Kinetic chain of overarm throwing in terms of joint rotations revealed by induced acceleration analysis

This study investigated how baseball players generate large angular velocity at each joint by coordinating the joint torque and velocity-dependent torque during overarm throwing. Using a four-segment model (i.e., trunk, upper arm, forearm, and hand) that has 13 degrees of freedom, we conducted the induced acceleration analysis to determine the accelerations induced by these torques by multiplying the inverse of the system inertia matrix to the torque vectors. We found that the proximal joint motions (i.e., trunk forward motion, trunk leftward rotation, and shoulder internal rotation) were mainly accelerated by the joint torques at their own joints, whereas the distal joint motions (i.e., elbow extension and wrist flexion) were mainly accelerated by the velocity-dependent torques. We further examined which segment motion is the source of the velocity-dependent torque acting on the elbow and wrist accelerations. The results showed that the angular velocities of the trunk and upper arm produced the velocity-dependent torque for initial elbow extension acceleration. As a result, the elbow joint angular velocity increased, and concurrently, the forearm angular velocity relative to the ground also increased. The forearm angular velocity subsequently accelerated the elbow extension and wrist flexion. It also accelerated the shoulder internal rotation during the short period around the ball-release time. These results indicate that baseball players accelerate the distal elbow and wrist joint rotations by utilizing the velocity-dependent torque that is originally produced by the proximal trunk and shoulder joint torques in the early phase.     

Upper extremity kinematic and kinetic adaptations during a fatiguing repetitive task

Repetitive low-force contractions are common in the workplace and yet can lead to muscle fatigue and work-related musculoskeletal disorders. The current study aimed to investigate potential motion adaptations during a simulated repetitive light assembly work task designed to fatigue the shoulder region, focusing on changes over time and age-related group differences. Ten younger and ten older participants performed four 20-min task sessions separated by short breaks. Mean and variability of joint angles and scapular elevation, joint net moments for the shoulder, elbow, and wrist were calculated from upper extremity kinematics recorded by a motion tracking system. Results showed that joint angle and joint torque decreased across sessions and across multiple joints and segments. Increased kinematic variability over time was observed in the shoulder joint; however, decreased kinematic variability over time was seen in the more distal part of the upper limb. The changes of motion adaptations were sensitive to the task-break schedule. The results suggested that kinematic and kinetic adaptations occurred to reduce the biomechanical loading on the fatigued shoulder region. In addition, the kinematic and kinetic responses at the elbow and wrist joints also changed, possibly to compensate for the increased variability caused by the shoulder joint while still maintaining task requirements. These motion strategies in responses to muscle fatigue were similar between two age groups although the older group showed more effort in adaptation than the younger in terms of magnitude and affected body parts.     

The role of the biceps brachii in shoulder elevation.

The biceps brachii is a bi-articular muscle affecting motion at the shoulder and elbow. While its' action at the elbow is well documented, its role in shoulder elevation is less clear. Therefore, the purpose of this project was to investigate the influence of shoulder and elbow joint angles on the shoulder elevation function of the biceps brachii. Twelve males and 18 females were tested on a Biodex dynamometer with the biceps brachii muscle selectively stimulated at a standardized level of voltage. The results indicated that both shoulder and elbow joint angles influence the shoulder joint elevation moment produced by the biceps brachii. Further analysis revealed that the elevation moment was greatest with the shoulder joint at 0 degrees and the elbow flexed 30 degrees or less. The greatest reduction in the elevation moment occurred between shoulder angles of 0 degrees and 30 degrees . The shoulder elevation moment was near zero when shoulder elevation reached or exceeded 60 degrees regardless of elbow angle. These results clarify the role of the biceps in shoulder elevation, as a dynamic stabilizer, and suggest that it is a decelerator of the arm during the throwing motion.     

Muscle moment arm and normalized moment contributions as reference data for musculoskeletal elbow and wrist joint models

A geometric musculoskeletal model of the elbow and wrist joints was developed to calculate muscle moment arms throughout elbow flexion/extension, forearm pronation/supination, wrist flexion/extension and radial/ulnar deviation. Model moment arms were verified with data from cadaver specimen studies and geometric models available in the literature. Coefficients of polynomial equations were calculated for all moment arms as functions of joint angle, with special consideration to coupled muscles as a function of two joint angles. Additionally, a “normalized potential moment (NPM)” contribution index for each muscle across the elbow and wrist joints in four degrees-of-freedom was determined using each muscle's normalized physiological cross-sectional area (PCSA) and peak moment arm (MA). We hypothesize that (a) a geometric model of the elbow and wrist joints can represent the major attributes of MA versus joint angle from many literature sources of cadaver and model data and (b) an index can represent each muscle's normalized moment contribution to each degree-of-freedom at the elbow and wrist. We believe these data serve as a simple, yet comprehensive, reference for how the primary 16 muscles across the elbow and wrist contribute to joint moment and overall joint performance.     

