Balance control during an arm raising movement in bipedal stance: which biomechanical factor is controlled?

In order to obtain new insight into the control of balance during arm raising movements in bipedal stance, we performed a biomechanical analysis of kinematics and dynamical aspects of arm raising movements by combining experimental work, large-scale models of the body, and techniques simulating human behavior. A comparison between experimental and simulated joint kinematics showed that the minimum torque change model yielded realistic trajectories. We then performed an analysis based on computer simulations. Since keeping the center of pressure (CoP) and the projection of the center of mass (CoM) inside the support area is essential for equilibrium, we modeled an arm raising movement where displacement of one or the other variable is limited. For this optimization model, the effects of adding equilibrium constraints on movement trajectories were investigated. The results show that: (a) the choice of the regulated variable influences the strategy adopted by the system and (b) the system was not able to regulate the CoM for very fast movements without compromising its balance. Consequently, we suggest that the system is able to maintain balance while raising the arm by only controlling the CoP. This may be done mainly by using hip mechanisms and controlling net ankle torque.     

A general Newtonian simulation of an n-segment open chain model

This paper presents a set of general Newtonian equations which govern the simulation of movement of a body represented by n open chain links. The input for the simulation consisted of the joint moment of force histories, lengths, masses and moments of inertia, the initial absolute angular displacements and velocities and, for the fixed or constrained axis of the nth segment, the acceleration history. Angular accelerations were then determined by solving n linear equations simultaneously, and angular velocities and displacements determined by integrating forwards. The final output was in the form of a graphical display of the linked figure. Applications of the simulation were demonstrated using three-segment representations of movements of the upper and lower extremities and a five-segment representation of a jump. Good agreement was achieved between the displayed angular displacements for the original and simulated movements. The potential for varying the input data has been examined and the implications of anticipating the effects of changed torques, inertial characteristics including attached prosthetic or sports implements and/or the initial conditions for a movement are discussed.     

Motor control of voluntary arm movements

The motor control of pointing and reaching-to-grasp movements was investigated using two different approaches (kinematic and modelling) in order to establish whether the type of control varies according to modifications of arm kinematics. Kinematic analysis of arm movements was performed on subjects' hand trajectories directed to large and small stimuli located at two different distances. The subjects were required either to grasp and to point to each stimulus. The kinematics of the subsequent movement, during which subject's hand came back to the starting position, were also studied. For both movements, kinematic analysis was performed on hand linear trajectories as well as on joint angular trajectories of shoulder and elbow. The second approach consisted in the parametric identification of the black box (ARMAX) model of the controller driving the arm movement. Such controller is hypothesized to work for the correct execution of the motor act. The order of the controller ARMAX model was analyzed with respect to the different experimental conditions (distal task, stimulus size and distance). Results from kinematic analysis showed that target distance and size influenced kinematic parameters both of angular and linear displacements. Nevertheless, the structure of the motor program was found to remain constant with distane and distal task, while it varied with precision requirements due to stimulus size. The estimated model order of the controller confirmed the invariance of the control law with regard to movement amplitude, whereas it was sensitive to target size.     

Regulation of angular impulse during two forward translating tasks

Angular impulse generation is dependent on the position of the total body center of mass (CoM) relative to the ground reaction force (GRF) vector during contact with the environment. The purpose of this study was to determine how backward angular impulse was regulated during two forward translating tasks. Control of the relative angle between the CoM and the GRF was hypothesized to be mediated by altering trunk-leg coordination. Eight highly skilled athletes performed a series of standing reverse somersaults and reverse timers. Sagittal plane kinematics, GRF, and electromyograms of lower extremity muscles were acquired during the take-off phase of both tasks. The magnitude of the backward angular impulse generated during the push interval of both tasks was mediated by redirecting the GRF relative to the CoM. During the reverse timer, backward angular impulse generated during the early part of the take-off phase was negated by limiting backward trunk rotation and redirecting the GRF during the push interval. Biarticular muscles crossing the knee and hip coordinated the control of GRF direction and CoM trajectory via modulation of trunk-leg coordination.     

