# Kinematics

## Submodules

### Jacobians

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

### Kinematics Introduction

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

### 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.

## 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.

### Solving Nonlinear Four-Bar Constraints

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

### Vector Constraint Equations

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

### Vectors and Vector Math

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

## Tutorials

### Graphical Synthesis

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

### 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.

### Solidworks Export Tutorial

Introduction This tutorial picks up from the Solidworks Kinematics 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.

### Solve Triangle

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

### Symbolic Constraint Equations with Pynamics

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