Some interesting takes on Stewart platforms

I was looking around on YouTube trying to lift good ideas for Stewart platforms and drives and found these. Blew me away on how ingenious they were. I don’t know how suitable the round one is for a man-carrying platform, but the linear bearing one looks doable and could be pretty inexpensive. Regular gear motors could be cheaper but the slide version doesn’t have to support all the weight directly. Might need to work out some math to know if there is an advantage. Obviously more investigating to do but thought I’d post them in case others haven’t seen these.

the second video is really rare, but i guess in our case really hard to achieve (i guess) about the first one... i really would like to have more physics knowledge to answer.... (i have not ) but... again, how could we do that kind of mechanism? one gear motor with an arm pulling the linear bearing car? or what is in your mind?

best regards

fer

Hey @ferslash, I’ve been thinking about it and nothing is free. This is confusing and I could be way off, but I believe the force to move the car at the base and the vertical motion would go with sines or cosines. That would introduce big nonlinearities but it’s not much different than when you use near 180 degrees of travel on a gear motor. It could be that if you matched the part of gear motor travel where the link is perpendicular to the output arm with the part of travel of the linear bearing/strut car is mostly vertical, you could have the nonlinearities cancel and get a linear motion overall.

Only thing is the rotary output of the gear motor itself would be nonlinear with the platform/strut movement. That might complicate the feedback path/method.

But since this method in effect would give the motor more leverage against the weight or accelerations of the platform, it would take away overall travel and speed for a given motor. So lower the gear motor gear ratio to get back speed, and you lose the load capability. So zero sum gain but maybe an advantage in making the output of a worm gear gearmotor linear. But that will take actual calculations to sort out and verify or not.

But the linear bearings could also add a fair amount of expense. I think the rotary gear and bearings would make the round one impractical for us. I just thought it was really cool.

@ferslash - Been thinking about it some more and there may be some advantages to the strut bases/cars on tracks way. First, I think worm gear motors with a link shoving a car wouldn't work so well. But linear actuators mounted on their sides could be hard mounted in the base instead of being above the base and pivoting. All actuator and limit switch wiring and would be contained in the base. Just plain struts above the base. It would eliminate the tube/rod that many use carbon fiber for and a special bearing for it to slide in, and it could even be cheaper overall. The cars could be just things with stock ball bearings on them to run on or in a C-channel, box, or rod/tube. I've seen others not that their rigs can try to lift corners during extreme moves so it the cars would need to maybe be similar to how rollercoasters stay on their tracks during negative Gs. The ball screw could be supported at both ends so no whipping when the car is at the motor end.

Lots to think about with this approach, but it might have some advantages and allow for a smaller sim overall since no big actuator tubes would be outside the frame. I think it could work. More to ponder...

I found the company that makes the linear version - Quanser.com. It apparently is rated at 100 kg "at high accelerations". There are some advantages to this design compared to worm gear and standard linear actuators. I’m sure some disadvantages too but this concept is definitely growing on me.

More details on it:

https://www.quanser.com/products/hexapod/

https://www.quanser.com/wp-content/uploads/2017/03/Hexapod-Datasheet-v1.2.pdf

OK, look past the hokey setup but check this out. This Quanser Hexapod can carry a lot of weight for being this small:



Now, in looking how they do it, check this. It’s low res but it shows the internal structure - sort of:



What they do is for each pair of struts, the mechanisms face and oppose each other. The flex joints are offset and that let’s each set of rails go all the way to the edges while using co-axial motors driving the ball screws.

So I started looking at linear bearings and found these entire kits with four recirculating ball bearing slides, two 16mm rods with full length support, and a ball screw with nut, bearings, and a flex coupling: http://a.co/h3KVkO5 (Amazon - $158 each set with discount)

The rails happen to have the proper mounting hole spacing for 8020.net Series 30 strut. The tops of each rail slide are 45mm square. Two parallel rails with four slides in a rectangle would be about four by five inches - spreading the load on four slides and being close to U-joint dimensions for a flex joint.

