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Updated: Jul 15, 2026

Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion
Published on: April 11, 2018
Maximum voluntary joint torque as a function of joint angle and angular velocity: model development and application
Dennis E Anderson1, Michael L Madigan, Maury A Nussbaum
1Department of Engineering Science and Mechanics, (MC 0219), Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA.
This study presents a new model for human strength, accounting for joint angle and velocity variations. This allows for more accurate comparisons in physical activity analyses.
Area of Science:
- Biomechanics
- Human Physiology
- Kinesiology
Background:
- Human strength measurements are crucial for analyzing physical activities.
- Existing methods often measure maximum voluntary torque at a single joint angle and angular velocity.
- Available strength significantly varies with joint position and velocity, necessitating dynamic considerations.
Purpose of the Study:
- To develop and validate a model predicting maximum voluntary joint torque based on joint angle and angular velocity.
- To incorporate physiological relationships between muscle force, length, and velocity into the model.
- To provide an efficient method for comparing calculated joint torques with maximum available joint torques during dynamic activities.
Main Methods:
- A mathematical model was developed using established physiological principles of muscle force-length and force-velocity relationships.
- The model was tested by fitting it to maximum voluntary joint torque data.
- Data were collected for isometric, concentric, and eccentric contractions across six lower limb movements (hip/knee extension/flexion, ankle plantar/dorsiflexion).
Main Results:
- Model parameters were successfully derived for each exertion direction, stratified by gender and age group.
- The model effectively captures the relationship between joint torque, angle, and velocity.
- The study provides specific model parameters for various lower limb movements.
Conclusions:
- The developed model offers an efficient way to account for strength variations due to joint angle and velocity.
- This model enhances the accuracy of comparing dynamic joint torques with maximal capabilities.
- It provides a valuable tool for biomechanical analyses of physical activities.
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