Dynamic interactions between limb segments during planar arm movement

Movement of multiple segment limbs requires generation of appropriate joint torques which include terms arising from dynamic interactions among the moving segments as well as from such external forces as gravity. The interaction torques, arising from inertial, centripetal, and Coriolis forces, are not present for single joint movements. The significance of the individual interaction forces during reaching movements in a horizontal plane involving only the shoulder and elbow joints has been assessed for different movement paths and movement speeds. Trajectory formation strategies which simplify the dynamics computation are presented.     

The bending stiffness of shoes is beneficial to running energetics if it does not disturb the natural MTP joint flexion

A local minimum for running energetics has been reported for a specific bending stiffness, implying that shoe stiffness assists in running propulsion. However, the determinant of the metabolic optimum remains unknown. Highly stiff shoes significantly increase the moment arm of the ground reaction force (GRF) and reduce the leverage effect of joint torque at ground push-off. Inspired by previous findings, we hypothesized that the restriction of the natural metatarsophalangeal (MTP) flexion caused by stiffened shoes and the corresponding joint torque changes may reduce the benefit of shoe bending stiffness to running energetics. We proposed the critical stiffness, k_cr, which is defined as the ratio of the MTP joint (MTPJ) torque to the maximal MTPJ flexion angle, as a possible threshold of the elastic benefit of shoe stiffness. 19 subjects participated in a running test while wearing insoles with five different bending stiffness levels. Joint angles, GRFs, and metabolic costs were measured and analyzed as functions of the shoe stiffness. No significant changes were found in the take-off velocity of the center of mass (CoM), but the horizontal ground push-offs were significantly reduced at different shoe stiffness levels, indicating that complementary changes in the lower-limb joint torques were introduced to maintain steady running. Slight increases in the ankle, knee, and hip joint angular impulses were observed at stiffness levels exceeding the critical stiffness, whereas the angular impulse at the MTPJ was significantly reduced. These results indicate that the shoe bending stiffness is beneficial to running energetics if it does not disturb the natural MTPJ flexion.     

Robot-based methodology for a kinematic and kinetic analysis of unconstrained,but reproducible upper extremity movement

Although arm movements play an important role in everyday life, there is still a lack of procedures for the analysis of upper extremity movement. The main problems for standardizing the procedure are the variety of arm movements and the difficult assessment of external hand forces. The first problem requires the predefinition of motions, and the second one is the prerequisite for calculation of net joint forces and torques arising during motion. A new methodology for measuring external forces during prespecified, reproducible upper extremity movement has been introduced and validated. A robot-arm has been used to define the motion and 6 degrees of freedom (DoF) force sensor has been attached to it for acquiring the external loads acting on the arm. Additionally, force feedback has been used to help keeping external loads constant. Intra-individual reproducibility of joint angles was estimated by using correlation coefficients to compare a goal-directed movement with robot-guided task. Inter-individual reproducibility has been evaluated by using the mean standard deviation of joint angles for both types of movement. The results showed that both inter- and intra-individual reproducibility have significantly improved by using the robot. Also, the effectiveness of using force feedback for keeping a constant external load has been shown. This makes it possible to estimate net joint forces and torques which are important biomechanical information in motion analysis.     

Inverse dynamic investigation of voluntary trunk movements in weightlessness: a new microgravity-specific strategy

