Introduction

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:

The length of the arc between the center of one tooth and the center of a tooth next to it. This is just pi (Π = 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, 14.5&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.

Image from Rapid Design through Virtual and Physical Prototyping

Image from Rapid Design through Virtual and Physical Prototyping

Some Rules

• The smaller the pressure angle, the smaller the base radius
• The addendum must be less than the dedendum
• The dedendum must be more than the difference between the pitch and the base radius.

Calculation Ratios

Ratio = # of teeth on the output gear (40)
        # of teeth on the input gear  (10)
		= 4/1 and is written down as 4:1

Designing

1. Do you want the gears to step up or step down? (speed up or slow down the performance).
2. Do you want the gears to run parallel, or at an angle of 90° to change the direction of the drive?
3. What size do you need to make them? (small space means making smaller gears and this can get tricky).

1. Choose the inside diameters of the wheels leaving 4mm between the two circles. Measure from center of one circle to the center of the other:
   
2. You want to make the teeth 1.75mm away from the perimeters of the circles. Making the end of the tooth .8mm in diameter is the smallest diameter that prints reliably on the Ditto Pro. You can make this diameter larger to create a more robust gear:
     
3. Draw parallel lines from the tangents of the small circle to the larger circle:
   
4. Create fillets where the parallel lines meet the larger circle:
   
5. Revolve the teeth around the center of the large circle:
   

Vocabulary

Reflection Questions

Designing Gears

Additional Resources

Rubber Band Gear Mechanism

Functional Differential Gear System

Planetary Gears

Blender Mechanical Gears

1. Open Blender
2. Open the Add-Ons panel by pressing CTRL+ALT+U
3. Navigate to Add Mesh:Extra Objects
4. Enable script by clicking on the box on the right hand side of the panel
5. Save User Settings CTRL+U
6. Close the panel
7. Press the Shift/a>Mesh>Extra Objects>Gears>Gear
8. You can change the script Parameters in the Toolbar Menu (T) Currently you need to set script parameters before doing any transforms or using modifiers.

Sketchup

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.
3. Create a gear by selecting Extensions→Render→Gear:
   
4. The dialog box allows you to specify:
   • Number of Teeth
   • Circular pitch, px
   • Pressure angle
   Leave Pressure angle alone—the 20° default is standard for off the shelf gears so is a good place to start.
   
   Choose 28 teeth with a circular pitch of 24. Click Apply, then close the dialog box. Your gear should be displayed:
   
   
   You can choose to not have a center hole at this point. You can either add it later in Inkscape or in OpenSCAD.
5. From Dustyn Roberts's Gear Tutorial
   

   Note on circular pitch: In Inkscape, the circular pitch is given in pixels, not inches. You will need to convert the number to inches in order to use the value in the equations. 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.

   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=Π/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=Π/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)	CD=(D1+D2)/2CD=(N1+N2)/2P

6. Click on the inner circle. There should be square and round handles on the object, which indicates it is an .svg object. Unfortunately, OpenSCAD can't read SVGs, so you'll need to convert the image to a path.
   
   Select the Node tool [N]. The handles on the object now look like gray squares.
   
7. Select Path→Object to Path [Shift+Ctrl+C]:
   
8. With every node selected [CTRL+A], click on Insert new nodes into selected segments:
   
   Press a few times if you want a smoother object, but don't overdo it:
   
9. Click Make selected segment lines.
   
   This looks much better. The lines are straight, but due to the number of segments, you see a curve:
   
10. You want the inner path to be a hole for a dowel. With the Node tool [N] selected click on the outer path then click on the inner path and select Path→Exclusion:
    
11. Select everything, then go to Document Properties [Shift+Ctrl+D] and click on Fit page to selection:
    
    
12. Save the file as something.dxf. You will need to select Desktop Cutting Plotter (R13) in the drop down box:
    
13. Disable all options in the dialog HELP box:
    
14. Save the file in the same folder that you will save your OpenSCAD file.
15. Take care not to overwrite your original .svg file. If you want to have the option to edit things later, save another version as an svg.
    
    Pro tip: It is much easier to work with objects than with paths.
16. You can export several .dxf files and combine them in OpenSCAD. If you use different paths, remember to union the different paths.
17. 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!
    
    This gear was generated with no center hole:
    
18. Save the file as something_else.dxf. You will need to select Desktop Cutting Plotter (R13) in the drop down box.
19. Launch OpenSCAD.
20. Save the .scad and .dxf files in the same directory.
21. Here is the code to linear extrude a dxf file::

    linear_extrude(height = 5)
    import (file = "drawing.dxf");

22. Now that you have your gears, you need to design a way to create a gear train. 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.
    • Use the circular pitch in pixels converted to inches (90 pixels per inch) to determine the diametral pitch in inches (Π/(pixels of circular pitch/90)) or in this case 11.781.
    All you need is that number (P=11.781) and the numbers of teeth (N1=28 and N2=14) on the two meshing gears to find the center distance (CD).
    
    Use the equation CD = (N1 + N2)/2P and you'll find that CD = 1.783. The distance between the first and second circle needs to be 1.783" or 45.2882 millimeters.
    
    Think about how to afix the gears in the train. Is one gear attached to a motor? Do you need to create a hub? Will you be using dowels? A 1/4" dowel is 6.35mm, so you would need to create a hole 6.75mm if you wanted the dowel to pressfit with the gear.
    
    

    //CD
    translate([-45.2882, 0,0])
    
    rotate([0,0,13])
    small();
    
    large();
    
    module large(){
        difference(){   
        translate([-32.5, -32.5,0])    
        linear_extrude(height =3)
            import (file = "large_gear.dxf");
            //dowel hole
            cylinder(r=3.275,h=3);
        }
    }
    module small(){
        difference(){
        translate([-32.5, -32.5,0])
        linear_extrude(height =3)
            import (file = "small_gear.dxf");
            //dowel hole
            cylinder(r=3.275,h=3);
         cylinder(r=3.275,h=3);
        }
    }

    
23. Compile (F6) and export( File→Export→Export as STL).
24. Open the .stl in NetFabb and repair if necessary.
25. Open The STL file in your slicer program and prepare the file for printing.

Water Wheel

• Outside Diameter: ~80mm
• Hole Diameter: ~4.25mm
• Assembled Thickness: ~25mm

Water Wheel