Geared, Reversible, Backdrivable CVT

Figured out perpendicular cam geometry. I was running into quite a few issues and managed to find a solution that fixed most of them. I pivoted from 6mm ID bearings to 32mm for the second stage of gears (the oscillating ones). I also realized that instead of moving the dog clutch directly, I have to mount another bearing around it with a 3d print mount. This not only allowed me to save tons of space, but now I only have to use one perpendicular cam because I can make the 3d prints 90 degrees offset, preserving phase. Here are some problems I ran into and how I tried fixing them:

• The 32mm bearings were hitting, so I changed up the main geometry and will be alternately adding flange space on each side of the main plate. There isn’t enough space for 2 flanges to be next to each other, but there’s enough space for 1 flange and a normal bearing to be next to each other (0.1mm of space).
• With my old design (screwing a sidways bearing directly on the dog clutch), I had to use two separate cams because the phase was not 90 degrees offset. However, with another bearing around the whole thing, I can change the angle to not be radial, making it exactly 90 degrees.

Looks like V2 will take the shape of a pentagon, and will soon look like a hexagon once I add the linear motion for the gear shifting mechanism.

I did tons of brainstorming and came up with a better replacement for the meshing/unmeshing gears (I actually had 2.5 hours more recorded the night before but lapse ran into a problem so they aren’t counted for here). I realized I could keep the gears in contact the entire time, and instead use a perpendicular CAM (idk what it’s called, it’s basically a CAM that has its offsets parallel to its axis of rotation) to engage a dog clutch onto the gears. The dog clutch basically has 0 chance of bad alignment because the clutch will self align. This hopefully makes everything much more reliable and efficient. To power this, I need a third gear directly connected to the input gear that takes the linear CAM below the input shaft (you can’t run it coaxially). To make it fit, I changed up some of the gear ratios. I soon plan to switch from 1.25 mm to 1mm modulus.

Continued sketching my V2. I spent most of my time visualizing the whole thing (I spent almost two hours sketching the thing out and doing the math). Here are some of the problems I ran into (and how I fixed them):

• I need the inputs on both sides to be powered, but I also want the output to be a pulley on the side (not in the center). This is impossible with a normal coaxial setup. Instead, I linked the first stage of gears (the one that has the ration changing mechanism) and will be changing up the linear motion mechanism.
• When connecting the first stage, it hit the output gear, so I had to change some of the geometry.
• As mentioned before, the radial force by the gear changing mechanism of V1 will probably cause the linear bearings to bind, so I’ll be changing this to a static linear-CAM type of motion for a constant force throughout the motion. Because I’m linking the first stage, everything will basically be inside a tube.

Did some math for the V2. I want the output to be at a constant speed, which means the gears have to be noncircular. The output right now actually isn’t even sinusoidal, and Claude and I had to do tons of weird trig to find the angle as a function of time. After graphing everything on Desmos, I figured out the ideal shape of the gears. Next, I’ll do more mastersketching, and export the shapes from Desmos into Onshape. In the image, the black curve is the position as a function of time, and the blue and red curves are the ideal gear shapes. Actually, now that I think about it, this is wrong and I need to change the whole thing.

I made some minor changes and I’m almost ready for a v2. I fixed up some of the spacers, changed the direction of the linkage that changes the ratio, changed some of the bearings. I also changed the coloring, and it looks much cleaner (I chose pink because I have pink filament loaded in, if you guys have any recommendations please tell me). Here are some fundamental problems with the current version and how I’ll fix them in the v2:

• The biggest problem is probably gears meshing. The entire thing has to be perfectly synchronized for the gears to mesh perfectly every time, which is obviously impossible. The only thing preventing jams right now is my prayers. However, backlash does give it some room for error. I’ll probably find a better gear tooth profile for my V2, but this is sort of a fundamental problems that will exist.
• The second biggest problem is that the gears oscillate from max speed to 0 speed every half-cycle, which means the speed will be constantly oscillating. This is easily fixable: in my V2, I’ll use more driving gears (probably 4) each active for a smaller fraction of their period. This combined with elliptical gears to counter the sine waves should make the output basically constant speed.
• The linkage for the gear changing has basically zero torque, and backlash will completely fry it. Also, this adds weird thrust forces on the linear bearings which will probably cause them to bind. In my V2, I’ll probably shift from a linkage to a linear CAM type of thing (I still have to figure it out).
• This is really big and wastes some space. My V2 will (hopefully) have better packaging and be smaller. This is achieved by putting the second layer of gears on the inside of the plate and praying there is enough space.

The uniform coloring makes it look way better. Once again, if you have any colors you think would look better, please tell me.

I basically finished up the linear motion for the CAM. All that remains is some minute adjustments.

Here’s some problems I ran into:

• The geometry was incredibly hard due to the lack of space, and I ended up just trying a bunch of possibilities and landing on one that worked decently. While I was planning to use belts, I switched to gears after I saw how little space there was.
• Screws were hitting the servo for the gear changing mechanism, so I rearranged it so the lip is on the outside of the plate, giving me a precious 4mm to work with.
• It was hard to come up with a way to ensure the full range of motion always happens. There’s nothing pushing the gears up after the CAM pushes it down. Initially, I was planning to do some complex linkage relying on the definition of an ellipse (the sum of distances from the foci is constant). I tried sketching it out but there was literally no space. At the end, I thought of tying a string to both gears and wrap it around an idler to keep the constant sum of distances.

This thing’s gonna look clean once everything is colored. All that remains is some minute adjustments and I can move on to a V2.

Started the linear motion for the CAM. I was initially thinking about using MGN3 linear rails until a realized that each rail is over 100 bucks. Instead, I decided on linear bearing based motion with 3mm rods similar to how the ratio changes. Here’s some problems I ran into:

• Cheap MGN rails were way too big so I decided on the linear bearings (I spent way too long searching for cheap MGN3 linear rails)
• I initially wanted to put the rods between the yellow and blue plate, but after sketching it I realized the tolerances were too sketchy.
• Initially I was going to do one main CAM in the center, but I realized when the CAM is pushing the shaft to the outside, the angle is weird so the force is basically transmitted perpendicular to the direction of the motion, which really cooks efficiency. So instead I decided on 2 smaller CAMS that are belted to the main gear.

some future/long term problems I need to fix:

• I don’t think there’s enough space for the belts and cams, so this whole design might be fried
• The 3mm rods aren’t constrained on their ends, so I have to figure out a way to do that (right now its only held by friction).
• The motion of the driven gear will oscillate a ton because of the CAM. One potential solution is to use elliptical gears and have the gears engage only in a certain phase where its speed is high (so its not stopping)
• There’s something similar to the coaxial effect from swerve drives in this gearbox too: I’m gonna call it the CVT effect. When the gear ratio changes, the linear motion makes the gear change phases. Something similar happens because of the CAM, but this isn’t that big of a problem. But when in doubt, assume software can account for it.

Mounted the CAM gear, added a front plate, and added screws. I ran into a problem where one of the hubs hits the belt to the lead screw so I changed up some of the geometry. The gearbox is starting to look pretty complicated and dense without the second most complicated part (the CAM). I am holding off coloring everything and pocketing till the very end because it’ll be very satisfying.

Finish up Linear Motion for CVT. Mounted the linear bearing, added the servo, and finalized the linkage so the actual CVT part now works. Now, I have to work on the CAM mechanism.