Present investigation faces the question of quantitative assessment of exchanged forces and torques at the restraints during whole body posture exercises in long-term microgravity. Inverse dynamic modelling and total angular momentum at the ankle joint were used in order to reconstruct movement dynamics at the restraining point, represented by the ankle joint. The hypothesis is that the minimisation of the torques at the interface point assumes a key role in movement planning in 0 g. This hypothesis would respond to an optimisation of muscles activity, a minimisation of energy expenditure and therefore an accurate control of body movement. Results show that the 0 g movement strategy adopted ensures that the integral of the net ankle moment between the beginning and the end of the movement is zero. This expected mechanical constraint is not satisfied when 0 g movement dynamics is simulated using terrestrial kinematics. This accounts for a significant imposed change of movement strategy. Particularly, the efficient compensation of the inertial effects of the segments in terms of total angular momentum at the ankle joint was evidenced. These results explain the exaggerated axial synergies, observed on kinematics and which moved centre of mass (CM) backward from its already backward initial positioning, as a tool for enhancing the compensation and achieving the desired minimisation of the torques exchanges at the restraints.     

Comparative analysis of methods for estimating arm segment parameters and joint torques from inverse dynamics

A common problem in the analyses of upper limb unfettered reaching movements is the estimation of joint torques using inverse dynamics. The inaccuracy in the estimation of joint torques can be caused by the inaccuracy in the acquisition of kinematic variables, body segment parameters (BSPs), and approximation in the biomechanical models. The effect of uncertainty in the estimation of body segment parameters can be especially important in the analysis of movements with high acceleration. A sensitivity analysis was performed to assess the relevance of different sources of inaccuracy in inverse dynamics analysis of a planar arm movement. Eight regression models and one water immersion method for the estimation of BSPs were used to quantify the influence of inertial models on the calculation of joint torques during numerical analysis of unfettered forward arm reaching movements. Thirteen subjects performed 72 forward planar reaches between two targets located on the horizontal plane and aligned with the median plane. Using a planar, double link model for the arm with a floating shoulder, we calculated the normalized joint torque peak and a normalized root mean square (rms) of torque at the shoulder and elbow joints. Statistical analyses quantified the influence of different BSP models on the kinetic variable variance for given uncertainty on the estimation of joint kinematics and biomechanical modeling errors. Our analysis revealed that the choice of BSP estimation method had a particular influence on the normalized rms of joint torques. Moreover, the normalization of kinetic variables to BSPs for a comparison among subjects showed that the interaction between the BSP estimation method and the subject specific somatotype and movement kinematics was a significant source of variance in the kinetic variables. The normalized joint torque peak and the normalized root mean square of joint torque represented valuable parameters to compare the effect of BSP estimation methods on the variance in the population of kinetic variables calculated across a group of subjects with different body types. We found that the variance of the arm segment parameter estimation had more influence on the calculated joint torques than the variance of the kinematics variables. This is due to the low moments of inertia of the upper limb, especially when compared with the leg. Therefore, the results of the inverse dynamics of arm movements are influenced by the choice of BSP estimation method to a greater extent than the results of gait analysis.     

The linear co-variance between joint muscle torques is not a generalized principle

In 1996, Gottlieb et al. [Gottlieb GL, Song Q, Hong D, Almeida GL, Corcos DM. Coordinating movement at two joints: A principle of linear covariance. J Neurophysiol 1996;75(4):1760–4] identified a linear co-variance between the joint muscle torques generated at two connected joints. The joint muscle torques changed directions and magnitudes in a synchronized and linear fashion and called it the principle of linear co-variance. Here we showed that this principle cannot hold for some class of movements. Neurologically normal subjects performed multijoint movements involving elbow and shoulder with reversal towards three targets in the sagittal plane without any constraints. The movement kinematics was calculated using the X and Y coordinates of the markers positioned over the joints. Inverse dynamics was used to calculate the joint muscle, interaction and net torques. We found that for the class of voluntary movements analyzed, the joint muscle torques of the elbow and the shoulder were not linearly correlated. The same was observed for the interaction torques. But, the net torques at both joints, i.e., the sum of the interaction and the joint muscle torques were linearly correlated. We showed that by decoupling the joint muscle torques, but keeping the net torques linearly correlated, the CNS was able to generate fast and accurate movements with straight fingertip paths. The movement paths were typical of the ones in which the joint muscle torques were linearly correlated.     

Age causes a redistribution of joint torques and powers during gait.

