Dynamics of Two-Link Musculoskeletal Chains during Fast Movements: Endpoint Force, Axial, and Shear Joint Reaction Forces

This study provides a dynamic model for a two-link musculoskeletal chain controlled by single-joint and two-joint muscles. The chain endpoint force, and the axial and shear components of the joint reaction forces, were expressed analytically as a function of the muscle forces or torques, the chain configuration, and the link angular velocities and accelerations. The model was applied to upper-limb ballistic push movements involving transverse plane shoulder flexion and elbow extension. The numerical simulation highlights that the shoulder flexion and elbow extension angular acceleration at the initial phase of the movement, and the elbow extension angular velocity and acceleration at the later phase of the movement, induce a proportional medial deviation in the endpoint force direction. The forearm angular velocity and acceleration selectively affect the value of the axial and shear components of the shoulder reaction force, depending on the chain configuration. The same goes for the upper arm and elbow. The combined contribution of the elbow extension angular velocity and acceleration may give rise to anterior shear force acting on the humerus and axial forearm traction force as high as 300 N. This information can help optimize the performance and estimate/control of the joint loads in ballistic sport activities and power-oriented resistance exercises.

Automated summary

This study presents a dynamic model for a two-link musculoskeletal chain controlled by different muscles. The model allows analytical expression of the joint reaction forces and chain endpoint force, based on muscle forces/torques, chain configuration, and link angular velocities/accelerations. The findings from numerical simulation reveal that angular acceleration of shoulder flexion and elbow extension at different phases of the movement influence the direction of the endpoint force. Forearm angular velocity and acceleration also impact the axial and shear components of the shoulder reaction force, depending on the chain configuration. The information obtained can be beneficial for optimizing performance and controlling joint loads in ballistic sports and resistance exercises.