Leg

This is what I’ve been working on for the past two weeks.

2008dec14-whole-leg-shot

The whole leg.

 Yeah, that’s what you get when an electrical engineer does mechanical design and fabrication. But more seriously, it does go to show that the type of research direction that a particular robotics research project takes on is probably very much influenced by the background of its researchers. And it’s not just the academic background. Cultural background (think about the Japanese and their fascination with humanoids), the stuff that makes an impression on us (especially the books one reads), the things we dream about and our individual aptitudes (I’m really bad with math) all strongly influence research methodologies. That’s just my observation though.

Anyway, what I’ve got here is a single ‘leg’, with the ankle and foot absent. There’s a hip joint and a knee joint, so that’s 4 degrees of freedom here.

Joints

The knee joint is actually just a hinge. Nothing much to say…

The ‘hip joint’ is just a ball and socket joint. I wouldn’t call the socket a hip just yet, the proper hip would ensure that this socket will be mounted in such a way as to provide the appropriate range of motion. Anyway, this joint was not easy to make at all. The ball is a wooden ball bought from Art Friend. The socket is, hold your breath for this, nine layers of 4mm(?)-thick acrylic stacked together, with holes of varying diameter drilled into them to accomodate the ball!! I know this is really lame…and its going to get even lamer! I made those holes using a drill (which I bought for this very purpose), i.e. by using the drill like a router. That’s really a very bad idea, I could never cut along the lines. Or maybe I’m just a toddler when it comes to handling a drill…Oh, btw, I got that drill only after I realised I had to give up trying to use a needle (heated with a blowtorch…@_@) to poke holes in a circle to punch out a circle. Another revelation: I was also naive enough to think that after I could make the holes perfectly, it would just be a matter of sanding down the sharp edges to obtain a smooth socket. Now you know what a mechanical idiot I am.

Of course I realised midway that this wasn’t feasible, so I started to drill with less care. It didn’t matter anymore because the new plan was to stack the acrylic pieces with their poorly drilled holes, throw a large piece of epoxy putty and squeeze everything in with the wood ball that I had. It’s not the best idea, and the socket isn’t a perfect hemisphere, but its good enough, for now. I might (will) have to deal with joint friction eventually, but I’m hoping that’s not necessary just yet. I also realised halfway through that I could fabricate the joint by resin casting (after stumbling across a tin of resin at Art Friend), but I felt it would take too much effort and time to get it right and I knew nothing about it then.

The socket actually covers half the sphere only. I had thought it would have to be more than that in order to retain the ball within the socket, as is the case with those standard designs. (in fact,  the only points of contact between ball and socket in those things are at the tip of the ball, and the lip where the ball is exposed to the outside. I can’t do that, because that means lots more friction.) However, I realised that this would excessively restrict the range of motion of the leg. That means the ball has to be retained in the socket (i.e. to prevent the joint from dislocating) by other means. Which happens to be the case too in humans. (In addition, the hip joint is angled outwards to increase the range of motion for hip abduction as compared to hip adduction) So yeah, its kind of slow, but that’s how I learnt that a ligament holds a joint together, and that a ligament is different from a tendon.

Hip joint closeup. The joint is a ball and socket type, held in place with rubber bands.

Hip joint closeup. The joint is a ball and socket type, held in place with rubber bands.

You can see in the picture that my ‘ligaments’ are basically rubber bands. (I don’t know how to get the right springs anyway) Well, they keep the leg (in its current form as pictured) from dislocating, but as actuators are added, this will happen eventually since the rubber bands will be stretched by the added weight. I might add more rubber bands, or add more attachment points. Still, when approaching the limits of the range of motion, it’s easy for the joint to dislocate, because the rubber bands aren’t pulling the ball hard enough into the socket. I’m looking for a smarter way than just adding more rubber bands, perhaps Gray’s Anatomy will provide some answers…

Actuators

Basically, the concept employed here has been plagiarised from nature. That means, having a pair of antagonistic muscles to (roughly speaking) control a single degree of freedom. A most evident example would be the biceps and the triceps, which control the angle of the elbow joint. Well, I can’t make muscles, pneumatics are too messy and expensive, the cheapest and most easily available stuff are electric motors. They’re also really easy to control. So my actuators will be motors directly driving a wheel that pulls a string.

Why am I doing it this way when most robots mount an expensive and very powerful geared motor at the joint itself? That’s because my key design requirements are that the actuator must be backdrivable, and that leg motion must be force controlled, not position controlled. Also, I would use a pair of motors working in an antagonistic fashion, instead of a single motor (as in TUlip the robot, see [1]), to give us a chance at avoiding backlash, which is inevitable given my shoddy construction skills.

