Hellow guys, Welcome to my website, and you are watching How to Design a Wheel That Rolls Smoothly Around Any Given Shape. and this vIdeo is uploaded by Morphocular at 2022-12-20T08:14:14-08:00. We are pramote this video only for entertainment and educational perpose only. So, I hop you like our website.
| Name | How to Design a Wheel That Rolls Smoothly Around Any Given Shape |
| Video Uploader | Video From Morphocular |
| Upload Date | This Video Uploaded At 20-12-2022 16:14:14 |
| Video Discription | Go to https://brilliant.org/Morphocular to get started learning STEM for free. The first 200 people get 20% off an annual premium subscription. In previous videos, we looked at how to find the ideal road for any given wheel shape and vice-versa, but what about getting two wheels to roll smoothly around each other? Would two such wheels work as gears? Episode 1: https://youtu.be/xGxSTzaID3k Episode 2: https://youtu.be/Y0aOxj5lrKY =Chapters= 0:00 - Intro 1:23 - Defining smooth rolling 2:30 - Sidenote about gears 3:16 - The Wheel-Coupling Equations 7:34 - Sanity check 9:24 - The partner for an ellipse 12:24 - The connection between ellipses and parabolas 13:23 - Finding self-coupling wheels 16:35 - The partner for a square 19:21 - A look back 20:20 - A fractal wheel?? 20:47 - Brilliant ad =============================== I would also like to thank the user @BeekersSqueakers whose comment I think it was that taught me that a partner wheel can be generated by first generating a road and then generating a wheel on its underside. This comment was directly responsible for inspiring the technique shown in this video to easily generate self-coupling wheels, and dramatically simplified the second half of this video! So a seriously genuine thank you to @BeekersSqueakers and to all those who actually took up the call to answer my challenge problems in a comment! They can have a surprisingly big impact sometimes! =============================== For a deeper dive into the concepts explored in these videos, take a look at the paper "Roads and Wheels," an article by Leon Hall and Stan Wagon that appeared in Mathematics Magazine, Vol. 65, No. 5 (Dec 1992). You can find it here: https://web.mst.edu/~lmhall/Personal/RoadsWheels/RoadsWheels.pdf =============================== CREDITS The music tracks used in this video are (in order of first appearance): "Rubix Cube", "Checkmate", "Ascending", "Orient", "Falling Snow" The track "Rubix Cube" comes courtesy of Audionautix.com =============================== Want to support future videos? Become a patron at https://www.patreon.com/morphocular Thank you for your support! =============================== The animations in this video were mostly made with a homemade Python library called "Morpho". If you want to play with it, you can find it here: https://github.com/morpho-matters/morpholib |
| Category | Education |
| Tags | math | calculus | roads and wheels | gears | differential equations | wheels | roads |
