular, the one-hand task was characterized by large intercompensated adjustments in different contributors to the total moment of force, which could be described as chain effects; such adjustments were all but absent in the other conditions. The findings may be interpreted within the framework of the reference configuration hypothesis, in which digit forces emerge due to the discrepancies between the actual and the centrally defined (reference) hand aperture.

Multifinger prehension: an overview

The authors review the available experimental evidence on what people do when they grasp an object with several digits and then manipulate it. The article includes three parts, each addressing a specific aspect of multifinger prehension. In the first part, the authors discuss manipulation forces (i.e., the resultant force and moment of force exerted on the object) and the digits' contribution to such forces' production. The second part deals with internal forces defined as forces that cancel each other and do not disturb object equilibrium. The authors discuss the role of the internal forces in maintaining the object stability, with respect to such issues as slip prevention, tilt prevention, and resistance to perturbations. The third part is devoted to the motor control of prehension. It covers such topics as prehension synergies, chain effects, the principle of superposition, interfinger connection matrices and reconstruction of neural commands, mechanical advantage of the fingers, and the simultaneous digit adjustment to several mutually reinforcing or conflicting demands.

Digit force adjustments during finger addition/removal in multi-digit prehension

We explored adjustments in multi-digit coordinated action on a hand-held object with finger addition and removal. The subjects (n = 7) kept a vertically oriented handle at rest using a prismatic grasp as if holding a glass of liquid and then either added one finger to the grasp, the index (I) or little (L) finger, or removed one finger. Three external torques were applied on the apparatus: clockwise, counterclockwise, and no torque. The individual digit forces and moments were recorded with six-component sensors. The change in grasping force, normal force of the thumb and virtual finger (VF, an imagined finger that generates the same mechanical effect as all fingers together), depended on the function of the manipulated finger, i.e. on whether the finger resisted external torque (torque agonist) or assisted it (torque antagonist). There was a significant increase of the grasping force when an antagonist was added or when an agonist was removed. These force increases were not necessary for slipping prevention: the normal forces prior to the manipulation were large enough to prevent slipping. All other finger manipulations exhibited no significant change in the grip force, except for the antagonist removal during the supination efforts (after removing the I finger the grasping force decreased). In contrast, the changes in the tangential force of the thumb depended on the manipulated finger, not on the finger function with respect to external torque. There was a significant thumb tangential force increase when the I finger was added or when the L finger was removed; opposite changes were seen when the L finger was added or the I finger was removed. The changes of the virtual finger (VF) tangential force were equal and opposite to the thumb tangential force alterations; these opposite changes caused changes in the moments, these forces generated. The changes in the moments of the tangential forces were counterbalanced by the opposite changes in the moments of normal forces such that the total moment remained constant and the handle orientation was maintained. At the level of individual finger (IF) forces two strategies of error compensation were found: (a) local error compensation--the opposite action of the neighboring finger, i.e. force decrease in response to a force increase (finger addition), and vice versa and (b) distant error compensation--similar action by a finger that is a torque antagonist to the manipulated finger. During the transient periods, the changes in the thumb and VF forces were simultaneous and equal in magnitude. The normal forces increased or decreased concurrently while the changes in the tangential forces were opposite in direction. The data support the existence of chain effects in the digit force adjustments to finger addition or removal. We conclude that the digit force adjustments during the object manipulation are controlled mainly in a feed-forward manner. The obtained data agree with the principle of superposition reported previously. The findings agree with earlier reports on the limited ability of CNS to organize synergies at two levels of a control hierarchy simultaneously.

Finger force perception during ipsilateral and contralateral force matching tasks

The aims of the present study were to compare matching performance between ipsilateral and contralateral finger force matching tasks and to examine the effect of handedness on finger force perception. Eleven subjects were instructed to produce reference forces by an instructed finger (index-I or little-L finger) and to reproduce the same amount force by the same or a different finger within the hand (i.e., ipsilateral matching task), or by a finger of the other hand (i.e., contralateral matching task). The results of the ipsilateral and contralateral tasks in the present study commonly showed that (1) the reference and matching forces were matched closely when the two forces were produced by the same or homologous finger(s) such as I/I task; (2) the weaker little finger underestimated the magnitude of reference force of the index finger (I/L task), even with the higher level of effort (relative force), but the two forces were matched when considering total finger forces; (3) the stronger index finger closely matched the reference force of the little finger with the lower level of relative force (i.e., L/I task); (4) when considering the constant errors, I/L tasks showed an underestimation and L/I tasks showed an overestimation compared to I/I tasks. There was no handedness effect during ipsilateral tasks. During the contralateral task, the dominant hand overestimated the force of the non-dominant hand, while the non-dominant hand attempted to match the absolute force of the dominant hand. The overall results support the notion that the absolute, rather than relative, finger force is perceived and reproduced during ipsilateral and contralateral finger force matching tasks, indicating the uniqueness of finger force perception.