At self-selected walking speeds, elderly compared with young adults generate decreased joint torques and powers in the lower extremity. These differences may be actual gait-limiting factors and neuromuscular adaptations with age or simply a consciously selected motor pattern to produce a slower gait. The purpose of the study was to compare joint torques and powers of young and elderly adults walking at the same speed. Twelve elderly and fourteen young adults (ages 69 and 21 yr) walked at 1.48 m/s over a force platform while being videotaped. Hip, knee, and ankle torques and powers were calculated from the reaction force and kinematic data. A support torque was calculated as the sum of the three joint torques. Extensor angular impulse during stance and positive work at each joint were derived from the torques and powers. Step length was 4% shorter and cadence was 4% higher in elderly adults (both P < 0.05) compared with young adults. Support angular impulse was nearly identical between groups, but elderly adults had 58% greater angular impulse and 279% more work at the hip, 50% less angular impulse and 39% less work at the knee, and 23% less angular impulse and 29% less work at the ankle compared with young adults (t-test, all P < 0.05). Age caused a redistribution of joint torques and powers, with the elderly using their hip extensors more and their knee extensors and ankle plantar flexors less than young adults when walking at the same speed. Along with a reduction in motor and sensory functions, the natural history of aging causes a shift in the locus of function in motor performance.     

A new approach to reaching control for tetraplegic subjects

A simple upper limb control strategy to guide reaching in preparation to grasp for tetraplegic subjects is proposed. The control is based on new studies of self-paced human arm movements involving rotations about the shoulder and elbow joints. An experimental study of reaching, while grasping, by able-bodied humans, allowed us to reduce the dimensionality of the control vector from two to a single variable. This was accomplished by detailed analysis of the synergy between shoulder and elbow joint angles. This study examined only movements in teh horizontal plane. In the experiments we varied: (a) the shape of targets; (b) their position relative to the initial position of the hand; and (c) the speed of reaching. A synergy between shoulder and elbow joint angles was found in most analysed movements, and it was characterized by a scaling parameter between elbow and shoulder angular velocities. The scaling parameter was determined from the target position presented in the visual perceptive field and initial shoulder and elbow angles. The same experimental setup in studies with tetraplegics with retained shoulder movements showed that this natural synergism is preserved even though the motor and sensory components of the upper limb are reduced or absent. Tetraplegics originally showed a very different reaching pattern, but after short training sessions they developed a reaching behaviour which was similar to able-bodied subjects. The results presented can be used in the following way: a tetraplegic subject lacking elbow extension and flexion may be fitted with an assistive system which will be volitionally controlled only from ipsilateral shoulder movements. The assistive system can comprise either a motorized brace, or a functional electrical stimulation system applied to elbow flexors and extensors. With this system volitional movements at the shoulder would bring the hand into the correct position to accomplish an assisted grasping motion.     

Three-dimensional model to predict muscle forces and their relation to motor variances in reaching arm movements

A three-dimensional (3-D) arm movement model is presented to simulate kinematic properties and muscle forces in reaching arm movements. Healthy subjects performed reaching movements repetitively either with or without a load in the hand. Joint coordinates were measured. Muscle moment arms, 3-D angular acceleration, and moment of inertias of arm segments were calculated to determine 3-D joint torques. Variances of hand position, arm configuration, and muscle activities were calculated. Ratios of movement variances observed in the two conditions (load versus without load) showed no differences for hand position and arm configuration variances. Virtual muscle force variances for all muscles except deltoid posterior and EMG variances for four muscles increased significantly by moving with the load. The greatly increased variances in muscle activity did not imply equally high increments in kinematic variances. We conclude that enhanced muscle cooperation through synergies helps to stabilize movement at the kinematic level when a load is added.     

