Fixation Biases towards the Index Finger in Almost-Natural Grasping

We use visual information to guide our grasping movements. When grasping an object with a precision grip, the two digits need to reach two different positions more or less simultaneously, but the eyes can only be directed to one position at a time. Several studies that have examined eye movements in grasping have found that people tend to direct their gaze near where their index finger will contact the object. Here we aimed at better understanding why people do so by asking participants to lift an object off a horizontal surface. They were to grasp the object with a precision grip while movements of their hand, eye and head were recorded. We confirmed that people tend to look closer to positions that a digit needs to reach more accurately. Moreover, we show that where they look as they reach for the object depends on where they were looking before, presumably because they try to minimize the time during which the eyes are moving so fast that no new visual information is acquired. Most importantly, we confirmed that people have a bias to direct gaze towards the index finger’s contact point rather than towards that of the thumb. In our study, this cannot be explained by the index finger contacting the object before the thumb. Instead, it appears to be because the index finger moves to a position that is hidden behind the object that is grasped, probably making this the place at which one is most likely to encounter unexpected problems that would benefit from visual guidance. However, this cannot explain the bias that was found in previous studies, where neither contact point was hidden, so it cannot be the only explanation for the bias.     

The spring-mass model for running and hopping

A simple spring-mass model consisting of a massless spring attached to a point mass describes the interdependency of mechanical parameters characterizing running and hopping of humans as a function of speed. The bouncing mechanism itself results in a confinement of the free parameter space where solutions can be found. In particular, bouncing frequency and vertical displacement are closely related. Only a few parameters, such as the vector of the specific landing velocity and the specific leg length, are sufficient to determine the point of operation of the system. There are more physiological constraints than independent parameters. As constraints limit the parameter space where hopping is possible, they must be tuned to each other in order to allow for hopping at all. Within the range of physiologically possible hopping frequencies, a human hopper selects a frequency where the largest amount of energy can be delivered and still be stored elastically. During running and hopping animals use flat angles of the landing velocity resulting in maximum contact length. In this situation ground reaction force is proportional to specific contact time and total displacement is proportional to the square of the step duration. Contact time and hopping frequency are not simply determined by the natural frequency of the spring-mass system, but are influenced largely by the vector of the landing velocity. Differences in the aerial phase or in the angle of the landing velocity result in the different kinematic and dynamic patterns observed during running and hopping. Despite these differences, the model predicts the mass specific energy fluctuations of the center of mass per distance to be similar for runners and hoppers and similar to empirical data obtained for animals of various size.     

The effect of torque direction and cylindrical handle diameter on the coupling between the hand and a cylindrical handle

Pheasant and O'Neill's torque model (1975) was modified to account for grip force distributions. The modified model suggests that skin friction produced by twisting an object in the direction of fingertips causes flexion of the distal phalanges and increases grip force and, thus, torque. Twelve subjects grasped a cylindrical object with diameters of 45.1, 57.8, and 83.2 mm in a power grip, and performed maximum torque exertions about the long axis of the handle in two directions: the direction the thumb points and the direction the fingertips point. Normal force on the fingertips increased with torque toward the fingertips, as predicted by the model. Consequently, torque toward the fingertips was 22% greater than torque toward the thumb. Measured torque and fingertip forces were compared with model predictions. Torque could be predicted well by the model. Measured fingertip force and thumb force were, on average, 27% less than the predicted values. Consistent with previous studies, grip force decreased as the handle diameter increased from 45.1 to 83.2 mm. This may be due not only to the muscle length-strength relationship, but also to major active force locations on the hand: grip force distributions suggest that a small handle allows fingertip force and thumb force to work together against the palm, resulting in a high reaction force on the palm, and, therefore, a high grip force. For a large handle, fingertip force and thumb force act against each other, resulting in little reaction force on the palm and, thus, a low grip force.     

