Arm Design Input -- Four Bar Linkages

[Sachiel7]

Hello All,

Well, we've begun to wrap up our team's strategy phase, and are entering our design phase.
Our Strategy calls for an Arm or Lift, capable of Capping a Tetra on top of the center tetra goal, even after some tetras have been added. We're looking for something to get us around (at minimum) 8 to (above expectation) 10 feet. It'd probably be nice for an average around 9 feet.
So, keeping that in mind, we also want to mind the KISS principle.
I presented the group with one of the older ppt presentations on arms + lifts, which demonstrated 4 common lifts; Elevator, Forklift, Four Bar, and Scissor.
Our group is interested in the four bar design, both for simplicity, and its capabilities.
I would like to hear any input from those who have tried either 4 bar, or something similar. I'd like to hear some of the pros and cons from experience.
Also, I would like to get some ideas from teams from last year who had successful capping lifts for the large platform goal.
I just want to see some designs from a different perspective, and get some first hand input on what works well (Since our arm last year wasn't that complicated, but cant achieve this years task)
So, any input you can offer would be helpful!
Thanks!

[ChrisH]

Originally Posted by Sachiel7

Hello All,

I would like to hear any input from those who have tried either 4 bar, or something similar. I'd like to hear some of the pros and cons from experience.
Also, I would like to get some ideas from teams from last year who had successful capping lifts for the large platform goal.
I just want to see some designs from a different perspective, and get some first hand input on what works well (Since our arm last year wasn't that complicated, but cant achieve this years task)
So, any input you can offer would be helpful!
Thanks!

In 2003 we use a 4bar for or "stacking" arm. I put stacking in quotes because we never used it for that in competition. It worked just fine though we did have a few problems in development.

4bars can be used to lift things reasonably efficiently, but you should be careful to remember about large torques and separation distances. Let's say that you are using a 4bar to lift 3 stacked tetras. To maximize the amount of lift you have mounted the fixed end of the 4bar at the top of the 60 inch envelope and let the arm hang down to the floor to fit in the box. We'll neglect loads from the gripper etc and focus on the tetras.

The highest load on the arm will be when the arm is straight out with the three tetras. Using the diagonal of the box your arm length is going to be at least 5' 6". Put 30lbs of tetras at the end of it (in dealing with loads always round up, with capabilities round down) you now have almost 2000 in lbs of moment around the fixed end of the arm that need to be reacted.

You could do that with a motor, but that would require a pretty substantial gearbox. The one we built in 2003 was a 1000:1 reduction on a CIM motor. We could lift a stack of 7 boxes 3 feet in about three seconds. Of course the stacks weren't stable enough to take being lifted like that, but that is beside the point here. To lift we applied a torque to the upper links (we had two in parallel for stability. I think you would need something similar here.

Another approach is the use a cable diagonally across the parallelogram formed by the 4 bar. In this case, assuming your 4bar was 6" deep, you would need a cable with something like 4000lbs of tension on it. The nice part is you don't have to pull it very far. But you do have to resist all of that load and transmit it into the structure somehow.

These problems aren't all that different from those of other arm systems and they are all solvable, you just have to think about them for a bit. In our case the 4bar was a little on the heavy side, but thinking about it later I could have probably reduced it substantially if I had tried a little harder. Our 4bar was originally designed to use the cable method. That puts all of the solid members in compression. Beams are rather unstable in compression and that limits the amount of speed holes I'm willing to put in. But when we went to install the cable, we couldn't get the motors to fit. So we built the gearbox. At that point the lower bars had hardly any load on them and I could have switched from 1x1x1/8 square to L-angle and saved weight, but that was no clear until after we had already made weight, so who cared?

One thing to note if you use a cable system. We needed cables running across both diagonals to ensure the lift would move in both directions. We discovered that the two cables move at different speeds at different parts of the travel. So at one end the pulling cable will be moving comparatively fast and the slack cable will be moving much slower. At the other end of the travel they will be reversed. this was another reason we went to the gearbox.

After all that, a 4bar is still a possible concept for this year. Having given it a fair amount of thought over the intervening years, I think we can deal with the minor issues.

One more thing, I wanted to precision drill the holes for the pins on our 4bar so the arms would be interchangeable. While I was out one day some people just went ahead and drilled them by hand. They did a good enough job that I didn't notice that they were hand drilled until we were trying to reassemble the 4bar after installing the gearbox. All of a sudden we couldn't figure out which arm went where. With four bars, four positions and two possible orientations we just couldn't figure out how to get it back together again. So we made the holes really big and sloppy. It didn't seem to hurt the operation. So a 4bar will work just fine with a lot of "play".

Sorry to take so long. I missed this post the day it came out and I've been off-line for a couple of days since then.

