This page describes the basics of Yeadon’s inertia model. It is expected that the user of this package has read Yeadon’s 1990 papers, especially Yeadon 1990-ii. There are four related papers, identified by numerals i-iv.
Here is a summary of his four papers:
- i: motivation, conceptual description of joints, obtaining orientation angles from film
- ii: modeling human geometry using stadium solids
- iii: inertia transforms and angular momentum of the stadium solids
- iv: simulation verification
Yeadon models a human using 39 stadium solids and 1 semi-ellipsoid (for the head). These 40 solids make up 11 rigid body segments, which are connected to each other via joints (e.g., the knee). This relatively simple geometry allows for one to swiftly calculate quantities relevant for dynamics. These quantities are mass, center of mass positions, and inertia tensors. These quantities can be obtained in the global reference frame, or in the local frame of a segment or solid.
One can use this package to incorporate a human into equations of motion, though this endeavor is left to the user. The package does not deal at all with angular momentum (the topic of paper iii).
There are a few differences between Yeadon’s model described in his publications and the model implemented in this package. Here are some of the bigger ones:
- In Yeadon’s model, the global frame of the human is defined in a complicated way that depends on the configuration of the human. In this package, the global frame does not depend on the configuration.
- In Yeadon’s model, the orientation of the legs are related to each other, so that there are less degrees of freedom than there are joint angles (generalized coordinates). No joint angles are coupled in this package.
- Yeadon provides the option of formulating the model with additional joints for the feet and hands. Here, the feet and hands are rigid parts of the legs and forearms, respectively.
- Yeadon labels the solids with indices starting from 1 (s1 is the first solid), while this package indexes the solids from 0 (s0 is the first solid). The labels for the segments (e.g. A1, J1, etc.) are unchanged.
- Both packages allow making the model symmetric (averaging both the two arms and the two legs), but do so in different ways. We average the input measurements for the limbs, and then proceed to compute masses, center of mass positions, and inertia tensors with these averaged measurements. Yeadon, however, enforces symmetry by averaging these three quantities as the last step (the measurements across limbs are not averaged).