Force and torque production in static multifinger prehension: biomechanics and control. I. Biomechanics

 We studied the coordinated action of fingers during static tasks involving exertion of force and torque on a handheld object. Subjects were asked to keep a handle with an attachment that allowed for independent change of the suspended load (0.5–2.0 kg) and external torque (0.375–1.5 N m) in a vertical position while applying minimal effort. Normal and shear forces were measured from the thumb; normal forces only were measured from the four fingers. Experimental results: (1) the thumb shear force increased during supination efforts and decreased during pronation efforts; (2) the total moment of the normal finger forces only counterbalanced approximately 50% of the external torque, hence shear forces accounted for approximately one-half of the total torque exerted on the object; (3) the total normal force increased with external torque, and the total force magnitude did not depend on the torque direction; (4) the forces of the `peripheral' (index and little) fingers depended mainly on the torque while the forces exerted by the `central' (middle and ring) fingers depended both on the load and torque; (5) there was a monotonic relationship between the mechanical advantage of a finger (i.e., its moment arm during torque production) and the force produced by that finger; and (6) antagonist finger moments acting opposite to the intended direction of the total moment were always observed – at low torques the antagonist moments were as high as 40–60% of the agonist moments. Modeling: A three-zone model of coordinated finger action is suggested. In the first zone of load/torque combinations, activation of antagonist fingers (i.e., fingers that generate antagonist moments) is necessary to prevent slipping. In the second zone, the activity of agonist fingers is sufficient for preventing slips. In the third zone, the performer has freedom to choose between either activating the antagonist fingers or redistributing activities amongst the agonist fingers. The findings of this study provide the foundation for neural network and optimization modeling described in the companion paper [Zatsiorsky et al. (2002) Biol Cybern DOI 10.1007/s00422-002-0320-7]. Received: 8 August 2001 / Accepted in revised form: 7 February 2002     

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.     

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-df force/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.     

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.     

Force and torque production in static multifinger prehension: biomechanics and control. II. Control

 The coordination of digits during combined force/torque production tasks was further studied using the data presented in the companion paper [Zatsiorsky et al. Biol Cybern this issue, Part I]. Optimization was performed using as criteria the cubic norms of (a) finger forces, (b) finger forces normalized with respect to the maximal forces measured in single-finger tasks, (c) finger forces normalized with respect to the maximal forces measured in a four-finger task, and (d) finger forces normalized with respect to the maximal moments that can be generated by the fingers. All four criteria failed to predict antagonist finger moments when these moments were not imposed by the task mechanics. Reconstruction of neural commands: The vector of neural commands c was reconstructed from the equation c=W ⁻¹ F, where W is the finger interconnection weight matrix and F is the vector of finger forces. The neural commands ranged from zero (no voluntary force production) to one (maximal voluntary contraction). For fingers producing moments counteracting the external torque (`agonist' fingers), the intensity of the neural commands was well correlated with the relative finger forces normalized to the maximal forces in a four-finger task. When fingers produced moments in the direction of the external torque (`antagonist' fingers), the relative finger forces were always larger than those expected from the intensity of the corresponding neural commands. The individual finger forces were decomposed into forces due to `direct' commands and forces induced by enslaving effects. Optimization of the neural commands resulted in the best correspondence between actual and predicted finger forces. The antagonist moments are, at least in part, due to enslaving effects: strong commands to agonist fingers also activated antagonist fingers. Received: 8 August 2001 / Accepted in revised form: 7 February 2002     

Tactile feedback plays a critical role in maximum finger force production

This study investigates the role of cutaneous feedback on maximum voluntary force (MVF), finger force deficit (FD) and finger independence (FI). FD was calculated as the difference between the sum of maximal individual finger forces during single-finger pressing tasks and the maximal force produced by those fingers during an all-finger pressing task. FI was calculated as the average non-task finger forces normalized by the task-finger forces and subtracted from 100 percent. Twenty young healthy right-handed males participated in the study. Cutaneous feedback was removed by administering ring block digital anesthesia on the 2nd, 3rd, 4th and 5th digits of the right hands. Subjects were asked to press force sensors with maximal effort using individual digits as well as all four digits together, with and without cutaneous feedback. Results from the study showed a 25% decrease in MVF for the individual fingers as well as all the four fingers pressing together after the removal of cutaneous feedback. Additionally, more than 100% increase in FD after the removal of cutaneous feedback was observed in the middle and ring fingers. No changes in FI values were observed between the two conditions. Results of this study suggest that the central nervous system utilizes cutaneous feedback and the feedback mechanism plays a critical role in maximal voluntary force production by the hand digits.     