The contribution of the wrist, elbow and shoulder joints to single-finger tapping

We aimed to determine the role of the wrist, elbow and shoulder joints to single-finger tapping. Six human subjects tapped with their index finger at a rate of 3 taps/s on a keyswitch across five conditions, one freestyle (FS) and four instructed tapping strategies. The four instructed conditions were to tap on a keyswitch using the finger joint only (FO), the wrist joint only (WO), the elbow joint only (EO), and the shoulder joint only (SO). A single-axis force plate measured the fingertip force. An infra-red active-marker three-dimensional motion analysis system measured the movement of the fingertip, hand, forearm, upper arm and trunk. Inverse dynamics estimated joint torques for the metacarpal-phalangeal (MCP), wrist, elbow, and shoulder joints. For FS tapping 27%, 56%, and 18% of the vertical fingertip movement were a result of flexion of the MCP joint and wrist joint and extension of the elbow joint, respectively. During the FS movements the net joint powers between the MCP, wrist and elbow were positively correlated (correlation coefficients between 0.46 and 0.76) suggesting synergistic efforts. For the instructed tapping strategies (FO, WO, EO, and SO), correlations decreased to values below 0.35 suggesting relatively independent control of the different joints. For FS tapping, the kinematic and kinetic data indicate that the wrist and elbow contribute significantly, working in synergy with the finger joints to create the fingertip tapping task.     

Long-latency reflexes of the human arm reflect an internal model of limb dynamics

A key feature of successful motor control is the ability to counter unexpected perturbations. This process is complicated in multijoint systems, like the human arm, by the fact that loads applied at one joint will create motion at other joints [1-3]. Here, we test whether our most rapid corrections, i.e., reflexes, address this complexity through an internal model of the limb's mechanical properties. By selectively applying torque perturbations to the subject's shoulder and/or elbow, we revealed a qualitative difference between the arm's short-latency/spinal reflexes and long-latency/cortical reflexes. Short-latency reflexes of shoulder muscles were linked exclusively to shoulder motion, whereas its long-latency reflexes were sensitive to both shoulder and elbow motion, i.e., matching the underlying shoulder torque. In fact, a long-latency reflex could be evoked without even stretching or lengthening the shoulder muscle but by displacing just the elbow joint. Further, the shoulder's long-latency reflexes were appropriately modified across the workspace to account for limb-geometry changes that affect the transformation between joint torque and joint motion. These results provide clear evidence that long-latency reflexes possess an internal model of limb dynamics, a degree of motor intelligence previously reserved for voluntary motor control [3-5]. The use of internal models for both voluntary and reflex control is consistent with substantial overlap in their neural substrates and current notions of intelligent feedback control [6-8].     

Effects of the Racket Polar Moment of Inertia on Dominant Upper Limb Joint Moments during Tennis Serve

This study examined the effect of the polar moment of inertia of a tennis racket on upper limb loading in the serve. Eight amateur competition tennis players performed two sets of 10 serves using two rackets identical in mass, position of center of mass and moments of inertia other than the polar moment of inertia (0.00152 vs 0.00197 kg.m²). An eight-camera motion analysis system collected the 3D trajectories of 16 markers, located on the thorax, upper limbs and racket, from which shoulder, elbow and wrist net joint moments and powers were computed using inverse dynamics. During the cocking phase, increased racket polar moment of inertia was associated with significant increases in the peak shoulder extension and abduction moments, as well the peak elbow extension, valgus and supination moments. During the forward swing phase, peak wrist extension and radial deviation moments significantly increased with polar moment of inertia. During the follow-through phase, the peak shoulder adduction, elbow pronation and wrist external rotation moments displayed a significant inverse relationship with polar moment of inertia. During the forward swing, the magnitudes of negative joint power at the elbow and wrist were significantly larger when players served using the racket with a higher polar moment of inertia. Although a larger polar of inertia allows players to better tolerate off-center impacts, it also appears to place additional loads on the upper extremity when serving and may therefore increase injury risk in tennis players.     

