scout3 actuator updates: here's what my MechE friend said - staring from ground-up [updates]
SECTION 1: Brainstorming and Ideas.../Priorities of Design
So I reached out to my friend who is a MechE, Carol, and asked her a bunch of questions about bearings and here are some of the things she said.
Hmm interesting. In terms of “correct” preload, it depends on what you’re going for (ie bearing preload is usually for increasing the system stiffness at the cost of system lifetime so assess the importance of those and make sure your calculations predict how the preload affects the lifetime). In this case you might end up jamming the bearing if the bolt is torqued down too tight. Anyways in terms of loading I don’t think anything bad will happen, you’re just not optimizing the load path. Like since you’re transferring load directly into the bolt why use an angular contact bearing? A regular deep groove ball bearing should work fine. I hope that helps.
If your goal is price then it’s likely the tolerances may not even meet what you would want for a roller bearing. It might be wise to look into sliding bearings (think like a sleeve bearing with no rolling elements). It will be orders of magnitude cheaper but you’ll have worse properties in terms of friction
I was saying that bearings require high tolerances and if you’re going for cheapness you might not get it requiring tight machining tolerances for a bearing surface
Yeah maybe focus on bearing constraints? If you purchase a bearing the manufacturer will likely specify tolerances for certain fits that will correspond with bearing life
Look into L10 predictions
Well you’ll still have to worry about tolerances in this case but it’s a much cheaper option. What you choose just depends on weighing all of your design requirements (price, lifetime, rpm, etc)
So I have a few conclusions coming out of this talk:
First, I really need to look into tolerances for bearings, what tolerance means for parts and things like that. This includes for the gears and for the rest of the parts as well.
Also if we are 3D printing all of these - we should look into what happens to the part if its printed at 220C and then cooled to room-temp!
https://3dprintergeeks.com/3d-printing-shrinkage-compensation/ so it does seem we can genuinly do something about shrinking during printing.
Here's the thing - there's two types of tolerances we need to deal with here:
First, the tolerance of bearings and other parts generally fitting together - tolerances in the design that help the final product work properly.
And the tolerance of the part for printing itself - figuring out how to print the part such that it actually ends up at the dimensions we want it to be at.
We're looking into this now because as we're choosing bearings Carol suggested this is very important. We also want to re-think the design as a whole a little bit so let's list down our priorities and requirements and then go learn about tolerances:
First cost, the design in total must be <$200 to make, ideally <$150.
Falcon is 139.99, rest of the box has to be: 60 dollars (not including printing)
0-Backlash is priority number 2, we want a gearbox where the output can be directly measured from the motor's encoder.
With this we want to add smooth power transmission.
The 3rd priority is the weight of the box (because if we keep the weight of the box down we can use lower gear ratios: 0.498952kgs is the falcon 500 weight and a 12V battery is 3.333904kgs. The current weight of chip2 is 25kgs. total (ish).
It also needs to sustain the external loads of the robot to the gearbox - it's a structural component of the design.
5th priority: 60Nm-80Nm of output torque meaning a total gear ratio of 13:1-18:1!
(We are using the Flacon 500 as a motor because all the controls and sensing are already in-built to the motor.)
So now that we've listed out requirements out I can kinda see we've been going about designing this in the wrong way. Look at all those priorities we have above output torque - but no matter since the output torque is still important and should hover around 80Nm.
I also think we have found a way to really keep the gears in place without having to like, you know, have them rub against the back wall here it is:
The herringbone gear: because the opposing axial forces will keep the gear in place!
So here is the game plan moving forward:
FIRST - I'm going to read the Cheetah 3 Actuator Design paper to see how they handled designing an actuator for legged robots.
SECOND - we'll get to designing this gearbox itself and we'll break it into parts. (1) the mounting face, (2) the box itself, (3) the motor mount/etc.
THIRD - I'm going to look into tolerances in general just to know what it all means, why it's important, how to do it properly.
So if we take a look at the first few pages of the cheetah paper we can see some interesting things off the bat:
Dogs galloping at 9m/s reach foot forces in the realm of 2.6 times their body weight.
And "A load-carrying robot walking at a slower speed could energetically benefit from a high gear ratio in comparison to an agile robot running at high speed.
So I think we also need to answer the question what kind of robot are we designing this for so let's just say our goal is NOT to make robot more like animals. Our goal is to make a robot that is easy to control, walks at a decent pace: 1.78816 m/s is average human walking pace that seems like a good target speed to aim for. So let's see what kind of forces these robots sustain at those kind of walking speeds:
we're max looking at a trot gate where the two diagonally opposite feet move synchronously to make the robot walk - if this is done at the speed of a human - how much force compared to the weight of the robot are we looking at?
I'm really just looking for a paper that tells us what the forces experience by a walking dog are. We have an upper bound go 2.6times the weight at running but what about walking? Basically, if we know the max torque we can output, then we can work backwards to find what the platform weight can be at max. Maybe we just need to do a quick calculation - back of the napkin - to see and then run some tests.
We should note that walking at even 1m/s is very dynamic and would require some level of force control on the platform. Let's assume 1m/s for now.
So the vertical forces the legs would need to sustain is greater than W/2 where W is the weight of the robot since the robot has only two legs on the ground at any time. The other force component comes from the impulse on the ground due to the robot's vertical velocity at contact but we can slow this down with the right springiness of the actuator to be able to assume this force on each leg (vertical) is about W/2.
And now let's look in the other direction... the reaction force to make the robot go forward we're going to look at the IEEE paper for this.
IEEE BIODOG PAPER:
First thing to note is according to the graphs on page "663" the max reading on the force sensor is 9V ~60N. So the question is - how much does BioDog weight?
The total weight of BioDog is ~20kgs. There are THREE legs on the ground at any time, so that's 60+60+60 = 180N of force over the three legs. So for slow walks it seems like the force on the legs of the robot is not much more than the force of the robot itself - this is about 1/3 the weight of the robot on each leg.
For safety - I think we're going to go with two legs off the ground 1/2 the weight of the robot on each leg and then a little more. So times 1.5 that makes it 3/4 the weight of the robot on each leg? Let's see if we can support that - what kind of actuators are we looking at and what kind of robot weight are we looking at.
Let's assume chip2 is 25kgs. And let's assume we can cut 1.2kgs of motor controllers, and maybe 1kg of wires, another kg of useless stuff taking us down to maybe 20-22kgs? Let's say we could get scout/chip to be 20kgs? That makes each leg needing to sustain around 10*1.5 = 15kgs. Let's run that though Matlab. - we're looking between 35-50Nm of torque - so total gear ratio of 18:1 seems like a good way to go. That can be a 3:1 and a 6:1! Or maybe a 9:1 and 2:1 let's seee?
WE'll put the higher ratio connected to the motor because we don't want to step up the torque so much that we have to deal with massive forces. We also don't want to make this gearbox huge so let's space optimize this. Figure out a good way to do that.
There's definitely one more thing in the Cheetah paper we want to look at, and that's the IMF or "impact mitigation factor" which defines the back-drivability of a gearbox. This is just to see where we would be on that scale. But we'll look into that tomorrow maybe.