• 4 weeks ago

## February 27, 2022

### Varying pitch screw robot build progress

Lots of progress on the jumping robot based on this mechanism.

To start off, here's a cross section of the core mechanism.

At the center of the mechanism is the varying pitch screw (or barrel cam).  The screw passes through a "nut" with two cam followers, which drives the screw axially as it turns.  The nut directly supports the rotor of an electric motor (specifically a T-motor RI50).  The screw passes through the center of the motor's stator, and is constrained by a guide bushing at the top, and 3 sets of guide rollers at the bottom, which roll in axial grooves on the screw and react the motor torque.

One kind of sketchy bit is that I'm measuring the rotor position through a 1:1 spur gear pair.  Ideally I would have used an off-axis encoder with a through bore to pass the screw.  I didn't do that though - I already have a few dozen of my mini cheetah motor drives on hand, and I actually couldn't find any appropriately sized thru-bore absolute encoders that were good for ~12k RPM.  I maybe could have used the iC Haus IC-MU (actually, one of the last things I did at the lab was make a version of my drive with that encoder IC, so most of the work is done already), but with the magnet target I need to clear the screw it's rated at exactly 12k RPM, which seemed like cutting it close.  Maybe eventually I'll do a purpose-built version of the motor drive for this, if the geared encoder turns out to be problematic.  Still, offsetting the encoder seemed like a better idea than offsetting the whole motor and having a belt or gears to transmit torque to the cam followers - this way the gears don't take any torque and can be plastic and very thin.

On to actually building the thing:

Machining the screw was quite a saga, and I actually ended up outsourcing the part.  I could have eventually finished it with the approach I was taking, but it ended up not being worth it for now.  It's the wrong shape for the 5-axis mill, so machining the full part required it to be broken into 3 separate pieces with two setups per piece, with extremely good alignment between operations required for smooth cam surfaces.  I did think about building some sort of dedicated rotary-CNC contraption, or rigging some mechanism to one of the local bridgeports with an encoder and motor driven rotary axis - maybe if I want to be able to rapidly revise this part I'll revisit one of those ideas.

Here's an example of one operation done on one of the parts.  For locating adjacent pieces and transferring torque, I put a hirth-esque coupling at the ends.  The plan was to drill all the way through the center of each part and clamp the whole thing together with a long tie rod down the center.

The little cylindrical bores on the sides were added for aligning the 2nd operation.  Indicating in the bore gave me the height and orientation offset of the part.

Here's the CAM tree for one operation:

Here's a pile of attempts:

I ended up outsourcing the part to none other than PCBWay.  Yes, that PCBWay.  They now do machining too.  I figured I'd upload the part and see what happened - last time I tried to get an earlier version of this part quoted by one of my usual Chinese prototyping shops, they quoted nearly $2k apiece in 7075. To my great surprise, I got back a quote for$170 with no complaints.  For that price I was half expecting to just get a cylinder in the mail, but a few weeks later the part appeared and looked pretty good - not immaculate, but good enough to get started.  The slot for the cams doesn't have the best finish, and you can faintly see a parting line in the center where they must have flipped the part around, but overall pretty good.

They even drilled the 5mm hole I had in CAD all the way down the center of the part - when I was trying to machine the part in 3 pieces, the hole was clearance for the tie rod down the center that would have clamped the pieces together.  I honestly meant to suppress the feature before uploading it, but I forgot and they drilled it anyway.  That's a 5mm diameter, 400mm long hole.  Even drilling from both sides, that's a 40:1 L:D drill, which is not something I'd ever want to deal with.

Next part up was the nut.  The nut has two cam followers that roll in the grooves in the screw, and holds rotor of the electric motor.  This is probably obvious, but the reason for having two (or more) cam followers rather than just one is to balance the forces on the nut.  The downside of more than one cam follower is that it sets an n-times higher constraint on the minimum pitch of the screw, which constrains the profile optimization.

I started out by turning all the cylindrical features on a manual lathe.  I was able to do everything in one operation, so everything is as concentric as possible.  I left a stub on the bottom so I could hold the part in a collet chuck on the mill.

Here it is before milling:

And after:

There's two undercuts inside cam follower bearing bores (cut with a home-made tool), which support the flanged bearings the cam followers spin in:

Typically, cam followers (a.k.a track rollers) are a needle bearing with an extra thick outer race, and the outer race rides against a cam surface.  I needed 3mm diameter cam followers, which aren't a thing, and even if they were, by the time the bearing OD was 3mm, the shaft diameter would probably be ~1mm and not strong enough for my loads anyways.  I flipped the usual cam follower arrangement to look like a spindle.  A pair of bearings (one flanged, one not) are housed by the rotor, and a solid 3mm shaft pokes in and engages the cam surface.