The rails sets are available in a number of different lengths and diameters but coming as full kits is kind of handy. With having the same dimensions as 80/20 strut, it makes it easy to order the parts ready-cut to assemble like a kit.

Still investigating but I think the 600 mm rails would make for a decent sized base for a 6 dof platform and probably carry the load of a full-frame sixer well.

Hi Zed, nice but I thing the following is a better look at it

Regards Jerry.

Ooooooops, you already had this video, Age may not weary us, but blindness doesn't help

Jerry.

seems a bit overpriced have you checked ali express?

Hey Bruce, I haven’t. Shipping is long and rightly or wrongly, I’m just leery buying through them. Big price difference?

If you dont mind waiting for the shipping its typically a lot less expensive than Amazon. They are pretty solid and some sellers will also customize slightly for you. There is some junk but a lot of the stuff that we buy elsewhere is made by the same manufacturers. they have a guarantee but i havent had to use it. I got ballscrews 6x1610x550 shipped for $150.00. I purchased othe rstuff also without issue.

Hi all, this Hexapod thing, just been thinking; I'm 90% sure able to build it!

But whom could program it?

Inverse kinematics or Forward kinematics looks really difficult to understand, let alone using C++ to code.

Or have I thought too much again

Just a thought (and probably not a bright one)

Jerry.

@Jerry Atrick - I don’t think it would really be that different from the motions people get from the linear actuator struts and would be simpler than the motions you get from gearmotors which seems to work fine. I don’t know, since I’m just getting into this, but I don’t know that programming is different between linear actuators and gearmotors anyway, is it?

I was trying to sort out range of motion yesterday and made a graph. In the method here, the strut length is fixed and the lower attachment points move along a track. In the graph I used 2 units of track length for each lower attachment point (2 feet) and struts of 2.25 units/feet (blue) and 3 units (red). The ranges of possible motions of the upper attachment point are then the areas that are colored in if I am thinking about this correctly. It should be easy to derive a similar graph for linear actuators and I’ll need to think how to do this for gearmotors with fixed strut length and lower attachment points that move in an arc.



But anyway, what I think this also gives is the range of forces and how that changes with strut length. With the 2.25' struts (blue), when the attachment point is at that lowest apex right in the middle (~0,1), each strut would form a 30, 60, 90 right triangle with its ball screw and track, and the force the actuators would need to resist would be twice the weight of that attachment point. Two actuators so each is resisting the full weight of that attachment point. I need to think about that some more, though. Might be thinking about that wrong. I may also be leaving out a term.

I’ll draw curves for regular linear actuators too but guess the range of motion of the upper attachment point will look like a curved diamond. I need to think about the forces there but think since linear actuators have all force applied along their axis, they would see the same forces at the low end of travel but the force just wouldn’t go to zero at the high end. This is why I think I’m not considering something in the other method. I think the full linear actuators should always see a higher force to act against compared to the other way.

Or I am thinking about this all wrong. It’s confusing and the geometry word problems in school were literally decades ago.

I’ll know more when I do the curve for linear actuators but this method probably has a lower overall range of motion than a comparably-sized rig with linear actuators. That may be fine for flight but maybe not as fine for more violent things like rally driving and such. I still think this method will be very simple to build, though, and possibly more compact.

Hi Zed, whom in this forum would understand this thinking obstacle better? and maybe a programmer would like to weigh in!

What do you think, should we put some feelers out, for some feedback?

Jerry

@Jerry Atrick - I’ve seen a few here list their occupations as engineering. Anyone with mechanical engineering for a background would be able to answer but there are also lots of online resources. But it’s also not really an obstacle I think. I need to be on my regular computer to draw up the range of motion of standard linear actuators but am pretty sure they will a lower range very similar to this (lower half of the curved diamond) but will have a pointy top where this is rounded. The forces that the ball screws in this will need to exert will be either the same or less than linear actuators since the weight of the platform is borne partly to completely by the rails depending on the position of the lower attachment car on the rail. With linears, those are always carrying the weight which will always be effectively increased due to the angles involved and always nearer the highest loading that this arrangement will see.