Age-related changes in finger coordination in static prehension tasks.

We studied age-related changes in the performance of maximal and accurate submaximal force and moment production tasks. Elderly and young subjects pressed on six dimensional force sensors affixed to a handle with a T-shaped attachment. The weight of the whole system was counterbalanced with another load. During tasks that required the production of maximal force or maximal moment by all of the digits, young subjects were stronger than elderly. A greater age-related deficit was seen in the maximal moment production tests. During maximal force production tests, elderly subjects showed larger relative involvement of the index and middle fingers; they moved the point of thumb force application upward (toward the index and middle fingers), whereas the young subjects rolled the thumb downward. During accurate force/moment production trials, elderly persons were less accurate in the production of both total moment and total force. They produced higher antagonistic moments, i.e., moment by fingers that acted against the required direction of the total moment. Both young and elderly subjects showed negative covariation of finger forces across repetitions of a ramp force production task. In accurate moment production tasks, both groups showed negative covariation of two components of the total moment: those produced by the normal forces and those produced by the tangential forces. However, elderly persons showed lower values of the indexes of both finger force covariation and moment covariation. We conclude that age is associated with an impaired ability to produce both high moments and accurate time profiles of moments. This impairment goes beyond the well-documented deficits in finger and hand force production by elderly persons. It involves worse coordination of individual digit forces and of components of the total moment. Some atypical characteristics of finger forces may be viewed as adaptive to the increased variability in the force production with age.     

Acceleration Workspace of Cooperating Multi-Finger Robot Systems

We present a mathematical method for acceleration workspace analysis of cooperating multi-finger robot systems using a model of point-contact with friction. A new unified formulation from dynamic equations of cooperating multi-finger robots is derived considering the force and acceleration relationships between the fingers and the object to be handled. From the dynamic equation, maximum translational and rotational acceleration bounds of an object are calculated under given constraints of contact conditions, configurations of fingers, and bounds on the torques of joint actuators for each finger. Here, the rotational acceleration bounds can be applied as an important manipulability index when the multi-finger robot grasps an object. To verify the proposed method, we used a set of case studies with a simple multi-finger mechanism system. The achievable acceleration boundary in task space can be obtained successfully with the proposed method and the acceleration boundary depends on the configurations of fingers.     

Incorporating the length-dependent passive-force generating muscle properties of the extrinsic finger muscles into a wrist and finger biomechanical musculoskeletal model

Dynamic movement trajectories of low mass systems have been shown to be predominantly influenced by passive viscoelastic joint forces and torques compared to momentum and inertia. The hand is comprised of 27 small mass segments. Because of the influence of the extrinsic finger muscles, the passive torques about each finger joint become a complex function dependent on the posture of multiple joints of the distal upper limb. However, biomechanical models implemented for the dynamic simulation of hand movements generally don’t extend proximally to include the wrist and distal upper limb. Thus, they cannot accurately represent these complex passive torques. The purpose of this short communication is to both describe a method to incorporate the length-dependent passive properties of the extrinsic index finger muscles into a biomechanical model of the upper limb and to demonstrate their influence on combined movement of the wrist and fingers. Leveraging a unique set of experimental data, that describes the net passive torque contributed by the extrinsic finger muscles about the metacarpophalangeal joint of the index finger as a function of both metacarpophalangeal and wrist postures, we simulated the length-dependent passive properties of the extrinsic finger muscles. Dynamic forward simulations demonstrate that a model including these properties passively exhibits coordinated movement between the wrist and finger joints, mimicking tenodesis, a behavior that is absent when the length-dependent properties are removed. This work emphasizes the importance of incorporating the length-dependent properties of the extrinsic finger muscles into biomechanical models to study healthy and impaired hand movements.     

Anticipatory synergy adjustments in preparation to self-triggered perturbations in elderly individuals

We tested the ability of healthy elderly persons to use anticipatory synergy adjustments (ASAs) prior to a self-triggered perturbation of one of the fingers during a multifinger force production task. An index of a force-stabilizing synergy was computed reflecting covariation of commands to fingers. The subjects produced constant force by pressing with the four fingers of the dominant hand on force sensors against constant upwardly directed forces. The middle finger could be unloaded either by the subject pressing the trigger or unexpectedly by the experimenter. In the former condition, the synergy index showed a drop (interpreted as ASA) prior to the time of unloading. This drop started later and was smaller in magnitude as compared with ASAs reported in an earlier study of younger subjects. At the new steady state, a new sharing pattern of the force was reached. We conclude that aging is associated with a preserved ability to explore the flexibility of the mechanically redundant multifinger system but a decreased ability to use feedforward adjustments to self-triggered perturbations. These changes may contribute to the documented drop in manual dexterity with age.     