Dynamic optimization: inverse analysis for the Yurchenko layout vault in women's artistic gymnastics

The use of dynamic optimization to compute the trajectory of joint torques is not popular due to the large amount of computation required, the choice of initial "guesstimates" of torque values and the mathematical sophistication required to understand the technique. Modern optimal control algorithms circumvent most of these objections to the method. It is our aim to demonstrate that the dynamic optimization technique is feasible for complex movements, using the Yurchenko layout vault as an example. A dynamic optimization method to compute joint torques so that the histories of the angular orientations of the model segments closely approximate the corresponding observed angular coordinate histories is demonstrated with the Yurchenko layout vault using an optimal control package. The objective function used is a measure of distance of fitted segment angles to the data, plus the distance of the fitted whole body centre of mass (CM), from the whole body CM computed from the data. Including the CM into the objective function, facilitates the optimization process so as to obtain a set of torques which reproduced the data. The paper shows that the approach works well for the task examined, that is, where the dynamics of the system change during a movement (impact to postflight).     

Effects of changes in segmental values and timing of both torque and torque reversal in simulated throws.

An overarm throw in the sagittal plane was simulated using a three-segment model representing the upper arm, forearm and hand plus ball. Torque inputs at each joint were turned on at systematically varied times and maintained constant once initiated. All simulations began from identical initial conditions. The aim was to determine the sequence of onset of joint torques which gave the maximal range which the ball would travel and the maximal velocity of the ball irrespective of direction. Best throws proved to be sequential in that joint torques were turned on in a proximal to distal (P-D) temporal sequence. The P-D sequence was also demonstrated by time of peak joint angular velocities. The P-D sequence also proved to be best when segmental constants and joint torques were changed. As this sequence is a common feature of skilled throwing and striking, it is concluded that the linked segmental nature of the limb, irrespective of normal muscle characteristics, primarily predisposes the system to the use of a P-D sequence. The algebraic sign of the shoulder and elbow torques was reversed instantaneously to represent the use of antagonistic muscles. This led to increased output if performed late in the throw and in a P-D sequence. It is concluded that the use of antagonism leads to beneficial redistributions of angular velocity amongst limb segments.     

Joint forces and torques when walking in shallow water

This study reports for the first time an estimation of the internal net joint forces and torques on adults' lower limbs and pelvis when walking in shallow water, taking into account the drag forces generated by the movement of their bodies in the water and the equivalent data when they walk on land. A force plate and a video camera were used to perform a two-dimensional gait analysis at the sagittal plane of 10 healthy young adults walking at comfortable speeds on land and in water at a chest-high level. We estimated the drag force on each body segment and the joint forces and torques at the ankle, knee, and hip of the right side of their bodies using inverse dynamics. The observed subjects' apparent weight in water was about 35% of their weight on land and they were about 2.7 times slower when walking in water. When the subjects walked in water compared with walking on land, there were no differences in the angular displacements but there was a significant reduction in the joint torques which was related to the water's depth. The greatest reduction was observed for the ankle and then the knee and no reduction was observed for the hip. All joint powers were significantly reduced in water. The compressive and shear joint forces were on average about three times lower during walking in water than on land. These quantitative results substantiate the use of water as a safe environment for practicing low-impact exercises, particularly walking.     

Effect of hip joint angle on concentric knee extension torque

This study tested the hypothesis that the effect of hip joint angle on concentric knee extension torque depends on knee joint angle during a single knee extension task. Twelve men performed concentric knee extensions in fully extended and 80° flexed hip positions with maximal effort. The angular velocities were set at 30° s⁻¹ and 180° s⁻¹. The peak torque and torques attained at 30°, 50°, 70° and 90° (anatomical position = 0°) of the knee joint were compared between the two hip positions. Muscle activations of the vastus lateralis, medialis, rectus femoris and biceps femoris were determined using surface electromyography. The peak torque was significantly greater in the flexed than in the extended hip position irrespective of angular velocity. The torques at 70° and 90° of the knee joint at both angular velocities and at 50° at 180° s⁻¹ were significantly greater in the flexed than in the extended hip position, whereas corresponding differences were not found at 30° (at either angular velocity) and 50° (at 30° s⁻¹) of the knee joint. No effect of hip position on muscle activation was observed in any muscle. These results supported our hypothesis and may be related to the force–length and force–velocity characteristics of the rectus femoris.     