Adjustments to local friction in multifinger prehension

The authors studied the effects of surface friction at the digit-object interface on digit forces and moments when 12 participants statically held an object in a 5-digit grasp. The authors changed low-friction contact (LFC) with rayon and high-friction contact (HFC) with sandpaper independently for each digit in all 32 possible combinations. Normal forces of the thumb and virtual finger (VF), an imagined finger with a mechanical effect equal to that of the 4 fingers, increased with the thumb at LFC or with an increase in the number of fingers at LFC. When the thumb was at LFC, the thumb tangential force decreased. The VF tangential force decreased when the number of fingers at LFC increased. The interaction of the local responses to friction and the synergic responses necessary to maintain the equilibrium explain the coordination of individual digit forces.

Perception of finger forces within the hand after index finger fatiguing exercise

The effect of fatigue on finger force perception within a hand during ipsilateral finger force matching was examined. Thirteen subjects were instructed to match a reference force of an instructed finger using the same or different finger within the hand before and after index finger fatigue. Absolute reference force targets for the index or little finger were identical during pre- and post-fatigue sessions. Fatigue was induced by a 60-s sustained maximal voluntary contraction (MVC) of the index finger. Index finger MVC decreased approximately 29%, while there was a non-significant (about 5%) decrease in the little finger MVC. The results showed that: (1) the absolute reference and matching forces of the instructed fingers were not significantly changed after fatigue, while the total forces (sum of instructed and uninstructed finger forces) were increased after fatigue. (2) The relative forces (with respect to corresponding pre- and post-fatigue MVCs) of the index finger increased significantly in both reference and matching tasks, while the relative forces of the little finger remained unchanged after fatigue. (3) Matching errors remained unchanged after fatigue when the fatigued index finger produced the reference force, while the errors increased significantly when the fatigued index finger produced the matching force. (4) Enslaving (difference between total and instructed finger forces) increased significantly after fatigue, especially during force production by the fatigued index finger and when the little finger produced matching forces at higher force levels. (5) Enslaving significantly increased matching errors particularly after fatigue. Taken together, our results suggest that absolute finger forces within the hand are perceived within the CNS during ipsilateral finger force matching. Perception of absolute forces of the fatigued index finger is not altered after fatigue. The ability of the fatigued index finger to reproduce little finger forces is impaired to a certain degree, however. The impairment is likely to be attributable to altered afferent/efferent relationships of the fatigued index finger.

Multi-digit maximum voluntary torque production on a circular object

Individual digit-tip forces and moments during torque production on a mechanically fixed circular object were studied. During the experiments, subjects positioned each digit on a 6-dimensional force/moment sensor attached to a circular handle and produced a maximum voluntary torque on the handle. The torque direction and the orientation of the torque axis were varied. From this study, it is concluded that: (1) the maximum torque in the closing (clockwise) direction was larger than in the opening (counter clockwise) direction; (2) the thumb and little finger had the largest and the smallest share of both total normal force and total moment, respectively; (3) the sharing of total moment between individual digits was not affected by the orientation of the torque axis or by the torque direction, while the sharing of total normal force between the individual digit varied with torque direction; (4) the normal force safety margins were largest and smallest in the thumb and little finger, respectively.

Elaborate force coordination of precision grip could be generalized to bimanual grasping techniques

Exceptional coordination of grip (G; the normal force that prevents slippage of the grasped object) and load force (L; the tangential force originating from the object's weight and inertia) has been interpreted as a part of evidence that both the anatomy and neural control of human hands have been predominantly designed for manipulation tasks. In the present study, we tested the hypothesis that the precision grasp (uses only the tips of fingers and the thumb of one hand) provides better indices of G and L coordination in static manipulation tasks than two bimanual grasps (palm-palm and fingers-thumb; both using opposing segments of two hands). However, in addition to a subtle difference in relative timing of G and L between the precision and two bimanual grasps, we only found that the fingers-thumb grasp is characterized with higher G/L ratio and somewhat higher modulation of G than not only the precision, but also the bimanual palm-palm grasp. However, all remaining data including the correlation coefficients between G and L demonstrated no difference among three evaluated grasping techniques. Therefore, we concluded that the elaborate G and L coordination associated with uni-manual grasps could be partly generalized to a variety of manipulation tasks including those based on bimanual grasping techniques. Taking into account the importance of manipulation tasks in both everyday life and clinical evaluation, future studies should extend the present research to both other grasping techniques and dynamic manipulation conditions.

