> For the complete documentation index, see [llms.txt](https://wvu-neuromint.gitbook.io/neuromint-resources/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://wvu-neuromint.gitbook.io/neuromint-resources/technical-guides/robot-design/kinematics-and-dynamics.md).

# Kinematics and Dynamics

This page contains links to Nick's notes on multi-link kinematics and dynamics. These notes begin with 2D systems and then continue with 3D systems.

## Lesson 1 - Degrees of Freedom, Complex Vector Notation

{% file src="/files/-Mi46rkBy6WZzDFTlQ\_E" %}
machineDesign01 - 2D basics
{% endfile %}

## Lesson 2 - Vector Loop Equations, Newton-Raphson Solver

{% file src="/files/-Mi47V\_QcrsOkWtbj9lv" %}
machineDesign02 - Vector loops
{% endfile %}

## Lesson 3 - Inverse Kinematics, Lagrange Multipliers

{% file src="/files/-Mi47u0XmBKiObs35egf" %}
machineDesign03 - Inverse kinematics
{% endfile %}

## Lesson 4 - Calculating Velocity and Acceleration

{% file src="/files/-Mi48A\_FRB0aMR2GpDaV" %}
machineDesign04 - Velocity and acceleration
{% endfile %}

## Lesson 5 - Inverse Dynamics

{% file src="/files/-Mi48V6bv\_XAIchqDGmP" %}
machineDesign05 - Inverse dynamics
{% endfile %}

## Lesson 6 - Inverse Dynamics for Redundant Systems

{% file src="/files/-Mi48jKTZAeIl6OU8Wf-" %}
machineDesign06 - Inverse dynamics redundant
{% endfile %}

## Lesson 7 - 3D Basics, Matrix Exponentials

{% file src="/files/-Miv4XAy2Zqyes\_REum8" %}
machineDesign07 - 3D kinematics
{% endfile %}

## Lesson 8 - 3D Rigid Body Motion, Coordinate Transformations

{% file src="/files/-Miv62hCLgyVVcvLn84S" %}

## Lesson 9 - 3D Rigid Body Velocity

{% file src="/files/-Miv9u\_55sS3hjkUhOOk" %}

## Lesson 10 - 3D Rigid Body Manipulator Forward Kinematics

{% file src="/files/Q1fILxObcOYjD8H70lyK" %}

## References

2D material comes from: Norton RL (1999) Design of machinery. 5th Ed. New York: McGraw-Hill.<br>

3D material comes from: Murray RM, Li Z, Sastry SS (1994) A Mathematical Introduction to Robotic Manipulation. Book, <https://doi.org/10.1201/9781315136370>. (This is available online as a pdf; just search Google Scholar).

A more up-to-date reference for the 3D material is: Lynch KM, Park FC (2017) Modern Robotics - Mechanics, Planning, and Control. (Legal preprint pdf: <http://hades.mech.northwestern.edu/images/7/7f/MR.pdf>). This book has an accompanying YouTube playlist: <https://youtube.com/playlist?list=PLggLP4f-rq02vX0OQQ5vrCxbJrzamYDfx>.