Matrix analyses of interaction among fingers in static force production tasks

The fingers on a hand show interactions in force production tasks. The interfinger connection matrices (IFMs) quantify these interactions (Li et al. 2002; Zatsiorsky et al. 2002b; Danion et al. 2003). The goal of the present study was to explore the differences in the IFMs of individual subjects and, in particular, to establish a procedure that may be used in the future for diagnostic purposes. Subjects (n=20) pressed downward maximally with ten different combinations of the four fingers, index (I), middle (M), ring (R), and little (L): I, M, R, L, IM, MR, RL, IMR, MRL, and IMRL. Voluntary activation of a subset of the four fingers was accompanied by an involuntary force production by fingers that were not intentionally activated (enslaving). Interfinger connection matrices were computed for each subject by the artificial neural network. The similarities/dissimilarities (proximities) between the individual matrices were determined. This procedure was performed twice: (a) for nonnormalized IFMs whose elements represented the amount of force (in newtons) exerted by a finger i in response to a unit command to a finger j; and (b) for normalized IFMs, after dividing the elements of each IFM by the total force produced by the four fingers acting together (the elements of the matrix are in percents). The 20×20 matrix of the proximities was subjected to multidimensional scaling (MDS) to reduce the number of dimensions and identify the major ones. To interpret the meaning of the computed dimensions, they were regressed on a set of finger force parameters described in the text. For the nonnormalized IFMs an interpretable dimension was the strength of the subjects. For the normalized IFMs two dimensions were interpreted: (a) the location of the point of resultant force application along the mediolateral axis that is defined by the pattern of force sharing among the fingers and (b) the total contribution of the enslaved forces into the total finger force. We speculate that the similarity of typical everyday tasks across the population promotes the similarity of the IMFs reflecting optimal hand functioning over these tasks. AcknowledgementsThis study was partly supported by NIH grants NS-35032, AR-048563 and AG-18751. The support from the Whittaker Foundation to Dr. Z.M. Li is also acknowledged.     

One Digit Interruption: The Altered Force Patterns during Functionally Cylindrical Grasping Tasks in Patients with Trigger Digits

Most trigger digit (TD) patients complain that they have problems using their hand in daily or occupational tasks due to single or multiple digits being affected. Unfortunately, clinicians do not know much about how this disease affects the subtle force coordination among digits during manipulation. Thus, this study examined the differences in force patterns during cylindrical grasp between TD and healthy subjects. Forty-two TD patients with single digit involvement were included and sorted into four groups based on the involved digits, including thumb, index, middle and ring fingers. Twelve healthy subjects volunteered as healthy controls. Two testing tasks, holding and drinking, were performed by natural grasping with minimal forces. The relations between the force of the thumb and each finger were examined by Pearson correlation coefficients. The force amount and contribution of each digit were compared between healthy controls and each TD group by the independent t test. The results showed all TD groups demonstrated altered correlation patterns of the thumb relative to each finger. Larger forces and higher contributions of the index finger were found during holding by patients with index finger involved, and also during drinking by patients with affected thumb and with affected middle finger. Although no triggering symptom occurred during grasping, the patients showed altered force patterns which may be related to the role of the affected digit in natural grasping function. In conclusion, even if only one digit was affected, the subtle force coordination of all the digits was altered during simple tasks among the TD patients. This study provides the information for the future studies to further comprehend the possible injuries secondary to the altered finger coordination and also to adopt suitable treatment strategies.     

The Force Synergy of Human Digits in Static and Dynamic Cylindrical Grasps

This study explores the force synergy of human digits in both static and dynamic cylindrical grasping conditions. The patterns of digit force distribution, error compensation, and the relationships among digit forces are examined to quantify the synergetic patterns and coordination of multi-finger movements. This study recruited 24 healthy participants to perform cylindrical grasps using a glass simulator under normal grasping and one-finger restricted conditions. Parameters such as the grasping force, patterns of digit force distribution, and the force coefficient of variation are determined. Correlation coefficients and principal component analysis (PCA) are used to estimate the synergy strength under the dynamic grasping condition. Specific distribution patterns of digit forces are identified for various conditions. The compensation of adjacent fingers for the force in the normal direction of an absent finger agrees with the principle of error compensation. For digit forces in anti-gravity directions, the distribution patterns vary significantly by participant. The forces exerted by the thumb are closely related to those exerted by other fingers under all conditions. The index-middle and middle-ring finger pairs demonstrate a significant relationship. The PCA results show that the normal forces of digits are highly coordinated. This study reveals that normal force synergy exists under both static and dynamic cylindrical grasping conditions.     