Detailed mechanics of membrane-membrane adhesion and separation. I. Continuum of molecular cross-bridges

The mechanics of membrane-membrane adhesion are developed for the approximation that the molecular cross-bridging forces are continuously distributed as a normal stress (force per unit area). The significance of the analysis is that the finite range of the cross-bridging forces and the microscopic contact angle are not assumed negligible. Since the cross-bridging and adhesion forces are finite range interactions, there are two membrane regions: a free zone where the membranes are not subject to attractive forces; and an adherent zone where the membranes are held together by attractive stresses. The membrane is treated as an elastic continuum. The approach is to analyze the mechanics for each zone separately and then to require continuity of the solutions at the interface between the zones. Final solution yields the membrane contour and stresses proximal to and within the contact zone as well as the microscopic contact angle at the edge of the contact zone. It is demonstrated that the classical Young equation is consistent with this model. The results show that the microscopic contact angle becomes appreciable when the strength of adhesion is large or the length of the cross-bridge is large; however, the microscopic contact angle approaches zero as the membrane elastic stiffness increases. The solution predicts the width of the contact zone over which molecular bonds are stretched. It is this boundary region where increased biochemical activity is expected. In the classical model presented here, the level of tension necessary to oppose spreading of the contact is equal to the minimal level of tension required to separate the adherent membranes. This behavior is in contrast with that derived for the case of discrete molecular cross-bridges where the possibility of different levels of tension associated with adhesion and separation is introduced. The discrete cross-bridge case is the subject of a companion paper.     

A technique to determine friction at the fingertips

This article proposes a technique to calculate the coefficient of friction for the fingertip- object interface. Twelve subjects (6 males and 6 females) participated in two experiments. During the first experiment (the imposed displacement method), a 3-D force sensor was moved horizontally while the subjects applied a specified normal force (4 N, 8 N, 12 N) on the surface of a sensor covered with different materials (sandpaper, cotton, rayon, polyester, and silk).The normal force and the tangential force (i.e., the force due to the sensor motion) were recorded. The coefficient of friction (mu(d)) was calculated as the ratio between the tangential force and the normal force. In the second experiment (the beginning slip method), a small instrumented object was gripped between the index finger and the thumb, held stationary in the air, and then allowed to drop. The weight (200 g, 500 g, and 1,000 g) and the surface (sandpaper, cotton, rayon, polyester, and silk) in contact with the digits varied across trials. The same sensor as in the first experiment was used to record the normal force (in a horizontal direction) and the tangential force (in the vertical direction). The slip force (i.e., the minimal normal force or grip force necessary to prevent slipping) was estimated as the force at the moment when the object just began to slip. The coefficient of friction was calculated as the ratio between the tangential force and the slip force. The results show that (1) the imposed displacement method is reliable; (2) except sandpaper, for all other materials the coefficient of friction did not depend on the normal force; (3) the skin-sandpaper coefficient of friction was the highest mu(d) =0.96+/-0.09 (for 4-N normal force) and the skin-rayon rayon coefficient of friction was the smallest mu(d) =0.36+/-0.10; (4) no significant difference between the coefficients of friction determined with the imposed displacement method and the beginning slip method was observed. We view the imposed displacement technique as having an advantage as compared with the beginning slip method, which is more cumbersome (e.g., dropped object should be protected from impacts) and prone to subjective errors owing to the uncertainty in determining the instance of the slip initiation (i.e., impeding sliding).     

A procedure to estimate normal and friction contact parameters in the stance phase of the human gait

A new approach to estimate normal and tangential contact parameters in the foot-ground contact during human gait was proposed. A correct estimation of the contact parameters would be very important in the resolution of predictive forward dynamic problems. The normal contact forces have been well estimated in the literature. But accurate estimation of tangential forces has not been reached yet. This work proposed a new procedure to accurately estimate friction forces. The approach has been based on the consideration of the modulus of the tangential force instead of its components. This modulus was introduced together with the modulus of the normal contact force and its two associated moments in an optimization algorithm to fit the contact forces provided by the model to the experimental data obtained with a force plate. An inverse dynamics problem was solved as a step previous to the optimization algorithm. The results showed that both the normal and tangential forces and the moments in the horizontal plane were in agreement with the experimental measurements. This work also analyzed the influence on the results of the friction law. The results obtained with the general friction law, which considered dry (static and dynamic) and viscous friction, were compared with results provided by simpler laws. The analysis of the components of the friction forces pointed out the importance of the Stribeck component in the resultant force instead of the viscous friction which played a minimal role. But for modelling the stick-slip transition, the implementation of a general friction law is necessary.     