And we know this form of platform actually does work from the videos and just by inspection. The only questions are how much of a difference the lower range of motion makes but without a head to head comparison would it be missed? I think where that will show up is vertical displacements / heave from center. This kind of platform wouldn’t have as much range in that motion - which would also show up in roll and pitch motions at their extremes on the ends of motion where upper attachment points are to lift. I need to draw that up to really know just how much of a difference.

Well, here is an interesting result. I put both curves on the same graph and used 2.25 units as the strut length for the sliding base hexapod as well as the collapsed strut length on a linear actuator. I used 3.6 units as the length of the fully extended strut to give a little room for the extended length not being the same as twice the collapsed and to make a nice diagram. The fully-extended length is just a guess and to be honest, I picked a value that made for a nice figure. Try your own lengths at https://www.math10.com/en/geometry/geogebra/fullscreen.html



The darker red area is how much movement is lost using this method. Not a factor of 2 but not that far off. So I guess first order of business is to think about the implications of this. The sideways motion looks like a wash. Even with an extended length of 4 units on a linear actuator, it's not a big difference in lateral motion. But heave is affected and so would the high side of pitch and roll.

This has been an interesting discussion to read. However it seems a substantial flaw in this design has been overlooked. The reason why the statement in the first sentence in quotes is true is because this design is totally non-linear. Take heaving for example, this design works the same as a scissor jack. If you've ever jacked up a vehicle with a scissor jack then you know that its hardest to twist the screw when the jack is at its lowest point and easiest when the jack is almost fully extended (this assumes a constant weight on the jack). At least when using gear motors with levers the non-linearity is equal when moving either direction from center position.

I didn't overlook the non-linearity, though and called it out early on. I didn't compare to a scissors jack but that is a good analogy and also correct that the nonlinearity on gearmotors would be equal in both directions if the throw was centered. They are still nonlinear though since it's a pushrod/crankshaft kind of arrangement. But the part of the graph where linear actuators would be most at a disadvantage and the forces they would have to overcome is at the bottom and in that, linear actuators and the sliding base hexapod look to be almost equally disadvantaged. Advantage still goes to the sliding base because it wouldn't be lifting the full weight as some would be supported by the rails.

Also, in thinking about using DC motors with speed controls, they respond to positional error. So even though more turns of the screw would be required to change the vertical position with the sliding base hexapod, the non-linearity turns into a compensation of sorts because the load is less and the motor would unload to higher RPM and make up somewhat for the nonlinearity. Linear actuators would unload some as the geometry changes but not to the extent that the sliding base version would.

To me, though, the biggest disadvantage of the sliding base hexapod is the lopping off the top of the motion curve. I think that's more of an issue than the nonlinearity since gearmotors see that same kind of thing at both ends of their travel especially if you use a lot of the arc. Stick to about 90 degrees of total travel and it's not nearly as bad but you lose motion too.

So I guess it comes down to sacrificing travel for mechanism. I still think the forces on the running gear for the sliding base hexapod would be lower since the rails would be taking part of the weight, motors could be smaller, currents lower, motor controllers could be sized smaller, and so on. The question is by how much. I need to look at the forces in earnest now. Gearmotors are ultimately the simplest drive but I don't like that they spend most of their time wearing just one part of the output gear. Linear actuators are the clear winner for travel.

More to consider I guess.

Hi Zed, hi BlazinH, Now I shouldn't say anything, because I know nothing; however I like the look of this thing and I thought why the hell not, throw a couple of 12Nm servos at it and see what happens.

Just as a test I mean, 1 axis, 1 rail, 2 rollers some pipe a bit of welding, and maybe it will work to an extent of making me happy and if it fails I could have 2 more axises on my CNC.

So forget about my maybe mechanical failures (soon to come)

I still have a question about the code to drive it?????????????????????????????????????

Now Zed, thank you for comforting me in an earlier chat about the code, but thats still the real question for me moving forward, or may backward!

Jerry.