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Mont Hubbard, Robin L. Hibbard, Maurice R. Yeadon, and Andrzej Komor

This paper presents a planar, four-segment, dynamic model for the flight mechanics of a ski jumper. The model consists of skis, legs, torso and head, and arms. Inputs include net joint torques that are used to vary the relative body configurations of the jumper during flight. The model also relies on aerodynamic data from previous wind tunnel tests that incorporate the effects of varying body configuration and orientation on lift, drag, and pitching moment. A symbolic manipulation program, “Macsyma,” is used to derive the equations of motion automatically. Experimental body segment orientation data during the flight phase are presented for three ski jumpers which show how jumpers of varying ability differ in flight and demonstrate the need for a more complex analytical model than that previously presented in the literature. Simulations are presented that qualitatively match the measured trajectory for a good jumper. The model can be used as a basis for the study of optimal jumper behavior in flight which maximizes jump distance.

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E. Yu Shapkova, A.V. Terekhov, and M.L. Latash

We studied the coordination of arm movements in standing persons who performed an out-of-phase arm-swinging task while stepping in place or while standing. The subjects were instructed to stop one of the arms in response to an auditory signal while trying to keep the rest of the movement pattern unchanged. A significant increase was observed in the amplitude of the arm that continued swinging under both the stepping and standing conditions. This increase was similar between the right and left arms. A dynamic model was developed including two coupled nonlinear van der Pol oscillators. We assumed that stopping an arm did not eliminate the coupling but introduced a new constraint. Within the model, superposition of two factors, a command to stop the ongoing movement of one arm and the coupling between the two oscillators, has been able to account for the observed effects. The model makes predictions for future experiments.

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Andrea Biscarini

A two-dimensional model has been developed to predict and explain the effects of the variation of muscle moment arms during dynamic exercises involving heavy external loads. The analytical dependence of the muscle moment arm on the joint angle and on the origin and insertion position was derived for an ideal uniaxial hinge joint, modeling the muscle as a cable following an idealized minimum distance path from the origin to insertion that wraps around the bony geometry. Analytical expressions for the ratios of muscular force and the joint restraining reaction components to the external load weight were deduced, for isokinetic and static exercises, as a function of joint angle, joint angular velocity, and the other geometric parameters defining the model. Therefore, external load weight, joint angular velocity, and constraints to joint range of motion may be adjusted reciprocally in order to control in advance the peak value of the components of the joint load during isokinetic exercises. A dynamic formulation of forearm flexion/extension was solved numerically under the condition of constant biceps force in order to highlight the key role played by the variation in muscle moment arm in preventing injury during lifting of external loads against gravity. For example, our analysis indicates that the mean and peak resultant joint loads decrease by 5% and 14%, respectively, as a result of the change in muscle moment arm that occurs over the range of motion.

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Ghazaleh Azizpour, Matteo Lancini, Giovanni Incerti, Paolo Gaffurini, and Giovanni Legnani

) crank center. The proposed dynamic model was recognized to be suitable for subjects with trunk mobility limitations. The customized HB that was classified as an arm-powered HB was exclusively intended for use in people with complete spinal cord injuries in their upper thorax. In the arm

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Alasdair R. Dempsey, Bruce C. Elliott, Bridget J. Munro, Julie R. Steele, and David G. Lloyd

Anterior cruciate ligament (ACL) injuries are costly. Sidestep technique training reduces knee moments that load the ACL. This study examined whether landing technique training alters knee moments. Nineteen team sport athletes completed the study. Motion analysis and ground reaction forces were recorded before and after 6 weeks of technique modification. An inverse dynamic model was used to calculate three-dimensional knee loading. Pre- and postintervention scores were compared using paired t tests. Maximal knee flexion angle during landing was increased following training. There was no change in valgus or flexion moments, but an increase in peak internal rotation moment. This increase in internal rotation moment may increase the risk of ACL injury. However, the increased angle at which the peak internal rotation moment occurred at follow up may mitigate any increase in injury risk by reducing load transmission.