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.     

A three-dimensional anatomical model of the human patello-femoral joint,for the determination of patello-femoral motions and contact characteristics

The object of this study is to develop a three-dimensional mathematical model of the patello-femoral joint, which is modelled as two rigid bodies representing a moving patella and a fixed femur. Two-point contact was assumed between the femur and patella at the medial and lateral sides and in the analysis, the femoral and patellar articular surfaces were mathematically represented using Coons' bicubic surface patches. Model equations include six equilibrium equations and eleven constraints: six contact conditions, four geometric compatibility conditions, and the condition of a rigid patellar ligament; the model required the solution of a system of 17 nonlinear equations in 17 unknowns, its response describing the six-degress-of-freedom patellar motions and the forces acting on the patella. Patellar motions are described by six motion parameters representing the translations and rotations of the patella with respect to the femur. The forces acting on the patella include the medial and lateral component of patello-femoral contact and the patellar ligament force, all of which were represented as ratios to the quadriceps tendon force. The model response also includes the locations of the medial and lateral contact points on the femur and the patella. A graphical display of its response was produced in order to visualize better the motion of the components of the extensor mechanism.Model calculations show good agreement with experimental results available from the literature. The patella was found to move distally and posteriorly on the femoral condyles as the knee was flexed from full extension. Results indicate that the relative orientation of the patellar ligament with respect to the patella remains unchanged during this motion. The model also predicts a patellar flexion which always lagged knee flexion.Our calculations show that as the angle of knee flexion increased, the lateral contact point moved distally on the femur without moving significantly either medially or laterally. The medial contact point also moved distally on the femur but moved medially from full extension to about 40° of knee flexion, then laterally as the knee flexion angle increased. The lateral contact point on the patella did not change significantly in the medial and lateral direction as the knee was flexed; however, this point moved proximally toward the basis of the patella with knee flexion. The medial contact point also moved proximally on the patella with knee flexion, and in a similar manner the medial contact point on the patella moved distally with flexion from full extension to about 40° of flexion. However, as the angle of flexion increased, the medial contact point did not move significantly in the medial-lateral direction.Model calculations also show that during the simulated knee extension exercise, the ratio of the force in the patellar ligament to the force in the quadriceps tendon remains almost unchanged for the first 30° of knee flexion, then decreases as the angle of knee flexion increases. Furthermore, model results show that the lateral component of the patello-femoral contact force is always greater than the medial component, both components increasing with knee flexion.     

Predicting the effect of surface texture on the qualitative form of prehension

Reach-to-grasp movements change quantitatively in a lawful (i.e. predictable) manner with changes in object properties. We explored whether altering object texture would produce qualitative changes in the form of the precontact movement patterns. Twelve participants reached to lift objects from a tabletop. Nine objects were produced, each with one of three grip surface textures (high-friction, medium-friction and low-friction) and one of three widths (50 mm, 70 mm and 90 mm). Each object was placed at three distances (100 mm, 300 mm and 500 mm), representing a total of 27 trial conditions. We observed two distinct movement patterns across all trials--participants either: (i) brought their arm to a stop, secured the object and lifted it from the tabletop; or (ii) grasped the object 'on-the-fly', so it was secured in the hand while the arm was moving. A majority of grasps were on-the-fly when the texture was high-friction and none when the object was low-friction, with medium-friction producing an intermediate proportion. Previous research has shown that the probability of on-the-fly behaviour is a function of grasp surface accuracy constraints. A finger friction rig was used to calculate the coefficients of friction for the objects and these calculations showed that the area available for a stable grasp (the 'functional grasp surface size') increased with surface friction coefficient. Thus, knowledge of functional grasp surface size is required to predict the probability of observing a given qualitative form of grasping in human prehensile behaviour.     

