Leg joints and physics...

MarkS

I'm designing a rather large multi-legged robot. I'm planning on using some rather high-torqe motors and gear boxes to move the joints. One thing I've been wondering is whether I should directly couple the gear box to the joint via a chain drive (emulating the way walkers are currently done), or to try a more biological approach? In the biological approach, I'd still use a chain, but the ends of the chain would have cables attached and the cables would be connected to the next leg segment. This would pretty much emulate a muscle/tendon/bone set up.

The big question is which would be better in terms of power and preformance? It looks to me that the typical set up of placing servos at the joints is necessitated solely by space and weight constraints. I would expect the biological system to outperform such a system, but I cannot figure out how to best determine this. The best way I can look at it is to consider a bone/joint as a lever with the beam (bone) cut in half at the fulcrum(joint). Current systems place the motor at the fulcrum while a biological system places the motor behind the fulcrum and uses tendons to pull on the beam directly. Physics is not my thing and the only way I can figure this out would be to build a half lever device, but I lack the tools to test the forces. I would guess that more torqe would be required to move the beam at the fulcrum than by pulling on the beam, but with the beam cut in half, I also guess that quite a bit, if not all, of the benefits of a lever would disappear.

Can anyone provide some insight here? It would be much appreciated.

Thanks,
Mark

kwinn

Referring to the attached picture, if you put the motors at joint B and C, then the motor at joint B has to move the weight of both arm segments and the motor at C. If you mount the motors at points A and B the motor at point A has to move the weight of both arm segments and the cables/pulleys from the motor at point B. If the cables/pulleys weigh less than the motor (which is usually the case) then you have greater force available at the end of the arm. The disadvantage would be greater complexity and lower precision due to cable stretch.

MarkS

So, in essence, it really doesn't matter. One way or the other, the motors are going to support the whole weight. Correct?

kwinn

No, how far out the motor is mounted does make a difference. The further out on the arm the motor is the more force it takes to lift or accelerate it.

Referring to the attached picture, if you put a mass at point A and it takes a force F to lift it, moving the mass to point B will require twice the force to lift it. The same applies to the motors on a robot arm.

MarkS

My point is that these are not arms, but legs. They will support the entire weight of the robot. Potentially any movement of a single leg segment can result in movement in the entire robot body. The only time this is not the case will be when the leg is being lifted off of the ground to move into another position.

The motors will be placed on the legs, close to the joints and parallel to the leg. Miter gears will be used due to the orientation of the motors, but placing the motors inline with the leg will allow the use of much more powerful motors in less space.

I guess my question is, which design would be best?

kwinn

Legs are a whole different ball game from arms. While what I said earlier is still valid, the torque required to lift a robot from the worst case position is so high that effect of the motor position is insignificant by comparison.

MarkS

That's what I was thinking. I'm leaning towards the cable system. The cable stretch would act as a shock adsorber. I want this to move similarly to a biological system and so it shouldn't be too precise.

roadrunner3g

you can try useing pneumatic pistons in some or all of the parts of the legs.

MarkS

I've thought about other alternatives to motors and I would use air muscles above all others. However, pneumatic systems (regardless if piston or air muscle) have several disadvantages. They require a large and very noisy compressor, between 2 and 4 typically motor driven air valves per cylinder/muscle and the total system cost would exceed the cost of a motor based system by an astromical sum. The speed of the joint is also limited by the valves. I priced commercial air muscles and the ones I would need run around $200 US PER MUSCLE! This robot will resemble a spider and have three-segmented legs. This means four joints per leg (the hip joint is actually two) and I would need no less than 2 muscles per joint. That's $1600 per leg just for the muscles and it would actually be better to use more than two per joint. Now figure in four valves per muscle at around $100 each and the cost per leg jumps to no less than $2800. Since the robot will have eight legs, we're up to $22,400 just for the valves and muscles! There is still all of the structural pieces and machining costs, all of the electronics and control systems, the compressor, which alone can run upwards of $1000, and all of the fittings and hoses needed for the pneumatic system. The cost of such a robot would easily exceed $30,000. Pneumatic cylinders actually cost more than air muscles, are slower and weight considerably more.

So, um, no.

Post Edited (MarkS) : 4/20/2009 6:24:03 AM GMT

Larry

Air muscles themselves are pretty easy to make from latex or silicone tubing and Poly wire loom. The issue might then be the solenoid air valves, but I've gotten those in CNC surplus houses for only $5-$10 each. They are usually 24 volt but many work at 18v. I run them off of power drill batteries. As for air, you can go a Long way with a pressure tank and regulator. If you measure power to weight ratios, it might be better than Batteries.

some links:
www.thirdwave.de/3w/tech/actuators/mckibben.pdf
brl.ee.washington.edu/Research_Past/Biologically_Based/Device_01_McKibben/Mckibben.html
brl.ee.washington.edu/Research_Past/Biologically_Based/Device_01_McKibben/Mckibben_Costruction.html

And video of them in action:

www.youtube.com/watch?v=pDvDfJL3--0
www.youtube.com/watch?v=YJbl61WmLoU&feature=related

MarkS

Solenoids are great for full-on and full-off applications, but not for precise flow control. For that, you'd need a proportional valve and they are not cheap. I have thought about making my own air muscles and they are simple to make, but I'm concerned about how well I can construct them. Sealing the ends of the tubes while still allowing air in and out and at the same time devising some sort of attachment system, all the while ensuring that the muscle can withstand thousands of cycles and the weight of the robot is no small feat. I'd have to have small parts machined and that will probably end up costing more than a commercially available muscle.

I really have given the motion control a great deal of thought. I've weighed the pros and cons of each different type of system and have gone back and forth between them all, but I keep ending up at a simple motor-based system. It is simply the cheapest and easiest system to construct.

Anyway, I think my original question has been answered.