Evaluation of a subject-specific female gymnast model and simulation of an uneven parallel bar swing

A gymnast model and forward dynamics simulation of a dismount preparation swing on the uneven parallel bars were evaluated by comparing experimental and predicted joint positions throughout the maneuver. The bar model was a linearly elastic spring with a frictional bar/hand interface, and the gymnast model consisted of torso/head, arm and two leg segments. The hips were frictionless balls and sockets, and shoulder movement was planar with passive compliant structures approximated by a parallel spring and damper. Subject-specific body segment moments of inertia, and shoulder compliance were estimated. Muscles crossing the shoulder and hip were represented as torque generators, and experiments quantified maximum instantaneous torques as functions of joint angle and angular velocity. Maximum torques were scaled by joint torque activations as functions of time to produce realistic motions. The downhill simplex method optimized activations and simulation initial conditions to minimize the difference between experimental and predicted bar-center, shoulder, hip, and ankle positions. Comparing experimental and simulated performances allowed evaluation of bar, shoulder compliance, joint torque, and gymnast models. Errors in all except the gymnast model are random, zero mean, and uncorrelated, verifying that all essential system features are represented. Although the swing simulation using the gymnast model matched experimental joint positions with a 2.15cm root-mean-squared error, errors are correlated. Correlated errors indicate that the gymnast model is not complex enough to exactly reproduce the experimental motion. Possible model improvements including a nonlinear shoulder model with active translational control and a two-segment torso would not have been identified if the objective function did not evaluate the entire system configuration throughout the motion. The model and parameters presented in this study can be effectively used to understand and improve an uneven parallel bar swing, although in the future there may be circumstances where a more complex model is needed.     

Effect of elastic-cord towing on the kinematics of the acceleration phase of sprinting

We studied the specificity of elastic-cord towing by measuring selected kinematics of the acceleration phase of sprinting. Nine collegiate sprinters ran two 20-m maximal sprints (MSs) and towed sprints (TSs) that were recorded on high-speed video (180 Hz). Sagittal plane kinematics of a 4-segment model of the right side of the body were digitized for a complete stride at the 15-m point for the fastest trial. Significant (p < 0.001) differences were observed for horizontal velocity of the center of mass (CoM), stride length (SL), and horizontal distance from the CoM of the foot to the CoM of the body. There was no significant difference in stride rate between the MS and TS conditions. Omega-squared analysis showed that elastic-cord towing accounted for most of the variance in acute changes in horizontal velocity (73%), SL (68%), and horizontal position of the CoM at foot contact (64%). Elastic-cord tow training resulted in significant acute changes in sprint kinematics in the acceleration phase of an MS that do not appear to be sprint specific. More research is needed on the specificity of TS training and long-term effects on sprinting performance.     

Maximum voluntary joint torque as a function of joint angle and angular velocity: model development and application to the lower limb

Measurements of human strength can be important during analyses of physical activities. Such measurements have often taken the form of the maximum voluntary torque at a single joint angle and angular velocity. However, the available strength varies substantially with joint position and velocity. When examining dynamic activities, strength measurements should account for these variations. A model is presented of maximum voluntary joint torque as a function of joint angle and angular velocity. The model is based on well-known physiological relationships between muscle force and length and between muscle force and velocity and was tested by fitting it to maximum voluntary joint torque data from six different exertions in the lower limb. Isometric, concentric and eccentric maximum voluntary contractions were collected during hip extension, hip flexion, knee extension, knee flexion, ankle plantar flexion and dorsiflexion. Model parameters are reported for each of these exertion directions by gender and age group. This model provides an efficient method by which strength variations with joint angle and angular velocity may be incorporated into comparisons between joint torques calculated by inverse dynamics and the maximum available joint torques.