In response to our latest Make It Last Build Series project, the Drawbot, Bill Ola Rasmussen posted a link to this piece he wrote on the math involved in V-plotter design. Thanks, Bill!
What is the optimal configuration of control lines for an area to be plotted? Obviously, we can't have a drawing area above the control lines — our friend gravity sees to that. But, can we do better than hand waving and "somewhere below the control lines" for the plot area? Yes: we think up some constraints and model them with math and code (two more friends!):
Tension: We can imagine that the control lines have to be under some tension in order to be effective. For the purposes of this article we say that both string tensions must be in the range [ m/2, m*1.5 ], where m is the mass of the plotter head. Lines can neither be too slack nor too heavily loaded. The effect of this constraint is to prevent any line from being too close to horizontal or too close to vertical.
Resolution: There is a change in resolution when we map a change of length in one or both of the strings into X and Y coordinates. I.e. Coordinate system conversion causes a non-uniform step resolution. We say that, for each control line, a one unit change causes at most a 1.4 unit change in the X,Y coordinate system. We limit plotting to the area of reasonable resolution. Here our definition of reasonable is a 40% change.
To implement these requirements, we need to know how to calculate them. The next few sections talk math and have pretty pictures.
V Plotter Design
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We are thrilled to the gills to be announcing the official "Call For Makers" for Maker Faire Bay Area 2011. From the announcement, by Faire Director Sherry Huss:
We are now accepting entries for the 6th Annual Maker Faire Bay Area, May 21 and 22, 2011 at the San Mateo Event Center. We look forward to reviewing your application.
* Maker Faire Bay Area: May 21 and 22, 2011
* Entry Open Date: February 4, 2011. Please enter early so we can reserve space for your exhibit.
* Entry Close Date: March 14, 2011
* Entry Form
Organized by the staff of MAKE magazine, Make: Online and CRAFT, Maker Faire is a newfangled fair that brings together science, art, craft, and engineering plus music in a fun, energized, and exciting public forum. The aim is to inspire people of all ages to roll up their sleeves and become makers. This family-friendly event showcases the amazing work of all kinds of makers - anyone who is embracing the DIY spirit and wants to share their accomplishments with an appreciative audience.
We encourage you to join the fun and enter a project to exhibit.
Read the rest of the Call
OK, that may not be the most exciting headline I've ever written, and I'm not sure the exclamation point really helps all that much.
But I am, personally, nonetheless very excited about cardboard bins right now, because thanks to them, for the first time in almost five years, I am no longer burdened by a giant unsorted junk parts bucket.
I have played around with a lot of part storage systems and I've finally decided that bins are where it's at. Unfortunately, "professional" plastic parts bin systems are prohibitively expensive for the number I need to satisfy my organizational compulsion. But these fold-up corrugated bins I bought off Amazon only cost 69 cents apiece, including shipping.
I took an old bookcase and added an extra "halfway" shelf to each level; 6" per shelf leaves plenty of room to toss parts into the bins without wasting space. The finished unit holds ninety 4 x 4.5 x 12" bins, which are labeled with a thermal-tape printer and arranged alphabetically. You can see the whole enchilada in my Flickr set.
Got a favorite parts storage hack? Let me know, below!
By George Hart for the Museum of Mathematics
I believe that in the future, 3D printing machines will commonly be used to make household parts, e.g., when you need to fix a broken appliance knob or handle. I put this into practice recently when I needed a replacement light dimmer knob and decided to make my own. So, I created this knob based on a lovely polyhedron, the rhombic enneacontahedron. It works well and looks like a little geodesic igloo on the wall.
This is a great opportunity to incorporate some mathiness around the house, so I made a second design, based on the (7,6,6) uniform tiling in the hyperbolic plane. Notice there are both 6-sided and 7-sided craters. At each corner, one 7-sided and two 6-sided craters meet.
If you have access to a 3D printer, you can make your own copies of these mathematical dimmer switches using the stl files available here. They fit right on the shafts of standard US dimmer switches.
See all of George Hart's Math Monday columns
Ranjit Bhatnagar whipped up this laser cut ocarina, and provides the plans so you can make your own. Not sure how to get started? Ranjit's running a laser whistle workshop Saturday 2/12/11 at NYC Resistor in Brooklyn.
Lego color wheel, above, from Brickshelf user Chris Behrens, inspired by that below, from Danish enthusiast Niels Bugge. What does it mean?!?
The 4-Bit Microcomputer Kit
from the Maker Shed
features a 20-key keypad, a 7-segment LED, and 7 individual LEDs. It comes pre-programmed with 7 different applications, and you can even program your own via the keypad. It's a fun retro kit, just begging to be hacked! Don't forget to check out the Gakken magazine 4-bit computer rollout party
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If you're considering NOT entering the 555 contest, be sure to peep their list of prizes before you make that decision. There's a pro Eagle license from Element 14, a scope and DMMs from Extech, XMEGA dev kits, XuLA boards, a Nexus S phone from Google, a couple of Fluke DMMs, a SumoBot competition kit from Digi-Key, and tons, tons more. Here are the rules. The deadline is March 1st. Enter early and often, and good luck!
Also, NYC hackerspace Alpha One Labs is suggesting a 555 focus for the 16th Global Synchronous Hackathon to be held the 19th of February -- a great opportunity to finish up your project in a single night.
I have a little box in the top drawer of my workbench that I think of as a kind of miniature trophy room. Every time I successfully remove a tamper-resistant, "security," or other PITA fastener, I toss it in the box. Last week it occurred to me that this might be a fun habit to share with the rest of the web. To that end, and with the gracious assistance of Flickr user Tom Magliery, I present the Tamper 'proof' screws and fasteners pool. If you're Flickr-friendly and have trophies of your own to share, please join us!
Don't miss the second episode of Make: Live, which airs this Wednesday night! Our theme is soldering and we'll have Limor "Ladyada" Fried from Adafruit Industries in studio and Marc deVinck, Maker Shed's Director of Product Development calling in via Skype. Not only that, but we'll also have another awesome giveaway. So be sure to set your soldering irons to 375 degress, head over to Make: Live, and join our garrulous friends in the chat room:Make: Live 02 - The Soldering Episode
Wednesday February 9th, 9pm ET/6pm PT
Watch at makezine.com/live
or on UStream