Inverse Dynamics


Inverse dynamics is one of the keystone analysis techniques used in biomechanics and gait labs. The purpose of this technique is to determine forces or toques needed to produce kinematic motions. In practice, we record human movements and use inverse dynamics to calculate the joint torques and powers our body must generate to perform said movements.

During movement, we activate muscles within our arms, legs and core, they generate forces and torques about our joints. We can record the movement of the human body (using motion capture system or video camera), but we do not know what is going on inside the body to produce the motion. Inverse dynamics is one method used quantify force production of the body -- to get kinetics from known kinematics.

The Basics

A motion capture system is used to track the motion (kinematics) of the body and limbs. Force plates record the ground reaction forces (GRFs).  Inverse dynamics uses a link-segment model. A typical leg linkage (shown below) might include foot, shank and thigh segments with joints located at the ankle, knee and hip. Based on recorded data (motion trajectories, GRFs) and simple dynamics principles (Newton-Euler equations)  we can reconstruct the net moments and powers about the joints.

What does inverse dynamics tell us?

NET joint moments, powers and forces

What does inverse dynamics NOT tell us?

  1. Contributions/activations of individual muscles

  2. Total amount of muscle work done (does not account for co-contraction of muscles)

  3. Internal bone-to-bone forces at joints

Other Assumptions/Limitations

  1. Assumes frictionless joints

  2. Assumes generalized, uniform and/or concentrated mass distribution

  3. Error in estimate of joint center of rotation

  4. Error propagation from distal to proximal joints

  5. Measurement errors (e.g., skin/motion artifacts, temporal or spatial misalignment between force plates and motion capture)

If this is inverse, what about forward dynamics?

Forward dynamics calculates the motion of the body based on known forces/torques. Experimentally, we can non-invasively record human motion (motion capture, IMUs, goniometers), but usually not forces and torques -- thus we primarily use inverse dynamics. Forward dynamics can be useful tool for simulation.