Do relevant shear forces appear in isokinetic shoulder testing to be implemented in biomechanical models?

Isokinetic dynamometers measure joint torques about a single fixed rotational axis. Previous studies yet suggested that muscles produce both tangential and radial forces during a movement, so that the contact forces exerted to perform this movement are multidirectional. Then, isokinetic dynamometers might neglect the torque components about the two other Euclidean space axes. Our objective was to experimentally quantify the shear forces impact on the overall shoulder torque, by comparing the dynamometer torque to the torque computed from the contact forces at the hand and elbow. Ten healthy women performed isokinetic maximal internal/external concentric/eccentric shoulder rotation movements. The hand and elbow contact forces were measured using two six-axis force sensors. The main finding is that the contact forces at the hand were not purely tangential to the direction of the movement (effectiveness indexes from 0.26 ± 0.25 to 0.54 ± 0.20), such that the resulting shoulder torque computed from the two force sensors was three-dimensional. Therefore, the flexion and abduction components of the shoulder torque measured by the isokinetic dynamometer were significantly underestimated (up to 94.9%). These findings suggest that musculoskeletal models parameters should not be estimated without accounting for the torques about the three space axes.     

The effect of weightbearing and external loading on anterior cruciate ligament strain

A force balance between the ligaments, articular contact, muscles and body weight maintains knee joint stability. Thus, it is important to study anterior cruciate ligament (ACL) biomechanics, in vivo, under weightbearing conditions. Our objective was to compare the ACL strain response under weightbearing and non-weightbearing conditions and in combination with three externally applied loadings: (1) anterior-posterior shear forces, (2) internal-external torques, and (3) varus-valgus moments. A strain transducer was implanted on the ACL of 11 subjects. All joint loadings were performed with the knee at 20 degrees of flexion. A significant increase in ACL strain was observed as the knee made the transition from non-weightbearing to weightbearing. During anterior shear loading, the strain values produced during weightbearing were greater than those of the non-weightbearing knee (shear loads <40N). At higher shear loads, the strain values became equal. During axial torsion, an internal torque of 10Nm strained the ACL when the knee was non-weightbearing while an equivalent external torque did not. Weightbearing significantly increased ACL strain values in comparison to non-weightbearing with the application of external torques and low internal torques (<3Nm). The strains became equal for higher internal torques. For V-V loading, the ACL was not strained in the non-weightbearing knee. However, weightbearing increased the ACL strain values over the range of moments tested. These data have important clinical ramifications in the development of rehabilitation protocols following ACL reconstruction since weightbearing has been previously thought to provide a protective mechanism to the healing graft.     

Close interdependence between passive and active soleus muscle torques in man: approach to the coregulation of the number of sarcomeres and length of the connective tissue

Soleus muscle has, to as great an extent as possible, been functionally isolated in man. A device previously described permitted measurement of the soleus torque as a function of the tibia-calcaneum angle, and not as a function of tibia-foot angle. This latter angle cannot be correctly related to soleus length, since the arch of the foot can not be considered as rigid throughout the experiment. Ankle movements were performed on a horizontal plane by successive increments of 5 degrees from full extension (plantar flexion) up to full flexion (dorsiflexion). Passive torques were measured for every angle. At the same angles, the total torques were recorded while the subject exerted a voluntary constant contraction which corresponded to 45% of the maximum integrated electromyographical activity of soleus muscle. The active torque-angle curve was obtained by subtracting, for the same angle, the passive from the total torques. It must be stressed that, when the muscle is maximally shortened, little or no torque was measured. For the angle corresponding to the top of the sub-maximal active curve (integrated electromyographic activity 45% of the maximum), the passive torque was about 1.75 Nm and showed no significant interindividual variations. This result contrasted with the marked interindividual shifts which affect both passive and active curves. This interdependence of passive and active curves in human soleus muscle is compatible with the results of a previous study in the cat showing the concomitant adaptations of sarcomere number and connective tissue length.     

