Prehension stability: experiments with expanding and contracting handle

Hierarchical and synergistic organization of control variables during the multi-digit grasp of a free and an externally fixed object

In the referent control theory, grip force emerges by designating the referent aperture (R_a) as a threshold position inside the object. This study quantified R_a and investigated whether the synergistic control of digit referent coordinate (RC) and apparent stiffness (k) depend on the external mechanical constraints on the hand-held object. Subjects held a motorized handle capable of adjusting the grip width and performed static multi-digit prehension tasks in which the handle was free and externally fixed in different conditions. The RC and k of individual digits were reconstructed from the changes in digit normal forces and the positions as the grip width was modulated. RCs of the thumb and virtual finger were used to calculate the width and midpoint of R_a, and synergy indices quantifying the task-specific covariation in the space of the digit normal forces and {RC, k} variables were computed. We found that the k and width of the R_a were larger when holding a free handle than the fixed handle. The higher stiffness in the free condition could be a strategy to ensure grip stability. The midpoint of R_a was skewed toward the virtual finger, reflecting different magnitudes of k for the two digits. Further, the normal forces and control variables {RC, k} displayed synergistic covariation for stabilization of the total grasping force. Finally, the synergies were weaker when the handle was externally fixed, demonstrating the dependence of synergies on external constraints. These results add to the current literature by demonstrating that grasp control involves modulation of digit apparent stiffness in addition to the referent coordinate and by identifying the synergistic organization of the control variables during static grasp.

Datasets of fingertip forces while grasping a handle with unsteady thumb platform

This article presents the fingertip forces and moments data of the individual fingers and thumb when the thumb was placed on an unsteady platform, when the mass of the handle was systematically increased and when the thumb normal force was restricted while grasping a handle. Further, this article also includes a dataset while the thumb makes vertical movements such as extension (or upward motion) and flexion movement (or downward motion) during the static holding of a handle. An instrumented five-finger prehension handle was designed with a vertical railing on the thumb side. A slider platform was placed over the railing to mount the thumb force sensor. Further, a laser displacement sensor was mounted on top of the handle towards the thumb side to record the displacement of the thumb platform. The dataset includes fingertip forces, orientation of the handle, and the displacement data of thumb platform. This data helps therapists assess the degree of thumb disability, the contribution of ulnar fingers in establishing static equilibrium of a handheld object.

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.

Inverse Saxophone—A Device to Study the Role of Individual Finger Perturbations on Grasp Stability

The efficient coordination of fingertip forces to maintain static equilibrium while grasping an object continues to intrigue scientists. While many studies have explored this coordination, most of these studies assumed that interactions of hands primarily occur with rigid inanimate objects. Instead, our daily interactions with living and nonliving entities involve many dynamic, compliant, or fragile bodies. This paper investigates the fingertip force coordination on a manipulandum that changes its shape while grasping it. We designed a five-finger perturbation system with linear actuators at positions corresponding to each finger that would protrude outward from the center of the handle or retract toward the center of the handle as programmed. The behavior of the perturbed fingers and the other fingers while grasping this device was studied. Based on previous experiments on expanding and contracting handles, we hypothesized that each finger would exhibit a comparable response to similar horizontal perturbations. However, the response of the little finger was significantly different from the other fingers. We speculate that the central nervous system demonstrates preferential recruitment of some fingers over others while performing a 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.

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.

Moving a hand-held object: Reconstruction of referent coordinate and apparent stiffness trajectories

This study used the framework of the referent configuration hypothesis and slow changes in the external conditions during vertical oscillation of a hand-held object to infer the characteristics of hypothetical control variables. The study had two main objectives: (1) to show that hypothetical control variables, namely, referent coordinates and apparent stiffness of vertical hand position and grip force can be measured in an experiment; and (2) to establish relation(s) between these control variables that yield the classic grip-force-load-force coupling. Healthy subjects gripped a handle and performed vertical oscillations between visual targets at one of five metronome-prescribed frequencies. A HapticMaster robot was used to induce slow changes in the vertical force applied to the handle, while the size of the handle was changed slowly leading to changes in the grip aperture. The subjects were instructed not to react to possible changes in the external forces. A linear, second-order model was used to reconstruct the referent coordinate and apparent stiffness values for each phase of the vertical oscillation cycle using across-cycle regressions. The reconstructed time profiles of the referent coordinates and apparent stiffness showed consistent trends across subjects and movement frequencies. To validate the method, these values were used to predict the vertical force and the grip force applied to the handle for movement cycles that were not utilized in the reconstruction process. Analysis of the coupling between the four variables, two referent coordinates and two apparent stiffness values, revealed a single strong constraint reflecting the coupling between the grip force and vertical force. We view these data as providing experimental support for the idea of controlling natural, multi-muscle actions with shifts in a low-dimensional set of referent coordinates.

