README.md
This repository contains the source code for the bioNC library, a python package for biomechanics and natural coordinates formalism.
Inverse and Forward approach are implemented.
## Status
 <a href="https://opensource.org/licenses/MIT"><img src="https://img.shields.io/badge/license-MIT-success" alt="License"/></a>
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# Table of Contents
-[Installation](#installation)
-[A first practical example](#a-first-practical-example)
-[Mathematical backends](#mathematical-backends)
-[Natural coordinates reminders](#natural-coordinates-reminders)
# Installation
- from conda:
```
conda install -c conda-forge bionc
```
- from source:
```
python setup.py install
```
# A first practical example
The easiest way to learn bionc is to dive into it.
So let's build our first model.
Please note that this tutorial is designed to recreate example which builds a lower limb model (Pelvis, Thigh, Shank, Foot). You can have look to [https://github.com/Ipuch/bioNC/blob/main/examples/model_creation/main.py](https://github.com/Ipuch/bioNC/blob/main/examples/model_creation/main.py)
<img src="./docs/inverse_kinematics_viz.png" alt="Inverse kinematics" width="200"/>
# Mathematical backends
This toolbox support two mathematical backends: `numpy` and `casadi`.
# Natural coordinates reminders
The $i$-th body in a biomechanism with $N$ bodies has generalized coordinates:
```math
Q_i = (u_{i}, r_{p_{i}}, r_{d_{i}}, w_{i}) \in \mathbf{R}^3 \times \mathbf{R}^3 \times \mathbf{R}^3 \times \mathbf{R}^3,
```
represented in natural coordinates.
- $u$: is the proximal vector in the global coordinate system.
- $r_p$: the position of the proximal point in the global coordinate system.
- $r_d$: the position of the distal point in the global coordinate system.
- $w$: is the distal vector in the global coordinate system.
The biomechanism generalized coordinates:
```math
Q = (Q_1, \dots, Q_N).
```
is the concatenation of all body coordinates.
To rigidify the body segments and to articulate them, two types of holonomic constraints are handled in this formalism: rigid-body constraints and joint constraints (also termed as kinematic constraints), denoted $\Phi^r(Q)$ and $\Phi^j(Q)$, respectively, and gathered in a common constraint function $\Phi$:
```math
\begin{align}
\Phi(Q) = \left(
\Phi^r(Q) \quad
\Phi^j(Q)
\right)^\top
\in \mathbf{R}^{6 \times N} \times \mathbf{R}^M.
\end{align}
```
# How to cite
Pierre Puchaud, Alexandre Naaim, & Anais Chaumeil. (2024). Ipuch/bioNC: CarpentersTogether (0.9.0). Zenodo. https://doi.org/10.5281/zenodo.10822669
```
@software{pierre_puchaud_2024_10822669,
author = {Pierre Puchaud and
Alexandre Naaim and
Anais Chaumeil},
title = {Ipuch/bioNC: CarpentersTogether},
month = mar,
year = 2024,
publisher = {Zenodo},
version = {0.9.0},
doi = {10.5281/zenodo.10822669},
url = {https://doi.org/10.5281/zenodo.10822669}
}
```
# Reference
This work is an implementation mostly inspired by the work of Dr. Raphael Dumas (Senior Researcher at IFSTTAR – University of Lyon) on three-dimensional multi-body modeling of the human musculoskeletal system.