Human plantarflexor stiffness to multiple single-stretch trials.

The purpose of this investigation was to determine the influence of different stretch velocities, different rates of pre-stretch force development, and different pre-stretch muscle lengths on the intrinsic stiffness exhibited by the quasi-statically contracting active human plantarflexors during multiple single-stretch trials at 20-60% of maximum isometric contraction. Subjects were positioned prone, with the knee flexed 1.57 rad(90 degrees), shank stabilized, and foot secured in a hard plastic orthotic. Slowly increasing isometric plantarflexion force was produced until the plantarflexors were stretched by a rapid 0.2 rad (12 degrees) dorsiflexion movement. Plantarflexion forces and ankle positions were determined during these stretches as well as during resting stretches when the muscle was inactive. Resting forces were subtracted from the active trials, forces converted to torques, and stiffnesses determined for the first 62 ms of the stretch. The slope of the stiffness vs pre-stretch torque relationship averaged 4.30 +/- 0.34 Nm rad-1 Nm-1. Little difference was found between stiffness determined through the single-stretch method and the results of previous studies employing different mechanical inputs. Differences in stiffnesses with different stretching velocities were caused by computational artifact rather than by differences in intrinsic muscular reaction. Faster rates of pre-stretch force increase prior to the stretch resulted in slightly lower stiffnesses. Different pre-stretch muscle lengths apparently did not result in different stiffnesses. The shape of the torque vs displacement curve was remarkably insensitive to the planned manipulations of the testing conditions, responding in a stereotypical manner.     

Indices of nonlinearity in finger force interaction

Experiments with force production by subsets of fingers within the human hand have shown that finger interaction may be significantly nonlinear. In particular, this nonlinearity is reflected in the phenomenon of force deficit, a drop of the peak force of a finger when several fingers act simultaneously. We describe nonlinear effects in force relations within finger pairs, triplets, etc. Finger forces are represented as the sums of components resulting from force interactions within all subsets of the explicitly involved (master) fingers. The values of these components computed at extreme values of control signals, zero and unity, are taken as indices of such elementary force interactions. Indices of the first order reflect purposeful force production by a single master finger and its effects on forces produced by other fingers (enslaving). Indices of the second order reflect additional influences from pairs of simultaneously recruited master fingers, etc. Force interaction indices were computed based on finger forces measured in earlier experiments. Signs of indices alternated with their order, being positive for the indices of the first order (enslaving), negative for the indices of the second order (force deficit), positive for the indices of the third order, and mostly negative for the indices of the fourth order. Indices of the third and fourth orders reflect phenomena of force interaction not reported earlier. The study emphasizes the importance of nonlinear interactions among finger forces and introduces a set of independent indices that can be used to quantify such interactions in different subpopulations and their possible changes with practice and/or rehabilitation of the hand function.     

The role of cutaneous feedback for anticipatory grip force adjustments during object movements and externally imposed variation of the direction of gravity

Grip force adjustments to changes of object loading induced by external changes of the direction of gravity during discrete arm movements with a grasped object were analyzed during normal and anesthetized finger sensibility. Two subjects were seated upright in a rotatable chair and rotated backwards into a horizontal position during discrete movements with a hand-held instrumented object. The movement direction varied from vertical to horizontal inducing corresponding changes in the direction of gravity, but the orientation of the movement in relation to the body remained unaffected. During discrete vertical movements a maximum of load force occurs early in upward and late in downward movements; during horizontal movements two load force peaks result from both acceleratory and deceleratory phases of the movement. During performance with normal finger sensibility grip force was modulated in parallel with fluctuations of load force during vertical and horizontal movements. The grip force profile adopted to the varying load force profile during the transition from the vertical to the horizontal position. The maximum grip force occurred at the same time of maximum load force irrespective of the movement plane. During both subjects' first experience of digital anesthesia the object slipped from the grasp during rotation to the horizontal plane. During the following trials with anesthetized fingers subjects substantially increased their grip forces, resulting in elevated force ratios between maximum grip and load force. However, grip force was still modulated with the movement-induced load fluctuations and maximum grip force coincided with maximum load force during vertical and horizontal movements. This implies that the elevated force ratio between maximum grip and load force does not alter the feedforward system of grip force control. Cutaneous afferent information from the grasping digits seems to be important for the economic scaling of the grip force magnitude according to the actual loading conditions and for reactive grip force adjustments in response to load perturbations. However, it plays a subordinate role for the precise anticipatory temporal coupling between grip and load forces during voluntary object manipulation.