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.     

Assessment of the accuracy of a human arm model with seven degrees of freedom

We are proposing a human arm model that consists of three rigid segments with seven degrees of freedom. The shoulder joint was modeled as a ball-and-socket joint and the elbow and wrist joints were modelled as skew-oblique joints. Optimal parameters for this model were calculated on the base of in vivo recordings with a spatial tracking system. The criterion of optimality was defined as the minimum of the mean-square deviation between the experimentally obtained sensor positions and orientations and their positions and orientations calculated by solving the direct kinematics problem. The minimal value of the direct kinematics error was found to be 0.5-0.6cm for sensor positions and 5-7 degrees for sensor orientations. We are proposing that these values serve as the assessment for the accuracy of the arm model.     

Dynamics of wrist rotations

Understanding the dynamics of wrist rotations is important for many fields, including biomechanics, rehabilitation and motor neuroscience. This paper provides an experimentally based mathematical model of wrist rotation dynamics in Flexion-Extension (FE) and Radial-Ulnar Deviation (RUD), and characterizes the torques required to overcome the passive mechanical impedance of wrist rotations. We modeled the wrist as a universal joint with non-intersecting axes. The equations of motion of the hand rotating about the wrist joint include inertial, damping, and stiffness terms, with parameter values based on direct measurements (stiffness) or measurements combined with data available in the literature (inertia, damping). We measured the wrist kinematics of six young, healthy subjects making comfortable and fast-paced wrist rotations (±15° in FE, RUD, and combinations) and inserted these kinematic data into the model of wrist rotation dynamics. With this we quantified the torques required to overcome the impedance of wrist rotations and evaluated the relative importance of individual impedance terms as well as interactions between the degrees of freedom. We found that the wrist's passive stiffness is the major impedance the neuromuscular system must overcome to rotate the wrist. Inertia and passive damping only become important for very fast movements. Unlike elbow and shoulder reaching movements, inertial interaction torques are negligible for wrist rotations. Interaction torques due to stiffness and damping, however, are significant. Finally, we found that some model terms (inertial interaction torques, axis offset, and, for moderately sized rotations, non-linearities) can be neglected with little loss of accuracy, resulting in a simple, linear model useful for studies in biomechanics, motor neuroscience, and rehabilitation.     

The mechanisms that enable arm motion to enhance vertical jump performance-a simulation study

The reasons why using the arms can increase standing vertical jump height are investigated by computer simulations. The human models consist of four/five segments connected by frictionless joints. The head-trunk-arms act as a fourth segment in the first model while the arms become a fifth segment in the second model. Planar model movement is actuated by joint torque generators. Each joint torque is the product of three variable functions of activation level, angular velocity dependence, and maximum isometric torque varying with joint angle. Simulations start from a balanced initial posture and end at jump takeoff. Jump height is maximized by finding the optimal combination of joint activation timings. Arm motion enhances jumping performance by increasing mass center height and vertical takeoff velocity. The former and latter contribute about 1/3 and 2/3 to the increased height, respectively. Durations in hip torque generation and ground contact period are lengthened by swinging the arms. Theories explaining the performance enhancement caused by arms are examined. The force transmission theory is questionable because shoulder joint force due to arm motion does not precisely reflect the change in vertical ground reaction force. The joint torque/work augmentation theory is acceptable only at the hips but not at the knees and ankles because only hip joint work is considerably increased. The pull/impart energy theory is also acceptable because shoulder joint work is responsible for about half of the additional energy created by arm swings.     

Upper limb joint angle measurement in occupational health

Usual human motion capture systems are designed to work in controlled laboratory conditions. For occupational health, instruments that can measure during normal daily life are essential, as the evaluation of the workers' movements is a key factor to reduce employee injury- and illness-related costs. In this paper, we present a method for joint angle measurement, combining inertial sensors (accelerometers and gyroscopes) and magnetic sensors. This method estimates wrist flexion, wrist lateral deviation, elbow flexion, elbow pronation, shoulder flexion, shoulder abduction and shoulder internal rotation. The algorithms avoid numerical integration of the signals, which allows for long-time estimations without angle estimation drift. The system has been tested both under laboratory and field conditions. Controlled laboratory tests show mean estimation errors between 0.06° and of 1.05°, and standard deviation between 2.18° and 9.20°. Field tests seem to confirm these results when no ferromagnetic materials are close to the measurement system.     