Knee joint closeup. The motor that was supposed to be part of the (never built) series elastic actuator is at the left.

Knee joint closeup. The motor that was supposed to be part of the (never built) series elastic actuator is at the left.

A shot of the actuator (cables not attached, they’re just dangling), positioned near the knee joint, can be seen above. It’s being secured with cable ties. There’s only one actuator here. The reel-like thing is actually some sewing machine accessory whose name I do not know. It’s really handy. The ‘coupler’ that attaches it to the motor shaft is actually just some part taken from an electronic interconnecting component, which kind of resembles a terminal block. The stuff isn’t centred properly, so the rotation is off-axis (if that’s the right way to describe it). But that’s okay, because I’m counting on the controller to resolve that issue.

The strings are nylon fishing lines. I thought I’d made a pretty intelligent choice, but after a few tries of tugging on the line to gauge the amount of force required of the actuator, it started to fray. Time to reconsider the earlier idea of using the wires inside a telephone line. I also realised that I had grossly underestimated the torque required of the motor in the actuator; Resting my palm at the end of the shank of the foot, I had difficulty tugging at the string to bring about knee extension. That would dash my hopes of enabling it to stand from a squatting position, which is the greatest load on the knee extensor.

So I might have no choice but to use geared motors after all. I wonder if I can find a gear ratio that works without making the joint too stiff. Actually, the guys who made TUlip also had this problem, but their answer is to use springs. The idea of using springs was pioneered by Pratt [2].

Comments

All permanent mounts were done with epoxy putty, which proved to be extremely handy. What other adhesive could have such strength and ease of use, and which isn’t as messy as the kind squeezed from a tube? On the other hand, the things that may have to be taken down or moved about were mounted with cable ties. Cable ties are wonderful things (I’ve got a large bag of them) if you don’t have access to a ready stock of nuts and screws.

Despite the crudeness of the hip joint, I believe that its a much better idea than having three rotary joints. Practically, something like that would demand precisely fabricated parts, and neither myself (nor nature) have the equipment to machine these things. Besides, I think that in a ball-socket joint, the axes of the 3 degrees of freedom (DOF) would intersect each other at close to a single point, unlike with 3 rotary joints stuck together.  Well, I really need to get myself educated in these matters, but it seems to me that this makes a difference. I remember trying to move these kinds of joints and getting stuck at some places…maybe these things are also called ’singularities’…Also, the ball-socket joint (more strictly speaking, two sliding surfaces constrained by ligaments) seems to be very attractive because it doesn’t have to be precisely built to work.

Which brings me to the next point about precision. I’m not a fan of precise engineering. Not to say we should do away with this manner of working, but it is prudent to consider if the same task can be performed in a more elegant manner that is more robust and less sensitive to manufacturing defects. I would emphasise the importance of design for robustness.

I have tight budget constraints, being funded from my own pocket money. While I’m willing to work on my technical skills, I just don’t have access to machinery. I would probably design everything in CAD and send it to a CNC machine if I could,  but presently that’s just not possible. My circumstances have heavily influenced my choice of materials. To fabricate something in a project, I need to spend considerable time scouting for materials. The wood sphere from the art supplies shop was used in the hip joint only because I was fortunate enough to come across it. Before that I was looking around in the supermarket and other places trying to find something that looked like a sturdy ball I could use for the joint, all efforts in vain. It is quite a challenge to look for items to adapt for a project. Very often this phase costs a lot of project time, and while I’ve been doing that sort of thing all my life, I still don’t think I’m very good at it. Or maybe I haven’t been very lucky.

At the present stage, this project is hardly a leg, being more of a feasibility test for an actuator concept. I know also that many others have done what I am attempting to do. Nonetheless I’m doing it with the hope that I could have my own hardware testbed to investigate some ideas about control and AI.

 References

This work is motivated and inspired by readings about human walking, and the related work performed by the Delft University of Technology on Passive Dynamic Walking, whose contributions must be acknowledged:

[1] Hobbelen, de Boer and Wisse (2008). System overview of bipedal robots Flame and TUlip, in 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems. (get it from http://www.dutchrobotics.net)

[2] G. A. Pratt and M. M. Williamson. Series Elastic Actuators. Proceedings
of IEEE International Conference on Intelligent Robots and Systems, 1995.(download it here: http://www.cc.gatech.edu/fac/Chris.Atkeson/legs/jh1c.pdf)

[3] J. Rose and J. G. Gamble.(2006). Human Walking, 3rd ed.

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