Perception of individual finger forces during multi-finger force production tasks

The present study examined perception of individual finger forces during multi-finger force production tasks. In an ipsilateral force matching paradigm, 12 healthy subjects were instructed to produce a reference force pre-determined at 30% MVC of involved fingers (varying from 1 to 4 fingers, visual feedback of total force, 5 s), and then to reproduce only the index or little finger portion of the total reference force (i.e., a portion of the sum, no visual feedback, 4 s) after a brief relaxation period (visual feedback of all finger forces, 3 s). The absolute force that individual fingers produced was approximately 30% of single-finger maximal force across different multi-finger reference force production tasks. During subsequent force matching, the index finger matching force was not significantly different from its own reference force, independent of the number of simultaneously activated fingers. The little finger, in contrast, produced significantly greater matching forces when three (middle, ring, and little) or four (index, middle, ring and little) fingers, but not two (ring and little) fingers, were simultaneously activated. The results suggest that index finger forces are more accurately estimated than little finger forces during multi-finger force production. The disparity in perception of individual finger forces is likely due to the ability of the central nervous system to partition and direct descending motor commands to the index finger.

Effects of friction at the digit-object interface on the digit forces in multi-finger prehension

The effects of surface friction at the digit-object interface on digit forces were studied when subjects (n=8) statically held an object in a five-digit grasp. The friction conditions were SS (all surfaces are sandpaper), RR (all are rayon), SR (S for the thumb and R for the four fingers), and RS (the reverse of SR). The interaction effects of surface friction and external torque were also examined using five torques (-0.5, -0.25, 0, +0.25, +0.5 Nm). Forces and moments exerted by the digits on a handle were recorded. At zero torque conditions, in the SS and RR (symmetric) tasks the normal forces of the thumb and virtual finger (VF, an imagined finger with the mechanical effect equal to that of the four fingers) were larger for the RR than the SS conditions. In the SR and RS (asymmetric) tasks, the normal forces were between the RR and SS conditions. Tangential forces were smaller at the more slippery side than at the less slippery side. According to the mathematical optimization analysis decreasing the tangential forces at the more slippery sides decreases the cost function values. The difference between the thumb and VF tangential forces, DeltaF (t), generated a moment of the tangential forces (friction-induced moment). At non-zero torque conditions the friction-induced moment and the moment counterbalancing the external torque (equilibrium-necessitated moment) could be in same or in opposite directions. When the two moments were in the same direction, the contribution of the moment of tangential forces to the total moment was large, and the normal forces were relatively low. In contrast, when the two moments were in opposite directions, the contribution of the moment of tangential forces to the total moment markedly decreased, which was compensated by an increase in the moment of normal forces. The apparently complicated results were explained as the result of summation of the friction-related (elemental) and torque-related (synergy) components of the central commands to the individual digits.

The effect of enslaving on perception of finger forces

The primary purpose was to examine the effect of enslaving on finger force perception during isometric finger force production using an ipsilateral force-matching paradigm. Fourteen subjects were instructed to produce varying levels of reference forces [10, 20, 30, and 40% maximal voluntary contraction (MVC)] force using one finger (index, I or little, L) and to reproduce these forces using the same finger (homo-finger tasks, I/I and L/L) or a different finger (hetero-finger tasks, I/L and L/I). Forces of all fingers were recorded. During homo-finger tasks, no differences were found in force magnitude or relative level of force (expressed as a proportion of MVC). The index finger matching force magnitudes were greater than the little finger reference force magnitudes, with significantly lower levels of relative force during L/I tasks; while the little finger matching forces underestimated the index finger reference forces with significantly higher levels of relative force during I/L tasks. The difference in the matching and reference forces by the instructed finger(s), i.e., matching error, was larger in hetero-finger tasks than in homo-finger tasks, particularly at high reference force levels (30, 40% MVC). When forces of all fingers were considered, enslaving (uninstructed finger forces) significantly minimized matching errors of the total force during both I/L and L/I hetero-finger tasks, especially at high reference force levels. Our results show that there is a tendency to match the absolute magnitude of the total force during ipsilateral finger force-matching tasks. This tendency is likely related to enslaving effects. Our results provide evidence that all (instructed and uninstructed) finger forces are sensed, thus resulting in perception of the absolute magnitude of total finger force.