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Suvobrata Mitra, Polemnia G. Amazeen, and Michael T. Turvey

We investigated the 1:1 frequency locking of two hand-held pendulums oscillated parallel to the body's coronal plane. In this configuration, anti-phase defined muscularly is in-phase defined spatially, and vice versa. Coordination equilibria measured by average relative phase were shifted less from muscular anti-phase than from muscular in-phase by detuning (unequal uncoupled pendulum frequencies) and were shifted less in both modes with vision than without. Variability of the equilibria, however, was ordered opposite to their degrees of shift and was unaffected by vision. Demonstrated subcritical pitchfork and tangent bifurcations conformed to the variability classification of anti- and in-phase coordination. Implications for dynamical models, hierarchical control, and definitions of coordination modes were discussed.

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Mary M. Rodgers, Srinivas Tummarakota, and Junghsen Lieh

A three-dimensional (3-D) inverse dynamic model of wheelchair propulsion was developed using the Newton-Euler method based on body coordinate systems. With this model, the arm was assumed to be three rigid segments (hand, forearm, and upper arm) connected by the wrist, elbow, and shoulder joints. A symbolic method was adopted to generate the equations of motion. The model was used to compute the joint forces and moments based on the inputs obtained from a 3-D motion analysis system, which included an instrumented wheelchair, video cameras, and a data acquisition system. The linear displacements of markers placed on the joints were measured and differentiated to obtain their velocities and accelerations. Three-dimensional contact forces and moments from hand to handrim were measured and used to calculate joint forces and moments of the segments.

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Rahman Davoodi and Gerald E. Loeb

Computer models of the neuromusculoskeletal systems can be used to study different aspects of movement and its control in humans and animals. SIMM with Dynamics Pipeline (Musculographics Inc., Chicago) and SD-Fast (Symbolic Dynamics Inc., Mountain View, CA) are software packages commonly used for graphic and dynamic simulation of movement in musculoskeletal systems. Building dynamic models with SIMM requires substantial C programming, however, which limits its use. We have developed Musculoskeletal Modeling in Simulink (MMS) software to convert the SIMM musculoskeletal and kinetics models to Simulink (Mathworks Inc., Natick, MA) blocks. In addition, MMS removes SIMM’s run-time constraints so that the resulting blocks can be used in simulations of closed-loop sensorimotor control systems.

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Daniel J. Wilson, Kyle Gibson, and Gerald L. Masterson


To evaluate the anterior shift of the body’s center of gravity (CG) and the associated inertial forces produced by 2 styles of a partial forward lunge.


Gait-analysis laboratory of a research institution.


10 healthy volunteers.


3 trials of each lunge.

Main Outcome Measures:

Kinematic data were collected, and inertial reaction forces were resolved into net compressive and shear forces using an inverse dynamic model.


Significantly (P < .001) greater anterior translation of the CG was found with an arms-in-front v arms-across-chest lunge style. No significant differences were found between the average peak inertial compressive and shear forces of the 2 styles (427 ± 184 N v 426 ± 187 N, −536 ± 113 N v −538 ± 127 N).


Anterior translation of the CG was larger with the arms-forward partial-lunge position, creating increased balance demands. Both styles produced clinically safe (posteriorly directed) inertial shear forces, with greater anterior CG shift with the arms-forward style.

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LeRoy W. Alaways, Sean P. Mish, and Mont Hubbard

Pitched-baseball trajectories were measured in three dimensions during competitions at the 1996 Summer Olympic games using two high-speed video cameras and standard DLT techniques. A dynamic model of baseball flight including aerodynamic drag and Magnus lift forces was used to simulate trajectories. This simulation together with the measured trajectory position data constituted the components of an estimation scheme to determine 8 of the 9 release conditions (3 components each of velocity, position, and angular velocity) as well as the mean drag coefficient CD and terminal conditions at home plate. The average pitch loses 5% of its initial velocity during flight. The dependence of estimated drag coefficient on Reynolds number hints at the possibility of the drag crisis occurring in pitched baseballs. Such data may be used to quantify a pitcher’s performance (including fastball speed and amount of curve-ball break) and its improvement or degradation over time. It may also be used to understand the effects of release parameters on baseball trajectories.