Postural differences in shoulder dynamics during pushing and pulling

Assessments of shoulder dynamics (e.g. the inertial, viscous, and stiffness properties of the joint) can provide important insights into the stability of the joint at rest and during volitional contraction. The purpose of this study was to investigate how arm posture influences shoulder dynamics while generating pushing or pulling torques in the horizontal plane. Sixteen healthy participants were examined in seven postures encompassing a large workspace of the shoulder. At each posture, the participant’s shoulder was rapidly perturbed while measuring the resultant change in shoulder torque about the glenohumeral axis. Participants were examined both at rest and while producing horizontal flexion and extension torques scaled to 15% of a maximum voluntary contraction. Shoulder stiffness, viscosity, and damping ratio were estimated using impedance-based matching, and changes in these outcome measures with torque level, elevation angle, and plane of elevation angle were explored with a linear mixed effects model. Shoulder stiffness was found to decrease with increasing elevation angles (p < 0.001) without subsequent changes in viscosity, leading to a greater damping ratios at higher elevation angles (p < 0.001). Shoulder stiffness, viscosity, and damping ratio (all p < 0.05) were all found to significantly increase as the plane of elevation of the arm was increased. The relationship between the viscosity, stiffness and the damping ratio of the shoulder is one that the central nervous system must regulate in order to maintain stability, protect against injury, and control the shoulder joint as the inertial and muscle contributions change across different arm postures.     

A three-dimensional, six-segment chain analysis of forceful overarm throwing.

A three-dimensional, six-segment model was applied to the pitching motion of three professional pitchers to analyze the kinematics and kinetics of the hips, upper trunk, humerus and forearm plus hand of both the upper limbs. Subjects were filmed at 250 frames per second. An inverse dynamics approach and angular momentum principle with respect to the proximal endpoint of a rigid segment were employed in the analysis. Results showed considerable similarities between subjects in the kinetic control of trunk rotation about the spine's longitudinal axis, but variability in the control of trunk lean both to the side and forward. The kinetics of the throwing shoulder and elbow joint were comparable between subjects, but the contribution of the non-throwing upper limb was minimal and variable. The upper trunk rotators played a key role in accelerating the ball to an early, low velocity near stride foot contact. After a brief pause they resumed acting strongly in a positive direction, though not enough to prevent trunk angular velocity slowing, as the musculature of the arm applied a load at the throwing shoulder. The interaction moment from the proximal segments assisted the forearm extensor in slowing flexion and producing rapid elbow extension near ball release. The temporal onset of muscular torques was not in a strictly successive proximal-to-distal sequence.     

Individual muscle force parameters and fiber operating ranges for elbow flexion-extension and forearm pronation-supination

We have quantified individual muscle force and moment contributions to net joint moments and estimated the operating ranges of the individual muscle fibers over the full range of motion for elbow flexion/extension and forearm pronation/supination. A three dimensional computer graphics model was developed in order to estimate individual muscle contributions in each degree of freedom over the full range of motion generated by 17 muscles crossing the elbow and forearm. Optimal fiber length, tendon slack length, and muscle specific tension values were adjusted within the literature range from cadaver studies such that the net isometric joint moments of the model approximated experimental joint moments within one standard deviation. Analysis of the model revealed that the muscles operate on varying portions of the ascending limb, plateau region, and descending limb of the force-length curve. This model can be used to further understand isometric force and moment contributions of individual muscles to net joint moments of the arm and forearm and can serve as a comprehensive reference for the forces and moments generated by 17 major muscles crossing the elbow and wrist.     

Constraints for joint angle control of the human arm

The targeting movements of a human arm were examined when restricted to a horizontal plane. The three joints at shoulder, elbow, and wrist are allowed to move. Thus, the system is redundant and needs constraints. A model calculation using a simple form of constraint is found to describe the experimental results: a cost function is applied to each joint. The constraint consists in minimizing the sum of the costs of all three joints. The cost functions might be interpreted as to describing the energy cost necessary to move the joint and/or represent a mechanism which avoids singularities.     

