Can you imagine I suddenly woke up and found that I was so excited when I finished the 2D drawing that I forgot to do the blog post? And I have 4 classes in the morning. Awesome. But anyway, it was a story of being tortured, and enjoy being tortured.
As I thought a gear system would be the most helpful to trace, I decided upon tracing No. 505 , a simple form of the epicyclic train.
Figure 1. mechanical movement No.505
And as many of you found out as well, life is not so easy. Tracing the image did not work, even if I processed the image beforehand. Adobe Illustrator traces the strokes as filled enclosed shapes. So I traced the entire object by hand with the image in the bottom layer.
The hardest part of tracing a gear is symmetry. It is not only a property that can be exploited to increase efficiency, but also necessary for the gear systems to work. Adobe Illustrator possesses the feature to automatically align your shapes and strokes to existing points or geometry center. Though this helped a lot, it was not designed very perfectly!!! It would be much easier if we can select two points and make them overlap with some function ( it might have this function but I did not know how?). Heaven knows what I experienced when aligning the lines.
I reasoned and decided to two separate layers in general. One for auxiliary lines, the other for the tracing. It messed up a little, as I’ll discuss in a minute, but it worked. I started from the smallest gear. Though I also approached the symmetry by creating a unit tooth, unlike some of you guys did, my unit tooth is a line path instead of a enclosed shape. (Figure 2 & 3)
Figure 2. one of my gears with the unit tooth highlighted in red
Figure 3. the enclosed unit tooth method, this is from Kelly Liang’s post
For my method, I treated the gears as a “ring” of teeth, with the outer edge of the teeth lying on the outer ring, and the groove on the inside.
Figure 4. treating the gears as “rings”, with inner and outer circles respectively tangential to the outer and inner circles of the other gear. The green lines are auxiliary lines
As how gears should work ideally, these rings overlap, and the inner and outer circles of one gear are respectively tangential to the outer and inner circles of the other gear, as shown above. By drawing such auxiliary lines, the teeth path would form a perfectly central symmetric gear when rotated around the center of the circle.
The teeth path is traced by connecting crosses of the diameters and the circles (Figure 5& 6)
.
Figure 5. connecting dots on the auxiliary lines for a unit tooth
Figure 6. a closer look, and actually this is the refined teeth, I’ll come back to it later
Once a unit tooth path was created, I copied and pasted it, rotated it 180, aligned it on the other side, grout these two opposite teeth together, and copied, pasted, rotated together, grouping more teeth to finish the entire gear. Adobe Illustrator does not allow rotating a figure around any selected point. It can only rotate around it dimensional center, i,e the center of the rectangle that encloses the shape. So by grouping the opposite teeth together, I could rotate them around the center of the circle. (Figure 6)
Figure 6. initial gear design, all teeth are trapezoids
The original tooth path was composed of simple trapezoids as in figure 6, all the corners are at the crossing of the diameter and the circle. And this turned out not to work, as the teeth are too big to fit other gears, so I refined the unit tooth path.(Figure 7)
Figure 7. adjusting the teeth shape
Same thing with the other gears, and Ta Da!!!(Figure 8 , 9 & 10)
Figure 8 The large gear with its auxiliary lines
Figure 9. with the original image hidden
Figure 10. with all the auxiliary lines hidden and ready to be played around, I slightly resized the smallest gear smaller, cause perfectly tangent actually doesn’t work
In the mean time, I noticed that if you try to connect the dots generated by the path in the auxiliary line layer, the line you do is in that layer as well. Not a big problem, as all paths can be hidden and locked individually in the layer panel. It’s just something I noticed. I can be a product improvement consultant : )
The most painful part was drawing diameters. You would think the auto-aligning function is very convenient–you are wrong. They sometimes got aligned to very close paths or points, and that was a disaster. Plus, when you copy paste, rotate, the figure appears at different place, so you have to align them by hand every single time. And sometimes, you get this
This!
and this!!!
Don’t try to zoom in, that was how I got blind.
The other method might be more efficient than mine from my perspective, though I haven’t tried it personally. However, this method designs tighter gear sets. And I could have used the gear maker tools available online : (
That’s it, and here are the link and file of my work.
507 mechanical movements link: http://507movements.com/mm_505.html
Ai file: 2D drawing gears-2cutqtl
