We asked Dustyn Roberts, who teaches a course at NYU’s Interactive Telecommunications Program (ITP), called Mechanisms and Things That Move, to contribute something on fabricating your own gears for our Physical Science and Mechanics theme. Dustyn has written a book, called Making Things Move. It’ll be out in the fall and we’ll have more about it, and likely a giveaway, then. Thanks, Dustyn! — Gareth
Gears are easy to understand, make, and use, if you know the vocabulary and can space the gears at the correct distance apart. One nice thing about gears is that if you know any two things about them – let’s say outer diameter and number of teeth — you can use some simple equations to find everything else you need to know, including the correct center distance between them. First, look over the anatomy of the spur gear pair in figure 1 and the vocab below.
Number of Teeth (N) Pitch Diameter (D): The circle on which two gears effectively mesh, about halfway through the tooth. The pitch diameters of two gears will be tangent when the centers are spaced correctly.Diametral Pitch (P): The number of teeth per inch of the circumference of the pitch diameter. Think of it as the density of teeth — the higher the number, the smaller and more closely spaced the teeth on a gear. Common diametral pitches for hobby-size projects are 24, 32, and 48. The diametral pitch of all meshing gears must be the same.Circular Pitch (p) = pi / P: The length of the arc between the center of one tooth and the center of a tooth next to it. This is just pi (I€ = 3.14) divided by the diametral pitch (P). Although rarely used to identify off the shelf gears, you may need this parameter when modeling gears in 2D and 3D software like we’re doing here. As with diametral pitch, the circular pitch of all meshing gears must be the same.Outside Diameter (Do): The biggest circle that touches the edges of the gear teeth. You can measure this using a caliper like Sparkfun.com’s # TOL-00067.Note: Gears with an even number of teeth are easiest to measure, since each tooth has another tooth directly across the gear. On a gear with an odd number of teeth, if you draw a line from the center of one tooth straight through the center across the gear, the line will fall between two teeth. So, just be careful using outside diameter in your calculations if you estimated it from a gear with an odd number of teeth.Center Distance (C): Half the pitch diameter of the first gear plus half the pitch diameter of the second gear will equal the correct center distance. This spacing is critical for creating smooth running gears.Pressure Angle: The angle between the line of action (how the contact point between gear teeth travels as they rotate) and the line tangent to the pitch circle. Standard pressure angles are, for some reason, 14.5A° and 20A°. A pressure angle of 20A° is better for small gears, but it doesn’t make much difference. It’s not important to understand this parameter, just to know that the pressure angle of all meshing gears must be the same.
Figure 1
All of these gear parameters relate to each other with simple equations. The equations in the table below come from the excellent (and free) design guide published by Boston Gear [PDF].
Making your own
This project is adapted from a blog post a student did in my first Mechanisms and Things That Move class at NYU’s ITP. We’ll design and fabricate spur gears using free software (Inkscape) and an online store (Ponoko.com) that does custom laser cutting at affordable prices out of a variety of materials. If you have access to a laser cutter at a local school or hackerspace, even better! You can also print out the template and fix it to cardboard or wood to cut the gears by hand.
Download and install Inkscape from www.inkscape.org. It’s a free, open-source vector based drawing program similar to Adobe Illustrator. It plays well with most modern Windows, Mac, and Linux operating systems (check FAQ for details).Go to www.ponoko.com/make-and-sell/downloads and download their Inkscape starter kit. This will give you a making guide (a PDF file) and three templates that relate to the sizes of materials Ponoko stocks. Unzip the file and save to somewhere you’ll remember.Open a new file in Inkscape. Under the file menu, go to Document Properties to get the window shown in Figure 2. Change the default units in the upper right hand corner to inches. Back in the main window, change the rulers from pixels to inches in the toolbar. Your screen should look like Figure 2. Once set, exit that window.
Figure 2
Note on circular pitch: In Inkscape, the circular pitch is given in pixels, not inches, as we’re used to using in the equations in the above table. You can get different gear ratios by just choosing a circular pitch that looks good and varying the teeth number, but if you want to make gears that interface with off the shelf gears, you need to pay a little bit more attention. By default in Inkscape there are 90 pixels in 1 inch. So if you set circular pitch to 24px in the gear tool as done above, that rounds to 0.267 inches (24/90 = 0.2666…). Since diametral pitch (P) = I€ / circular pitch (p), the diametral pitch (P) in inches is = I€ / 0.267 = 11.781. You will not find any off the shelf gears with a diametral pitch of 11.781. As mentioned earlier, common diametral pitches are 24, 32, and 48. So if you plan to make gears to play nice with off the shelf gears, start with the diametral pitch of your off the shelf gear and use the equations in the table to work backwards to what your circular pitch should be in pixels in Inkscape.
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Note: Once you open your free account, go to My Accounts –> Preferences to set your shipping hub to Ponoko – United States (or the closest location to you). Mine was accidentally set to New Zealand so my shipping charges were curiously high until I figured this out.
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BIO: Dustyn Roberts is a traditionally-trained engineer with non-traditional ideas about how engineering can be taught. She started her career at Honeybee Robotics, as an engineer on the Sample Manipulation System project for NASA’s Mars Science Laboratory mission, scheduled for launch in 2011. After consulting with two artists during their residency at Eyebeam Art + Technology Center in NYC in 2006, she founded Dustyn Robots (www.dustynrobots.com) and continues to engage in consulting work ranging from gait analysis to designing guided parachute systems. In 2007, she developed a course for NYU’s Interactive Telecommunications Program (ITP) called Mechanisms and Things That Move that led to writing a book called Making Things Move: DIY Mechanisms for Inventors, Hobbyists, and Artists, due out in fall 2010. Dustyn holds a BS in Mechanical and Biomedical Engineering from Carnegie Mellon University, an MS in Biomechanics & Movement Science from the University of Delaware, and will begin a PhD program in Mechanical Engineering at NYU-Poly in August this year. Media coverage of her work has appeared in Time Out New York, IEEE Spectrum, and other local organizations. She lives in New York City with her partner, Lorena, and cat, Simba.
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