Shoulder muscle function depends on elbow joint position: an illustration of dynamic coupling in the upper limb

Shoulder muscle function has been documented based on muscle moment arms, lines of action and muscle contributions to contact force at the glenohumeral joint. At present, however, the contributions of individual muscles to shoulder joint motion have not been investigated, and the effects of shoulder and elbow joint position on shoulder muscle function are not well understood. The aims of this study were to compute the contributions of individual muscles to motion of the glenohumeral joint during abduction, and to examine the effect of elbow flexion on shoulder muscle function. A three-dimensional musculoskeletal model of the upper limb was used to determine the contributions of 18 major muscles and muscle sub-regions of the shoulder to glenohumeral joint motion during abduction. Muscle function was found to depend strongly on both shoulder and elbow joint positions. When the elbow was extended, the middle and anterior deltoid and supraspinatus were the greatest contributors to angular acceleration of the shoulder in abduction. In contrast, when the elbow was flexed at 90°, the anterior deltoid and subscapularis were the greatest contributors to joint angular acceleration in abduction. This dependence of shoulder muscle function on elbow joint position is explained by the existence of dynamic coupling in multi-joint musculoskeletal systems. The extent to which dynamic coupling affects shoulder muscle function, and therefore movement control, is determined by the structure of the inverse mass matrix, which depends on the configuration of the joints. The data provided may assist in the diagnosis of abnormal shoulder function, for example, due to muscle paralysis or in the case of full-thickness rotator cuff tears.     

Interaction torque contributes to planar reaching at slow speed

Background

How the central nervous system (CNS) organizes the joint dynamics for multi-joint movement is a complex problem, because of the passive interaction among segmental movements. Previous studies have demonstrated that the CNS predictively compensates for interaction torque (INT) which is arising from the movement of the adjacent joints. However, most of these studies have mainly examined quick movements, presumably because the current belief is that the effects of INT are not significant at slow speeds. The functional contribution of INT for multijoint movements performed in various speeds is still unclear. The purpose of this study was to examine the contribution of INT to a planer reaching in a wide range of motion speeds for healthy subjects.

Methods

Subjects performed reaching movements toward five targets under three different speed conditions. Joint position data were recorded using a 3-D motion analysis device (50 Hz). Torque components, muscle torque (MUS), interaction torque (INT), gravity torque (G), and net torque (NET) were calculated by solving the dynamic equations for the shoulder and elbow. NET at a joint which produces the joint kinematics will be an algebraic sum of torque components; NET = MUS - G - INT. Dynamic muscle torque (DMUS = MUS-G) was also calculated. Contributions of INT impulse and DMUS impulse to NET impulse were examined.

Results

The relative contribution of INT to NET was not dependent on speed for both joints at every target. INT was additive (same direction) to DMUS at the shoulder joint, while in the elbow DMUS counteracted (opposed to) INT. The trajectory of reach was linear and two-joint movements were coordinated with a specific combination at each target, regardless of motion speed. However, DMUS at the elbow was opposed to the direction of elbow movement, and its magnitude varied from trial to trial in order to compensate for the variability of INT.

Conclusion

Interaction torque was important at slow speeds. Muscle torques at the two joints were not directly related to each other to produce coordinated joint movement during a reach. These results support Bernstein's idea that coordinated movement is not completely determined by motor command in multi-joint motion. Based on the data presented in this study and the work of others, a model for the connection between joint torques (muscle and passive torques including interaction torque) and joint coordination is proposed.     

System and modelling errors in motion analysis: implications for the measurement of the elbow angle in cricket bowling

The system and modelling errors of two fundamentally different motion capture systems (opto-reflective vs. video-based) were tested under various conditions, to determine their ability to accurately measure flexion-extension of the elbow angle in cricket bowling. A mechanical arm was used for all testing, that enabled known elbow flexion-extension and abduction ("carry") angles to be manually set. The root mean squared (RMS) error of 0.6 degrees for the opto-reflective system (Vicon-612) was more accurate in reconstructing a known angle than the video-based system (Peak Motus) (RMS error 2.3 degrees ) in the laboratory, when the same mathematical procedure (model) was applied to calculate the elbow flexion-extension angle. When different models were applied to the raw marker trajectories collected using the video-based system, RMS was lowest for the external marker segmental cluster models (2.3 degrees ) compared with 9.4 degrees for the vector and 4.5 degrees for the projected vector approaches, where joint centres were visually approximated. Real world, field-based comparisons using the video-based system showed that occluding the arm and therefore the shoulder, elbow and wrist joint centre locations by placing a shirt on the arm, increased RMS error for both vector (7.8 degrees -9.0 degrees ) and projected vector (4.3 degrees -5.1 degrees ) modelling approaches.