Zenon Mazur

An improved inverse dynamics formulation for estimation of external and internal loads during human sagittal plane movements.

Planar musculoskeletal models are common in the inverse dynamics analysis of human movements such as walking, running and jumping. The continued interest in such models is justified by their simplicity and computational efficiency. Related to a human planar model, a unified formulation for both the flying and support phases of the sagittal plane movements is developed. The actuation involves muscle forces in the lower limbs and the resultant muscle torques in the other body joints. The dynamic equations, introduced in absolute coordinates of the segments, are converted into useful compact forms using the projective technique. The solution to a determinate inverse dynamics problem allows for the explicit determination of the external reactions (presumed to vanish during the flying phases) and the resultant muscle torques in all the model joints. The indeterminate inverse dynamics problem is then focused on the assessment of muscle forces and joint reaction forces selectively in the supporting lower limb. Numerical results of the inverse dynamics simulation of sample sagittal plane movements are reported to illustrate the validity and effectiveness of the improved formulation.

Contact modeling and inverse dynamics identification of the handspring front somersault in pike position

Handspring front somersaults are explosive and exciting events consisting of several distinct ballistic motion and support phases, in which the gymnast contacts the springboard/mat and the table, respectively, with his feet and hands. The purpose of this article is to develop an effective formulation for the inverse dynamics simulation of all the vaults that are suitable for analyses in two dimensions. A planar model of a jumper composed of 16 rigid segments connected by 15 hinge joints is used in the computations. The determinate inverse dynamics formulation, developed in Cartesian coordinates of the segments, allows for the explicit estimation of the resultant muscle torques in the joints and external reactions (up to three components) during the analyzed vaults. By using a projection method, the analysis is then confined to the lower limbs. A computational scheme for the indeterminate inverse dynamics is proposed to distribute the previously assessed net torques in the limbs into the respective muscle forces based on static optimization solution. The reaction forces in the lower limb joints are finally determined following the projection-based formulation. Some numerical results of the inverse dynamics simulation of the handspring front somersault in pike position are reported.

Assessment of external and internal loads in the triple jump via inverse dynamics simulation.

The triple jump is a demanding athletics event that, after an approach run, consists of three consecutive phases: the hop, the bound, and the jump. During the involved three take-off actions a jumper is exposed to increased risk of injury due to the high impact forces from the ground and powerful muscle/tendon efforts, which are further reflected in the internal loads of the lower limb joints. While external ground reactions can possibly be measured using force platforms, in vivo measurements of the internal loads are practically not feasible. The purpose of the paper is to present the development of an effective formulation for the inverse dynamics simulation of the triple jump, based on the jumper dynamical model and non-invasive kinematic recordings of the movement. The developed simulation model serves for the analysis of all the triple jump phases, irrespective of whether the jumper is in flight or in contact with the ground with one of his feet, and is focused on effective assessment of the external reactions on the supporting leg as well as the muscle forces and joint reaction forces in the leg. Some numerical results of inverse dynamics simulation of the triple jump are reported.

Biomechanical Assessment of Motor Abilities in Male Handball Players During the Annual Training Macrocycle

Abstract Introduction. The aim of the study was to determine the torque of the knee extensors and flexors of the lead lower limb, the torque of the shoulder extensors and flexors of the dominant upper limb, and the torque generated by the muscles of the kinematic chain going from the trail lower limb to the hand of the dominant limb in male handball players during the annual training macrocycle. Changes in jump height and throwing velocity were also investigated. Material and methods. The study involved 13 handball players from a Polish second-league team. The measurements were performed four times: at the beginning of the preparation period, at the beginning of the season, at the end of the first part of the season, and at the end of the second part of the season. Torque was measured in isokinetic and isometric conditions. Jumping ability was tested using a piezoelectric platform, and throwing velocity was measured with a speed radar gun. Results. The study found statistically significant differences between the relative torque values of the knee extensors (p < 0.002) and flexors (p < 0.003) of the lead leg measured in isokinetic conditions between the first three measurements and the final one. Isokinetic measurement of the torque of the muscles of the kinematic chain going from the trail leg to the hand of the dominant arm decreased in a statistically significant way at the end of the season. As for the results of the measurement of the torque of the shoulder extensors and flexors in static conditions, no statistically significant differences were observed between the four measurements. However, statistically significant differences were noted in jumping ability and throwing velocity in the annual training macrocycle. Conclusions. The results of the study indicate that there is a need to perform regular assessments of players’ strength and jumping ability during the competition period. There is a need to modify the training methods used during the preparation period and in the second part of the season as well as to individualise training at the end of the competition period.