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.     

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.     

Distinct haptic cues do not reduce interference when learning to reach in multiple force fields

Background

Previous studies of learning to adapt reaching movements in the presence of novel forces show that learning multiple force fields is prone to interference. Recently it has been suggested that force field learning may reflect learning to manipulate a novel object. Within this theoretical framework, interference in force field learning may be the result of static tactile or haptic cues associated with grasp, which fail to indicate changing dynamic conditions. The idea that different haptic cues (e.g. those associated with different grasped objects) signal motor requirements and promote the learning and retention of multiple motor skills has previously been unexplored in the context of force field learning.

Methodology/Principle Findings

The present study tested the possibility that interference can be reduced when two different force fields are associated with differently shaped objects grasped in the hand. Human subjects were instructed to guide a cursor to targets while grasping a robotic manipulandum, which applied two opposing velocity-dependent curl fields to the hand. For one group of subjects the manipulandum was fitted with two different handles, one for each force field. No attenuation in interference was observed in these subjects relative to controls who used the same handle for both force fields.

Conclusions/Significance

These results suggest that in the context of the present learning paradigm, haptic cues on their own are not sufficient to reduce interference and promote learning multiple force fields.     

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.     

Primary motor cortex neuronal discharge during reach-to-grasp: controlling the hand as a unit

This study has begun to test the hypothesis that aspects of hand/object shape are represented in the discharge of primary motor cortex (M1) neurons. Two monkeys were trained in a visually cued reach-to-grasp task, in which object properties and grasp forces were systematically varied. Behavioral analyses show that the reach and grasp force production were constant across the objects. The discharge of M1 neurons was highly modulated during the reach and grasp. Multiple linear regressions models revealed that the M1 discharge was highly dependent on the object grasped, with object class, volume, orientation and grasp force as significant predictors. These findings are interpreted as evidence that the CNS controls the hand as a unit.     

Mesoscopic analysis of motion and conformation of cross-bridges

The orientation of a cross-bridge is widely used as a parameter in determining the state of muscle. The conventional measurements of orientation, such as that made by wide-field fluorescence microscopy, electron paramagnetic resonance (EPR) or X-ray diffraction or scattering, report the average orientation of 10¹²–10⁹ myosin cross-bridges. Under conditions where all the cross-bridges are immobile and assume the same orientation, for example in normal skeletal muscle in rigor, it is possible to determine the average orientation from such global measurements. But in actively contracting muscle, where a parameter indicating orientation fluctuates in time, the measurements of the average value provide no information about cross-bridge kinetics. To avoid problems associated with averaging information from trillions of cross-bridges, it is necessary to decrease the number of observed cross-bridges to a mesoscopic value (i.e. the value affected by fluctuations around the average). In such mesoscopic regimes, the averaging of the signal is minimal and dynamic behavior can be examined in great detail. Examples of mesoscopic analysis on skeletal and cardiac muscle are provided.     

Competitive exclusion in a vector-host model for the dengue fever

 We study a system of differential equations that models the population dynamics of an SIR vector transmitted disease with two pathogen strains. This model arose from our study of the population dynamics of dengue fever. The dengue virus presents four serotypes each induces host immunity but only certain degree of cross-immunity to heterologous serotypes. Our model has been constructed to study both the epidemiological trends of the disease and conditions that permit coexistence in competing strains. Dengue is in the Americas an epidemic disease and our model reproduces this kind of dynamics. We consider two viral strains and temporary cross-immunity. Our analysis shows the existence of an unstable endemic state (‘saddle’ point) that produces a long transient behavior where both dengue serotypes cocirculate. Conditions for asymptotic stability of equilibria are discussed supported by numerical simulations. We argue that the existence of competitive exclusion in this system is product of the interplay between the host superinfection process and frequency-dependent (vector to host) contact rates. Received 4 December 1995; received in revised form 5 March 1996     