ChrisH

[Sachiel7]

Thanks for the input. I would also like to know how pnuematics could be integrated as actuators for the arm. Our arm is not currently planned to be strikingly large, but large enough to go from the top pivot mounted near the back of our bot at around 4.75 to 4.5' high (from ground level), to around 8-9' high at the end upon raising (including the height of our assembly on the end). There are two things I wanted to address: Counter Balancing. We're hoping to counterbalance the arm (from the actuation point) to eliminate most of the load except the tetra. Also, we're only looking at manipulating one tetra at a time. On top of all that, we hope to use pneumatics to provide our actuation. The point of actuation will likely not be located right at the 4.75' mount for the bar, but closer to the center, no farther than 2/3 of our arm's length from the end.
SO (*huff huff*) With all that said,
Roughly, what kind of equations can I use to get an idea of what kind of load I'm talking about here? We still aren't 100% determined for our Grabber, so the sizes aren't set, But, lets assume our Tetra Manipluator is 1' long in from the front of our bot. We're utilizing the 38" for our front-back dimension. If we're mounting the Supports for the pivots about 5-6" off the ground, the pivot for the arm is roughly 4' from our chassis. Running through the math, our arm sections would be roughly 4.5' long, or less. So, we'd acheive a heigth of around 8 ft. or so.
My question is, lets say we mount a piston 18" out from the pivot (I'd probably make it more) to supply our upward force on the lower of the pivoting bars. If I used a Piston (or 2 pistons, one on each side) Roughly how many lbs of force am I looking at pushing? Do I just add up the weight of all the items being raised? I'm referring to the Pneumatics Manual, p. 12/19. The talbe lists the extend and retract forces of the pistons in pounds. So, if our arm weighs 30lbs plus tetra, (I'm just pulling out of the air, I'm not sure how much our design will weigh) would it be safe to assume one could use a piston with 40+ pounds of force extended?
My Guess would go something like this:
There is 48" from the point of Actuaction to the end of the arm, where the 10 lbs of tetra is sitting. This gives me roughly 480 in lbs. How does that translate into Pneumatics?
I think I may be getting a few units or my math mixed up (It's been a REALLY long day)
But I'd like an idea of what kind of pneumatics could be integrated.

[Gary Dillard]

Shayne:

Before giving you the short answer I'd like to discuss and explain "4-bars" a little bit here if you'll indulge me - someone asked what one was in another thread and I thought it more appropriate to answer here and refer him to this post. I searched and didn't find another thread that explains it - if anyone finds a better source please post it.

Generally speaking, a 4-bar mechanism is one where an input rotation or translation of one joint of a link or "bar" in an assembly results in a unique displacement path of some point fixed to another link or "bar". If you have two links pinned to your chassis or "ground" at separate points and pinned together at one point, you have a 3-bar; the ground between the 2 links counts as one bar and each link counts as one bar. The 3-bar has only one position and it is fixed. If you separate the 2 links and pin them to an additional link, you now have a 4-bar. For any rotational position of the first link, there is a unique position and orientation of the other 2 links (and therefore of any point on them). This is a traditional 4-bar, where the input angle is determined by the position of a driving motor on the input axis.

There are other mechanisms that are technically 4-bars but not usually referred to that way. If instead of adding an additional link to the 3-bar mechanism you made one of the links a linear actuator, you would have a slider crank (or crank slider since it's really the input) The slider itself is considered a bar (or was when I was in college ages ago).

If you attached an actuator to the traditional 4-bar as an input, you would actually have a six bar (there is only 1 bar for ground for all three fixed points), but this is really just an extension of a 4-bar; note that any additional 2 links (or link and slider) added to the stack will still only have one unique trajectory for a given input. Thus a scissors is really just a stack of 4-bars. Also note that a scissors doesn't have to move in a veritcal or linear direction; our lift last year actually started out facing away from the bar and then arced toward the bar.

Now to your questions....
I have a very smart friend who once told me "sliders are for people who couldn't figure out how to make a mechanism work". Usually it becomes a matter of packaging though; rotating joints are generally lower loss because you can use bearings rather than rolling or sliding surfaces, and you can concentrate the structure around the load which is always at the same point. However, there's no doubt that a good telescope or lift can be very compact for the same amount of displacement as a large mechanism. I've seen both used to great success, but probably equally as often have seen problems with both because of poor engineering (ourselves included). I like to think I get smarter every year at this so here's my biggest couple of pointers in working out the design:

1) Don't overlook out-of-plane loads. Mechanisms look great 2-dimensionally but don't behave that way. Dynamics of moving can put lots of torque and bending in directions that your mechanism isn't designed to accommodate.

2) Structures and mechanisms are frequently mutually exclusive. If you use small pins and bearings relative to the structure stiffness, every joint is a loss of stiff load path. This is the reason scissors are usually a poor choice - there's no good load path out of plane. Use big bearings and joints.

You asked the question about pneumatic loads, and you need to look at it from a different perspective with mechanisms - it's called virtual work. If you are lifting 10 pounds 8 feet you are doing 80 foot pounds of work. If your actuator extends 1 foot in order to do that, you have a mechanical advantage of 1/8, so it will take 10/(1/8) or 80 pounds of force for that foot. You can sum the component weights individually for this - how far does the tetra move, how far does the center of the first link move, etc. Here's where counter weighting and springs come into effect - the weight moving down is doing work, the tension spring retracting is doing work - those help based on their mechanical advantage.

It sounds from your discussion that it's just a simple slider crank, with the actuator attached to the lifting shaft. In this case the mechanical advantage is just the ratio of the lever arms as you said. However, consider using mechanical advantage to your advantage. When the arm is horizontal you have the highest load from the moment, and your vertical displacement per angle of input is the highest so your required work/force is very high. Try adding an additional linkage such that when the actuator extends, the output arm displacement speed is inverted - slowly at the side and quickly at the top when the moment is lower. It effectively averages the load requirement and lets you use a smaller actuator to get the same amount of work.

I hope this helps; good luck.

[Sachiel7]

This may give you an idea of our arm design:

http://www.raptar.net/ArmAnim.gif

The 2' piston is temporary (I hope) and I'm still workin' on it. But this is the just.

Some of our team's mentors worked out the math, so we've got our forces down pat

Thanks for the info though.