# Kinematics

## Submodules

### Jacobians

A Jacobian is a matrix that collects the partial derivatives of rates of change between two vectors.

Go to Jacobians### Kinematics Introduction

Prototyping in Paper A second step is to ideate, mock-up, and prototype candidate mechanisms in paper.

Go to Kinematics Introduction### Singularities and Solver Problems

Many of the devices you will prototype are highly nonlinear mechanisms which may have certain charactersitics which are hard to solve for in your typical CAD sketcher.

Go to Singularities and Solver Problems### Solving Kinematics Numerically with Python

## Introduction

This module takes you through solving the motion of a device by using a numerical nonlinear solver to solve a complex system of constraint equations. We will be using a number of Python packages to do this.

Go to Solving Kinematics Numerically with Python### Solving Nonlinear Four-Bar Constraints

Turn on inline plotting %matplotlib inline import required packages import pynamics from pynamics.

Go to Solving Nonlinear Four-Bar Constraints### Vector Constraint Equations

v,w perpendicular Here the intuition is that perpendicular lines have an angle of $\theta$ between them.

Go to Vector Constraint Equations### Vectors and Vector Math

A $\vec{v}$ defines a magnitude and direction in $n$-dimensional space.

Go to Vectors and Vector Math## Tutorials

### Graphical Synthesis

A popular way of deriving the desired kinematics of a device graphically has also been employed for centures.

Go to Graphical Synthesis### Sketching 2D Kinematics in CAD

Introduction Steps Create a planar sketch Turn off the background color in Solidworks by changing the background to plain white in the options at the top of the viewport window.

Go to Sketching 2D Kinematics in CAD### Solidworks Export Tutorial

Introduction This tutorial picks up from the Solidworks Kinematics Tutorial

Go to Solidworks Export Tutorial### Solidworks Kinematics Tutorial

Solidworks is an attractive way to model popup devices because you can interact with the three-dimensional kinematics of your popup device.

Go to Solidworks Kinematics Tutorial### Solve Triangle

This example shows how to solve geometric constraints for a triangle of given length sides

Go to Solve Triangle### Symbolic Constraint Equations with Pynamics

Import libraries import pynamics from pynamics.system import System from pynamics.frame import Frame from pynamics.

Go to Symbolic Constraint Equations with Pynamics## Topics

- Chebychev–Grübler–Kutzbach criterion (counting degrees of freedom)
- Constraints
- http://www1.cs.columbia.edu/~allen/F15/NOTES/frames.pdf
- http://smpp.northwestern.edu/savedLiterature/Spong_Textbook.pdf
- http://www1.cs.columbia.edu/~allen/F15/NOTES/forwardspong.pdf
- http://www1.cs.columbia.edu/~allen/F15/NOTES/forwardkin2.pdf
- http://www1.cs.columbia.edu/~allen/F15/NOTES/invkin.pdf
- http://www1.cs.columbia.edu/~allen/F15/NOTES/stanfordinvkin.pdf
- http://www1.cs.columbia.edu/~allen/F15/NOTES/jacobians.pdf