Kinematics
Tutorials
Graphical Synthesis
A popular way of deriving the desired kinematics of a device graphically has also been employed for centures.
Go to Graphical SynthesisSketching 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 CADSolidworks Export Tutorial
Introduction This tutorial picks up from the Solidworks Kinematics Tutorial
Go to Solidworks Export TutorialSolidworks 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 TutorialSolve Triangle
This example shows how to solve geometric constraints for a triangle of given length sides
Go to Solve TriangleSymbolic 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 PynamicsOthers
Jacobians
A Jacobian is a matrix that collects the partial derivatives of rates of change between two vectors.
Go to JacobiansKinematics Introduction
Prototyping in Paper A second step is to ideate, mock-up, and prototype candidate mechanisms in paper.
Go to Kinematics IntroductionSingularities 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 ProblemsSolving 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 PythonSolving Nonlinear Four-Bar Constraints
Turn on inline plotting %matplotlib inline import required packages import pynamics from pynamics.
Go to Solving Nonlinear Four-Bar ConstraintsVector Constraint Equations
v,w perpendicular Here the intuition is that perpendicular lines have an angle of $\theta$ between them.
Go to Vector Constraint EquationsVectors and Vector Math
A $\vec{v}$ defines a magnitude and direction in $n$-dimensional space.
Go to Vectors and Vector MathTopics
- 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