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Descrição
This example is based on the following resources:
http://blog.makezine.com/archive/2010/06/make-your-own-gears.html
http://repraprip.blogspot.com/2011/05/inkscape-to-openscad-dxf-tutorial.html
http://www.iheartrobotics.com/search/label/OpenSCAD
Gear basics
If you know any two things about gears—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.
- Number of Teeth (N)
- How many teeth are there in the gear
- 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:
- 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, 14.5&Acir;° and 20°. A pressure angle of 20° 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.
- Addendum:
- how much the tooth protudes beyond the pitch radius
- Dedendum:
- how deep goes the tooth before any fillet take place
- Pressure angle:
- The angle between the radial direction and the tangent to the tooth at the pitch circle. 20 is a good value.
<dd>The length of the arc between the center of one tooth and the center of a tooth next to it. This is just pi (ï€ = 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.<br /><br /></dd>
<dt><span class="em">Outside Diameter (Do):</span></dt>
<dd>The biggest circle that touches the edges of the gear teeth. You can measure this using a caliper like Sparkfun.com's # TOL-00067.<br /><br />
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.
Some Rules
The value of the base circle is based on pressure angle.
- 1.The smaller the pressure angle, the smaller the base radius
- 2. The addendum must be less than the dedendum
- 3. The dedendum must be more than the difference between the pitch and the base radius.
All of these gear parameters relate to each other with simple equations.
| To Get | You Have | Equation |
|---|---|---|
| Diametrical Pitch(P) Number of teeth per unit length |
Circular Pitch(p)
Number of Teeth(N) & Pitch Diameter(D) Number of Teeth(N) & Outside Diameter (Do) |
P=Ï€/p P=N/D P=(N+2)/Do(approx) |
| Circular Pitch(p) Length of the arc from one tooth to the next |
Diametrical Pitch (P) | p=Ï€/P |
| Pitch Diameter(D) | Number of Teeth(N) & Diametrical Pitch(P)
Outside Diameter (Do) &Diametrical Pitch(P) |
D=N/P D=Do-2/P |
| Number of Teeth(N) | Diametrical Pitch(P) & Pitch Diameter(D) | N=P*D |
| Center Distance(CD) | Pitch Diameter(D)
Number of Teeth(N) & Diametrical Pitch(P)
|
Instruções
InkScape to OpenSCAD
- 1. Open Inkscape (www.inkscape.org — free, open-source vector based drawing program ) and create a new document (CTRL+N).
- 2. Under the file menu, go to Document Properties and change the default units in the upper right hand corner to inches (SHIFT+CTRL+D). This will change the rulers from pixels to inches.
- 9. With every node selected,click on "Insert new nodes into selected segments".
Press a few times if you want a smoother object, but don't overdo it.
- 10. Click "Make selected segment lines".
This looks much better. The lines are straight, but due to the sheer numbers, you see a curve! - 11.Select everything, then go to Document Properties [Shift+Ctrl+D] and Fit page to selection.
- 12. Now save the file as something.dxf. You will need to select Desktop Cutting Plotter (R13) in the type drop down box.
The dialog HELP box tells you that you can only export certain elements—lowpolylines, which will export. - 13.Save the file in the same folder that you will save your openSCAD file
- 14. Take care not to overwrite your original .svg file if you want to be able to edit things later. It's much easier to work with objects than paths.
- 15.Open OpenSCAD
- 16. Remember to put the .scad and .dxf file in the same directory).
- 17. Here is the code
linear_extrude(file = "something.dxf", height = 10, center = true); - 18.You can export several .dxf files and combine them in OpenSCAD. If you use different paths, remember to union the different paths.
- 19. Add a cylinder in the center of the gear so that use can attach it to a base. You could make a 1/4" dowel (6.35mm). Or attach Tony Buser's pin connector to the end of your dower. In that case your radius will be 5.
- 20. Compile and export
- 21. Open the .stl in NetFabb and repair if necessary
- 22. Open in ReplicatorG and print
- 23. Since 1 gear will not do much for you, make at least one more. For your second gear select 14 teeth and keep the same pressure angle and circular pitch of the first gear so that your gears mesh - only change the number of teeth!
- 24.Now that you have your gears, create a base with holes spaced the correct distance apart so that you can mount the gears and make them spin.
You need to calculate what the center distance (CD) of your gears.
- Both of your gears have a circular pitch of 24 px, a pressure angle of 20°.
- The big gear has 28 teeth and the small one has 14.
- The circular pitch in pixels to a diametral pitch in inches of 11.781.
Use the equation CD = (N1 + N2)/2P and you'll find that CD = 1.783. - 25. In OpenSCAD create a new document.
- 26. Create a base that is large enough to fit the two gears
- 27. Create 2 holes in your base.
.25 inches = 6.35 millimeters and you need your holes to be .5 millimeter more so that the dowel fits.
Alternatively, use Tony Buser's pin connections
- 28.The distance between the first and second circle needs to be 1.783" ( 45.2882 millimeters).
- 29. Compile, export, check and repair, print
<li>3. Create a gear: <span class="em">Extensions>Render>Gear</span>.
<br /><br /><hr /></li>
<li>4. The dialog box allows you to specify
<ul><li>Number of Teeth</li>
<li>Circular pitch, px</li>
<li>Pressure angle</li>
</ul>
Leave Pressure angle alone — the 20° default is standard for off the shelf gears so is a good place to start.
<br /><br />
Chose 28 teeth with a circular pitch of 24. Click Apply, then Close the dialog box, your gear should be displayed.
<br /><br /><hr /></li>
<li>5.<small>From Dustyn Roberts's Gear Tutorial</small><br />
<blockquote>
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) = π/circular pitch (p), the diametral pitch (P) in inches is = π/ 0.267 = 11.781. You will not find any off the shelf gears with a diametral pitch of 11.781. 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.
<li>6. There should be square and round handles on the object, which indicates it is an .svg object, which OpenSCAD can't read.<br /><br /><hr /></li>
<li>7. You need to convert it to a path. [Shift+Ctrl+C]<br /><br /><hr /></li>
<li>8. Select the node tool [N]. The handles on the object now look like gray squares. This indicates you have a path.
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