Prehension stability: experiments with expanding and contracting handle

We studied adjustments in digit forces and moments during holding a vertically oriented handle under slow, externally imposed changes in the width of the grasp. Subjects (n = 8) grasped a customized motorized handle with five digits and held it statically in the air. The handle width either increased (expanded) or decreased (contracted) at a rate of 1.0, 1.5, or 2.0 mm/s, while the subjects were asked to ignore the handle width changes, and their attention was distracted. External torques of 0.0, 0.25, and 0.5 Nm were applied to the handle in two directions. Forces and moments at the digit tips were measured with six-component sensors. The analysis was performed at the virtual finger (VF) and individual finger (IF) levels (VF is an imagined finger that produces the same wrench, i.e., the force and moment, as several fingers combined). In all the tasks, the normal VF and thumb forces increased with the handle expansion and decreased with the handle contraction. Similar behavior was seen for the thumb tangential force. In contrast, the VF tangential force decreased with the handle expansion and increased with the handle contraction. The changes in the tangential forces assisted the perturbations in the tasks requiring exertion of the supination moments and annulled the perturbation in the pronation effort tasks. In the former tasks, the equilibrium was maintained by the changes of the moments of normal forces, whereas in the latter tasks, the equilibrium was maintained by the changes of the moments of the tangential forces. Analysis at the IF level has shown that the resultant force and moment exerted on the object could arise from dissimilar adjustments of individual fingers to the same handle width change. The complex adjustments of digit forces to handle width change may be viewed as coming from two sources. First, there are local spring-like adjustments of individual digit forces and moments caused by both mechanical properties of the digits and the action of spinal reflexes. These stiffness-like reactions mainly assist in perturbing the rotational equilibrium of the object rather than in maintaining it. Second, there are tilt-preventing adjustments defined by the common task constraints that unite the digits into a task-specific synergy. The "virtual springs theory" developed in robotics literature is insufficient for describing the phenomena observed in human grasping.

Maintaining rotational equilibrium during object manipulation: linear behavior of a highly non-linear system

We address issues of simultaneous control of the grasping force and the total moment of forces applied to a handheld object during its manipulation. Six young healthy male subjects grasped an instrumented handle and performed its cyclic motion in the vertical direction. The handle allowed for setting different clockwise (negative) or counterclockwise torques. Three movement frequencies: 1, 1.5 and 2 Hz, and five different torques: -1/3, -1/6, 0, 1/6 and 1/3 Nm, were used. The rotational equilibrium was maintained by two means: (1) Concerted changes of the moments produced by the normal and tangential forces, specifically anti-phase changes of the moments during the tasks with zero external torque and in-phase changes during the non-zero-torque tasks, and (2) Redistribution of the normal forces among individual fingers such that the agonist fingers--the fingers that resist external torque--increased the force in phase with the acceleration, while the forces of the antagonist fingers--those that assist the external torque--especially, the fingers with the large moment arms, the index and little fingers, stayed unchanged. The observed effects agree with the principle of superposition--according to which some complex actions, for example, prehension, can be decomposed into elemental actions controlled independently--and the mechanical advantage hypothesis according to which in moment production the fingers are activated in proportion to their moment arms with respect to the axis of rotation. We would like to emphasize the linearity of the observed relations, which was not prescribed by the task mechanics and seems to be produced by specific neural control mechanisms.

Prehension synergies during nonvertical grasping, II: Modeling and optimization

This study examines various optimization criteria as potential sources of constraints that eliminate (or at least reduce the degree of) mechanical redundancy in prehension. A model of nonvertical grasping mimicking the experimental conditions of Pataky et al. (current issue) was developed and numerically optimized. Several cost functions compared well with experimental data including energylike functions, entropylike functions, and a ''motor command'' function. A tissue deformation function failed to predict finger forces. In the prehension literature, the ''safety margin'' (SM) measure has been used to describe grasp quality. We demonstrate here that the SM is an inappropriate measure for nonvertical grasps. We introduce a new measure, the ''generalized safety margin'' (GSM), which reduces to the SM for vertical and two-digit grasps. It was found that a close-to-constant GSM accounts for many of the finger force patterns that are observed when grasping an object oriented arbitrarily with respect to the gravity field. It was hypothesized that, when determining finger forces, the CNS assumes that a grasped object is more slippery than it actually is. An ''operative friction coefficient'' of approximately 30% of the actual coefficient accounted for the offset between experimental and optimized data. The data suggest that the CNS utilizes an optimization strategy when coordinating finger forces during grasping.

Prehension synergies during nonvertical grasping, I: experimental observations

The mechanical complexities of rotating an object through the gravity field present a formidable challenge to the human central nervous system (CNS). The current study documents the finger force patterns selected by the CNS when performing one-, two-, and four-finger grasping while holding an object statically at various orientations with respect to vertical. Numerous mechanically "unnecessary" behaviors were observed. These included: nonzero tangential forces for horizontal handle orientations, large internal forces (i.e., those in excess of equilibrium requirements) for all orientations, and safety margins between 50 and 90%. Additionally, none of the investigated measures were constant across orientations or could be represented as a simple trigonometric function of orientation. Nonetheless, all measures varied in systematic (and sometimes symmetric) ways with orientation. The results suggest that the CNS selects force patterns that are based on mechanical principles but also that are not simply related to object orientation. This study is complemented by a second paper that provides an in-depth analysis of the mechanics of nonvertical grasping and accounts for many of the observed results with numerical optimization (see Part II - current issue). Together, the papers demonstrate that the CNS is likely to utilize optimization processes when controlling prehensile actions.