A method to study precision grip control in viscoelastic force fields using a robotic gripper

Instrumented objects and multipurpose haptic displays have commonly been used to investigate sensorimotor control of grasping and manipulation. A major limitation of these devices, however, is the extent to which the experimenter can vary the interaction dynamics to fully probe sensorimotor control mechanisms. We propose a novel method to study precision grip control using a grounded robotic gripper with two moving, mechanically coupled finger pads instrumented with force sensors. The device is capable of stably rendering virtual mechanical properties with a wide dynamic range of achievable impedances. Eight viscoelastic force fields with different combinations of stiffness and damping parameters were implemented, and tested on eight healthy subjects performing 30 consecutive repetitions of a grasp, hold, and release task with time and position constraints. Rates of thumb and finger force were found to be highly correlated (r>0.9) during grasping, revealing that, despite the mechanical coupling of the two finger pads, subjects performed grasping movements in a physiological fashion. Subjects quickly adapted to the virtual dynamics (within seven trials), but, depending on the presented force field condition, used different control strategies to correctly perform the task. The proof of principle presented in this paper underscores the potential of such a one-degree-of-freedom robotic gripper to study neural control of grasping, and to provide novel insights on sensorimotor control mechanisms.

Factors affecting grip force: anatomy, mechanics, and referent configurations

The extrinsic digit muscles naturally couple wrist action and grip force in prehensile tasks. We explored the effects of wrist position on the steady-state grip force and grip-force change during imposed changes in the grip aperture [apparent stiffness (AS)]. Subjects held an instrumented handle steady using a prismatic five-digit grip. The grip aperture was changed slowly, while the subjects were instructed not to react voluntarily to these changes. An increase in the aperture resulted in an increase in grip force, and its contraction resulted in a proportional drop in grip force. The AS values (between 4 and 6 N/cm) were consistent across a wide range of wrist positions. These values were larger when the subjects performed the task with eyes open as compared to eyes-closed trials. They were also larger for trials that started from a larger initial aperture. After a sequence of aperture increase and decrease to the initial width, grip force dropped by about 25% without the subjects being aware of this. We interpret the findings within the referent configuration hypothesis of grip-force production. The results support the idea of back-coupling between the referent and actual digit coordinates. According to this idea, the central nervous system defines referent coordinates for the digit tips, and the difference between the referent and actual coordinates leads to force production. If actual coordinates are not allowed to move to referent ones, referent coordinates show a relatively slow drift toward the actual ones.

Task dependency of grip stiffness--a study of human grip force and grip stiffness dependency during two different tasks with same grip forces

It is widely known that the pinch-grip forces of the human hand are linearly related to the weight of the grasped object. Less is known about the relationship between grip force and grip stiffness. We set out to determine variations to these dependencies in different tasks with and without visual feedback. In two different settings, subjects were asked to (a) grasp and hold a stiffness-measuring manipulandum with a predefined grip force, differing from experiment to experiment, or (b) grasp and hold this manipulandum of which we varied the weight between trials in a more natural task. Both situations led to grip forces in comparable ranges. As the measured grip stiffness is the result of muscle and tendon properties, and since muscle/tendon stiffness increases more-or-less linearly as a function of muscle force, we found, as might be predicted, a linear relationship between grip force and grip stiffness. However, the measured stiffness ranges and the increase of stiffness with grip force varied significantly between the two tasks. Furthermore, we found a strong correlation between regression slope and mean stiffness for the force task which we ascribe to a force stiffness curve going through the origin. Based on a biomechanical model, we attributed the difference between both tasks to changes in wrist configuration, rather than to changes in cocontraction. In a new set of experiments where we prevent the wrist from moving by fixing it and resting it on a pedestal, we found subjects exhibiting similar stiffness/force characteristics in both tasks.

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.

Stabilization of the total force in multi-finger pressing tasks studied with the 'inverse piano' technique

When one finger changes its force, other fingers of the hand can show unintended force changes in the same direction (enslaving) and in the opposite direction (error compensation). We tested a hypothesis that externally imposed changes in finger force predominantly lead to error compensation effects in other fingers thus stabilizing the total force. A novel device, the "inverse piano", was used to impose controlled displacements to one of the fingers over different magnitudes and at different rates. Subjects (n=10) pressed with four fingers at a constant force level and then one of the fingers was unexpectedly raised. The subjects were instructed not to interfere with possible changes in the finger forces. Raising a finger caused an increase in its force and a drop in the force of the other three fingers. Overall, total force showed a small increase. Larger force drops were seen in neighbors of the raised finger (proximity effect). The results showed that multi-finger force stabilizing synergies dominate during involuntary reactions to externally imposed finger force changes. Within the referent configuration hypothesis, the data suggest that the instruction "not to interfere" leads to adjustments of the referent coordinates of all the individual fingers.

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.

