Phase shift between joint rotation and actuation reflects dominant forces and predicts muscle activation patterns

Area of Science:

• Biomechanics
• Locomotion Analysis
• Comparative Physiology

Background:

• Actuation work during behavior is resisted by inertia, elastic forces, gravity, and viscosity.
• Existing dimensionless numbers (e.g., Froude, Reynolds) use ratios of two forces, limiting broad comparisons across different animal sizes and speeds.
• A comprehensive dimensionless number is needed to compare behaviors across orders of magnitude of limb length and cycle period.

Purpose of the Study:

• To propose a novel dimensionless number that integrates gravitational, inertial, elastic, and viscous forces.
• To express this dimensionless number, the phase shift (ϕ), as a function of limb length and cycle period for terrestrial walking using allometric scaling.
• To utilize scale-dependent values of ϕ to explain and predict electromyographic (EMG) patterns in walking animals.

Main Methods:

• Development of a new dimensionless number, the phase shift (ϕ), representing the relationship between limb displacement and actuator force.
• Application of allometric scaling laws to relate ϕ to limb length and cycle period in terrestrial locomotion.
• Correlation of scale-dependent ϕ values with observed electromyographic (EMG) activity in various animal models.

Main Results:

• The phase shift (ϕ) successfully relates gravitational, inertial, elastic, and viscous forces in a single dimensionless parameter.
• Allometric scaling provides a predictive relationship between ϕ, limb length, and cycle period for terrestrial walking.
• Scale-dependent ϕ values correlate with and predict observed electromyographic (EMG) patterns across different animal gaits.

Conclusions:

• The phase shift (ϕ) offers a unified framework for analyzing and comparing animal locomotion across diverse scales.
• This dimensionless number advances our understanding of how dominant forces influence motor control and neural activation patterns.
• The findings provide a powerful tool for predicting biomechanical and physiological responses in locomotion studies.