These are the two cam followers with bearings:

These can just barely be inserted from the inside through the central bore in the rotor.  I'd probably change up this arrangement a little if I had to remake the rotor as it was pretty tricky to assemble, but this design did minimize the cantilever of the cam followers, and very solidly supports the thrust loads on the cam followers (due to both cam scrubbing and centripetal acceleration from the rotor spinning)

Here's the nut assembled (minus the motor rotor), with bearings:

A view down the center to one of the cam followers:

For testing, I turned two Delrin bushings to keep the screw centered in the nut.  These will be removed once the real supports for the screw are made:

With everything properly constrained, the mechanism works pretty smoothly:

I post-machined a stock nylon spur gear, which mounts to the nut to drive the commutation encoder:

Next parts up were the two halves of the motor housing.  Here's a probably very boring video of machining one half, condensed down to 5 minutes:

The RI50 stator was slip-fit into the motor housing with retaining compound on the OD (Loctite 648).

I potted the windings in a low-viscosity thermally conductive epoxy to improve the thermal conductivity.

I 3d-printed an expanding mold for the ID of the stator.  The part on the left was a close fit to the stator ID and has a tapered bore.  It tapers down to a knife-edge at the bottom - this sharp plastic edge seals against the motor housing when compressed, without the need for explicit sealing elements like o-rings.  The conical plug on the right presses the mold down, and expands it into the ID of the stator to take up any gaps.  The mold parts were sanded smooth, and wiped down in an easy-to-clean grease, to keep the epoxy from sticking.

I filled the motor from the bottom-up by sticking a luer lock syringe needle on the end of a mixing nozzle, and inserting the needle down the stator slots in-between the coils to the bottom of the motor housing:

Here it is after filling with epoxy, while the mold is still in place:

At the top of the mechanism, the screw is centered by a close-fitting Tivar HPV (extra slippery UHMW) bushing.

At the top of the bushing, there's an end-of-travel bumper made from a square cross section o-ring.  This will take the edge off any impacts were the screw still has velocity at the end of travel.  The o-ring is glued to the bushing with some Loctite 380 Black Max

Here's the motor drive mount attached.  The motor drive mount is an HP MJF 3d-printed part.  At the center is a pair of bearings fan aluminum shaft with a tiny diametric magnet pressed into the end, for sensing the rotor position.  The spur gear in the motor drive mount meshes with the spur gear on the rotor, as seen two pictures down.

On the opposite side of the assembly from the guide bushing, there will be a set of guide rollers.  There are three rollers each that run in three axial grooves along the screw.  The axial grooves are shallow enough that they don't interfere with the spiral cam slots in the screw, and the 3 rollers per groove allow at least one of the rollers to always be engaged, even as the rollers pass over the cam slots.

It's partially the fault of my job, and partially the fault of having a 5-axis mill at home, but all my parts are getting bad.  Below is the piece that holds the nine guide rollers.  It doesn't have any walls thicker than ~1.5mm, has holes bored from every which way, and has a bunch of weird undercuts.

Cross section of the guide rollers assembly.  The internal bosses visible in the picture above space the guide roller bearing inner races away from the walls of the part.

Here's how the part fits up to the motor assembly.  The black ring at the end is another square o-ring bumper.  I still need to make the guide rollers.

And finally, here's a view of the assembly in its current state.  Just a few little parts left before it's ready for some testing - not jumping to start out, probably launching something of equivalent mass.  Either something's going to get launched very high, the mechanism is going to explode, or both, so it will be exciting regardless.

1. Thanks for the tips on the thermally conductive epoxy! :D

2. Will the actuator be fixed within the body, or will it have some amount of angle/tilt movement relative to the body? It seems like the moving CoM of the screw might make reaction-wheel-only control system pretty complicated.

1. I'm planning on having the actuator fixed to the body, as opposed to gimbaling the actuator (like the old Leg Lab hoppers, for example)

The COM of the robot shouldn't move too much as the screw extends, the screw + foot is ~15% of the total mass.

I think for short jumps, gimballing the leg is probably a better strategy than reaction wheels, but I suspect that for long jumps a reaction wheel might be better, since the robot can correct in the air, as opposed to jumping and hoping the initial conditions where right. I'm also leaning towards having a preferential direction with a higher torque reaction wheel though - e.g. in the "pitch" direction having a larger diameter flywheel with a geared motor driving it, rather than direct drive. It would probably be too bulky to do in more than one axis though.

3. Oh my god Ben. This was well worth the wait. Stunning design, what a beauty, and a pleasure to read. Grateful for all the helpful small hints and tips along the way. You are an amazing human and a amazing engineer!

4. Hi! Just wanted to pop in and say that your blog has been an ongoing inspiration for a few years, and I might just end up an engineering student at some point because of this. Thanks for sharing what you do!

5. So much fun to follow along! I am very grateful that you are sharing these adventures!

6. Enjoyed reading the article above , really explains everything in detail,the article is very interesting and effective.Thank you and good luck for the upcoming article