4 DOF leg mechanics and torque requirements

[Th232]

Hi all, recently I've been struck by the urge to make a hexapod. So far, apart from general design I've done some basic calculations to determine the torques on each of the joints when the robot is at rest. Here's a simplified cross-section of the robot.



When the robot is at rest, joint 4 should be stressed the most, being the furthest away from the load. When the robot is in motion however, there're two cases:
* Leg is being lifted and moved forward. A less stressful case, the leg should be relatively light compared to the rest of the body since I'm not hanging a kilo off the end of it or anything.
* Leg is on the ground and moving the robot forward. Firstly, during this case joint 4 should still be under more stress than joint 3, right? Second, relative to joint 4, is there a way of getting a ballpark estimate of how much torque joints 1 and 2 will require? Going through the statics was easy enough, but hammering out moments of inertia and so on is something I'm hoping to avoid unless necessary.

A bit more on the design of this robot:

* I'm hoping to use RX-24Fs for joints 1 and 2 due to their higher speed, but if they won't have enough power then there's really no point. I'll also be using brackets with bearings (designed/milled by me) so that the radial load on the servo itself should be minimised.
* Also planning to use RX-64s for joints 3 and 4, with the possibility of bumping joint 4 up to an EX-106+ if so required.
* Power requirements will be huge (especially if I need to use EX-106+s). I've taken this into consideration and am planning for a rather large LiPo pack. And firewalls, should it decide to vent with flame. Different voltages for the -24Fs and -64/-106s has also been considered.

Any thoughts on this would be greatly appreciated.

P.S.: Admin, I wasn't sure whether this should be here or in the Humanoid/Walker/Crawler section, please move if this is the wrong section!

[Gertlex]

The largest load in this case will be joint 3, not joint 4. I forget how to explain why...

[Zenta]

The largest load in this case will be joint 3, not joint 4. I forget how to explain why...

That's correct. The horizontal distance from J3 to the tars/foot is larger than it is for the J4. In most cases J3 (femur servo) take the largest load.

[cire]

Hi all, recently I've been struck by the urge to make a hexapod. So far, apart from general design I've done some basic calculations to determine the torques on each of the joints when the robot is at rest. Here's a simplified cross-section of the robot.



When the robot is at rest, joint 4 should be stressed the most, being the furthest away from the load. When the robot is in motion however, there're two cases:
* Leg is being lifted and moved forward. A less stressful case, the leg should be relatively light compared to the rest of the body since I'm not hanging a kilo off the end of it or anything.

When the leg is being lifted and being moved forward, there is less load on the motors. Do remember that when you move the legs forward, the other legs that are still in contact with the ground see that load (double the load not including dynamics of the system if you move 3 legs at a time)

* Leg is on the ground and moving the robot forward. Firstly, during this case joint 4 should still be under more stress than joint 3, right? Second, relative to joint 4, is there a way of getting a ballpark estimate of how much torque joints 1 and 2 will require? Going through the statics was easy enough, but hammering out moments of inertia and so on is something I'm hoping to avoid unless necessary.

The torques on joints 1 and 2 will depend heavily on how your robot walks (speed and movement mainly) as well as the mass of the robot. I'm not sure the scale of your robot, but generaly these joints have much less torque on them then what joint 3 or 4 would have on them. Also Joint 3 will generally see more torque then joint 4, see my diagram at the bottom.

A bit more on the design of this robot:

* I'm hoping to use RX-24Fs for joints 1 and 2 due to their higher speed, but if they won't have enough power then there's really no point. I'll also be using brackets with bearings (designed/milled by me) so that the radial load on the servo itself should be minimised. All of the Robotis Dynamixels have bearings available for the bracket mounting if you didn't know. However I think it is cool if you make your own bearing mounts so go for it! Also, if you are calculating torques based on the specs for ANY hobby servo's "Holding torque" keep in mind this is not a "continuous holding torque". The motors are capable of holding the toruqe, but the servo will overheat over time (a few minutes depending on how close you are to the limit). I'm not sure what the exact level of torque they can handle continuously, so you would have to test that yourself. It probably is at least 1/2 of that though.
* Also planning to use RX-64s for joints 3 and 4, with the possibility of bumping joint 4 up to an EX-106+ if so required.
* Power requirements will be huge (especially if I need to use EX-106+s). I've taken this into consideration and am planning for a rather large LiPo pack. And firewalls, should it decide to vent with flame. Different voltages for the -24Fs and -64/-106s has also been considered.

Any thoughts on this would be greatly appreciated.

P.S.: Admin, I wasn't sure whether this should be here or in the Humanoid/Walker/Crawler section, please move if this is the wrong section!

This diagram might help you understand what Gertlex was talking about for joint 3 seeing more torque then 4.

[Th232]

Thanks for the feedback everyone, seems I was going the wrong way by calculating the torque using the force from the load instead of the reaction.

Out of curiosity, why is it that way? Going back to my mechanics textbook (and cantilever beams in particular), it's saying the torque should increase the further you get from the load, and not the reaction force. A quick test with my arm and a weight in my hand is saying a similar thing, when my forearm is horizontal the torque exerted at my elbow is nowhere near zero, while at my wrist it's pretty low.

I believe you guys since experience trumps theory, but I just can't see why the torque is being calculated using the reaction force and not the load.

Been 2 years since I last did mechanics, I guess it's showing...

Oh, and Cire, thanks heaps for the additional tips, I'd forgotten about the remaining legs when I'm moving some legs forward!

[cire]

What you were thinking would be true if lets say, the 1 leg you were looking at was rigidly mounted to the ground, with no other legs supporting the robot. In a multi legged robot configuration, the legs are rigidly mounted to the body of the robot. So really, the reaction is at the body and the load is at the point where the leg touches the ground. In my diagram the load is 0 on the 2nd joint, because the leg is vertical and the moment arm is zero distance. Of course you would have some kind of load on that leg since it won't always be vertical when you walk.

I made a quad that demonstrated the (almost) vertical leg last year, here is the video:

I wouldn't recommend loading your robot up like that though, a few weeks later i stripped a few gears out of some of the motors when showing off how much it could carry..

[Th232]

Ahh, that makes sense now. Thanks a lot for that explanation!

And that's a crazy amount of weight on that robot! Very impressive.

[Gertlex]

I think what it is, is that you can't evaluate internal loads/torques by looking at the overall structure. You need to do sections, and then your FBD only balances the external loads for those sections. Alas, I'm too lazy to make diagrams. x)

[Th232]

That's pretty much what I'm doing Gertlex, slicing it and determining the shear stress and moments at the point I've sliced it.

Results are coming out better than I expected, given that this whole thing weighs about 8.5 kg according to my model in Inventor. Still need to add sensors (or placeholders for them) though.

Out of curiosity, has anyone found out how much of a radial load RX-24Fs can take? Robotis didn't know when I asked, and I can save a good 200 grams per leg if I use the thrust washer kit, but I'm still leaning towards making my own brackets for better stability.

[Gertlex]

That's some serious weight. What's the payload?

In case you wondered (I did...), 4DoF AX-12 quads tend to be about 3 kg or so. Insanity Wolf (RX-64, 3dof quad) is 5.5 kg.