Multi-finger prehension: control of a redundant mechanical system

The human hand has been a fascinating object of study for researchers in both biomechanics and motor control. Studies of human prehension have contributed significantly to the progress in addressing the famous problem of motor redundancy. After a brief review of the hand mechanics, we present results of recent studies that support a general view that the apparently redundant design of the hand is not a source of computational problems but a rich apparatus that allows performing a variety of tasks in a reliable and flexible way (the principle of abundance). Multi-digit synergies have been analyzed at two levels of a hypothetical hierarchy involved in the control of prehensile actions. At the upper level, forces and moments produced by the thumb and virtual finger (an imagined finger with a mechanical action equal to the combined mechanical action of all four fingers of the hand) co-vary to stabilize the gripping action and the orientation of the hand-held object. These results support the principle of superposition suggested earlier in robotics with respect to the control of artificial grippers. At the lower level of the hierarchy, forces and moments produced by individual fingers co-vary to stabilize the magnitude and direction of the force vector and the moment of force produced by the virtual finger. Adjustments to changes in task constraints (such as, for example, friction under individual digits) may be local and synergic. The latter reflect multi-digit prehension synergies and may be analyzed with the so-called chain effects: Sequences of relatively straightforward cause-effect links directly related to mechanical constraints leading to non-trivial strong co-variation between pairs of elemental variables. Analysis of grip force adjustments during motion of hand-held objects suggests that the central nervous system adjusts to gravitational and inertial loads differently. The human hand is a gold mine for researchers interested in the control of natural human movements.

Spatio-Temporal Human Grip Force Analysis via Sensor Arrays

This study describes a technique for measuring human grip forces exerted on a cylindrical object via a sensor array. Standardised resistor-based pressure sensor arrays for industrial and medical applications have been available for some time. We used a special 20 mm diameter grip rod that subjects could either move actively with their fingers in the horizontal direction or exert reactive forces against opposing forces generated in the rod by a linear motor. The sensor array film was attached to the rod by adhesive tape and covered approximately 45 cm² of the rod surface. The sensor density was 4/cm² with each sensor having a force resolution of 0.1 N. A scan across all sensors resulted in a corresponding frame containing force values at a frame repetition rate of 150/s. The force value of a given sensor was interpreted as a pixel value resulting in a false-colour image. Based on remote sensed image analysis an algorithm was developed to distinguish significant force-representing pixels from those affected by noise. This allowed tracking of the position of identified fingers in subsequent frames such that spatio-temporal grip force profiles for individual fingers could be derived. Moreover, the algorithm allowed simultaneous measurement of forces exerted without any constraints on the number of fingers or on the position of the fingers. The system is thus well suited for basic and clinical research in human physiology as well as for studies in psychophysics.

Sensorimotor control of contact force

Interacting with objects in the environment introduces several new challenges for motor control: the potential for instability, external constraints on possible motions and novel dynamics. Grasping and manipulating objects provide the most elaborate examples of such motor tasks. We review each of these topics and suggest that when sensory feedback is reliable, it is used to adapt the motion to the requirements imposed by the object. When sensory feedback is unreliable, subjects adapt the stiffness of muscles and joints to the task's requirements. One of the simplifications introduced in the control of such movements is a reduction in the effective number of degrees of freedom (sensorimotor axes and muscle synergies) and recent findings and methodological considerations relevant to this topic are discussed.

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.

Detection of changes in grip forces on a sliding object

Holding a slipping object in hand requires adjustment of grip forces. The aim of the study was to develop a method for measuring the temporal and spatial distribution of grip forces during the holding of a slipping object in the hand. A special grip rod with a measuring film containing 200 resistor-based pressure sensors equally distributed over 50 cm(2) was developed, providing a system that has a spatial resolution of 5 mm, a temporal resolution of 1/150 Hz and a force resolution 0.05 N. A force-change-detection algorithm was constructed to detect and separate pressure and position of individual fingers. The algorithm is a modification of a classical Gaussian random field theory algorithm for detecting significant data [Rogerson PA. Change detection thresholds for remotely sensed images. J Geog Syst 2002;4:85-97]. The modification takes the signal strength into account to reduce false positive detection in low grip force situations. The grip force measuring system and the force-change-detection algorithm allow measurement of the forces exerted by any number of fingers simultaneously without any constraints on finger position and are suitable for basic and clinical research in human and animal physiology as well as for psychophysics studies.

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.

Prehension synergies in the grasps with complex friction patterns: local versus synergic effects and the template control

We studied adjustments of digit forces to changes in the friction. The subjects held a handle statically in a three-digit grasp. The friction under each digit was either high or low, resulting in eight three-element friction sets (such grasps were coined the grasps with complex friction pattern). The total load was also manipulated. It was found that digit forces were adjusted not only to the supported load and local friction, but also to friction at other digits (synergic effects). When friction under a digit was low, its tangential force decreased and the normal force increased (local effects). The synergic effects were directed to maintain the equilibrium of the handle. The relation between the individual digit forces and loads agreed with the triple-product model: f(i)(n) = k(i)((2))k(i)((1))L, where f(i)(n) is normal force of digit i, L is the load (newtons), k(i)((1)) is a dimensionless coefficient representing sharing the total tangential force among the digits (summation operator k(i)((1)) = 1.0), and k(i)((2)) is a coefficient representing the relation between the tangential and normal forces of digit i (the overall friction equivalent, OFE). At each friction set, the central controller selected the grasping template -- a three-element array of k(i)((2))k(i)((1)) products -- and then scaled the template with the load magnitude.