Neural correlates of internal-model loading

Skilled object manipulation requires knowledge, or internal models, of object dynamics relating applied force to motion , and our ability to handle myriad objects indicates that the brain maintains multiple models . Recent behavioral studies have shown that once learned, an internal model of an object with novel dynamics can be rapidly recruited and derecruited as the object is grasped and released . We used event-related fMRI to investigate neural activity linked to grasping an object with recently learned dynamics in preparation for moving it after a delay. Subjects also performed two control tasks in which they either moved without the object in hand or applied isometric forces to the object. In all trials, subjects received a cue indicating which task to perform in response to a go signal delivered 5-10 s later. We examined BOLD responses during the interval between the cue and go and assessed the conjunction of the two contrasts formed by comparing the primary task to each control. The analysis revealed significant activity in the ipsilateral cerebellum and the contralateral and supplementary motor areas. We propose that these regions are involved in internal-model recruitment in preparation for movement execution.     

The superposition principle applied to grasping an object producing moments outside anatomically-defined axes

The superposition principle suggests that motor commands can be divided into individually controlled components that summate to produce complex motor actions. Previous studies have examined the validity of this principle in human grasping by changing moments acting on an object about a single anatomically-defined axis and asking subjects to hold the object while their forearm was constrained. Superposition was reflected as separate control of the grip force and moments required to prevent object slip and maintain orientation. The objective of this study was to examine the robustness of this principle by: 1) expanding the range of tasks to include those where moments act on an object with respect to moment arms not necessarily in line with the anatomically-defined axes; 2) asking subjects to hold the object in an unconstrained manner. Ten subjects were asked to lift and hold an object vertically under eighteen moment conditions. Force and moment data from all digits were analysed using principal components analysis (PCA). Different PCAs were run for variable sets corresponding to moments about the long axis of the forearm (M(x)), the vertical (M(y)) and grip (M(z)) axes, and for the entire dataset (M(3D)). The PCA showed grip force and moment variables on separate PCs for the M(x), M(y), and M(3D) variable sets. The M(3D) PCA also showed a separation of variables corresponding to moments about each anatomically-defined axis. Thus, the present results show that the superposition principle holds during natural manipulation of an object experiencing external moments outside the anatomically-defined axes.     

A contact model to simulate human–artifact interaction based on force optimization: implementation and application to the analysis of a training machine

Musculoskeletal multibody models are increasingly used to analyze and optimize physical interactions between humans and technical artifacts. Since interaction is conveyed by contact between the human body and the artifact, a computationally robust modeling approach for frictional contact forces is a crucial aspect. In this contribution, we propose a parametric contact model and formulate an associated force optimization problem to simultaneously estimate unknown muscle and contact forces in an inverse dynamic manner from a prescribed motion trajectory. Unlike existing work, we consider both the static and the kinetic regime of Coulomb’s friction law. The approach is applied to the analysis of a leg extension training machine with the objective to reduce the stress on the tibiofemoral joint. The uncertainty of the simulation results due to a tunable parameter of the contact model is of particular interest.     

An analytical approach to the problem of inverse optimization with additive objective functions: an application to human prehension

We consider the problem of what is being optimized in human actions with respect to various aspects of human movements and different motor tasks. From the mathematical point of view this problem consists of finding an unknown objective function given the values at which it reaches its minimum. This problem is called the inverse optimization problem. Until now the main approach to this problems has been the cut-and-try method, which consists of introducing an objective function and checking how it reflects the experimental data. Using this approach, different objective functions have been proposed for the same motor action. In the current paper we focus on inverse optimization problems with additive objective functions and linear constraints. Such problems are typical in human movement science. The problem of muscle (or finger) force sharing is an example. For such problems we obtain sufficient conditions for uniqueness and propose a method for determining the objective functions. To illustrate our method we analyze the problem of force sharing among the fingers in a grasping task. We estimate the objective function from the experimental data and show that it can predict the force-sharing pattern for a vast range of external forces and torques applied to the grasped object. The resulting objective function is quadratic with essentially non-zero linear terms.