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"slider-crank"-style lift mechanism. What workaround to avoid dead point/singularity?
3

"slider-crank"-style lift mechanism. What workaround to avoid dead point/singularity?

"slider-crank"-style lift mechanism. What workaround to avoid dead point/singularity?

(OP)
Hi, I am trying to design a lifting mechanism for a quite large (in area not weight) platform that only uses rotation for its actuation. I have a design that uses a mechanism similar to the slider-crank and I want to maximize the total height the platform can travel.

This is a sketch of my design:



The rotation is going to be executed by a motor at the red dot and my dilemma is about the behavior of the two arms when they reach the position at the middle of above image. I think this is called a singularity or dead point.

If the platform is going down, the way I have suggested in the sketch, at that point I see a weak mechanical position when the platform will tend to fall more than it should because of its weight. This is where I would loose precision in movement and I need a solution to overcome this. Is this true? What are the weak points of this design? Just a note: there is going to be direction changes in rotation at arbitrary positions.

A preloaded spring was suggested to me but I don't exactly know how should that be setup, to which direction is better? Is there any other (simple/cheap) solution employed by other such mechanisms/robot arms?

I am also thinking about having gears at the green dot ends of both arms but that would introduce backlash when the rotation would be reversed.

PS: I don't want to change the slider-crank-based design to a leadscrew or something else, dut to other factors it has to be rotational.

Thank you for your suggestions.

RE: "slider-crank"-style lift mechanism. What workaround to avoid dead point/singularity?

If the drive has to be rotational, I would strongly consider using a roller chain and sprockets as the drive. I've seen it work successfully. Attach a driver pin to a single chain link. Insert that diver pin into a slot on your guided moving carriage.

RE: "slider-crank"-style lift mechanism. What workaround to avoid dead point/singularity?

Use a 4:1 length ratio between the crank arm and the connecting rod, and if that won't fit work your way down to a ratio that will fit. The crank arm to connecting rod length ratio as-shown in the graphic is too close to unity.

RE: "slider-crank"-style lift mechanism. What workaround to avoid dead point/singularity?

Yeah - at the crossing point there is zero load capacity, hence the dead spot.

If you add a fixed sprocket at the drive end and a sprocket at the pivot of the driven lever with a chain around them then the second sprocket will be driven to orbit the first and have moment continuity to continuously carry the load. A similar mechanism is used in orreries to drive moons around the planets. http://ecg.mit.edu/george/lego/orrery.html

RE: "slider-crank"-style lift mechanism. What workaround to avoid dead point/singularity?

3
I have built this mechanism on several occasions, and it works beautifully, at large or small scale, with fine pitch timing belts and with #40 roller chain:

https://video.search.yahoo.com/video/play;_ylt=A2K...

... sorry about the long link.

The mechanism comprises a fixed sprocket of size 2N, about the center of which a primary arm is driven by obvious means, and a secondary arm free to rotate at the tip of the primary arm, and driven in rotation by a sprocket of size N. The two arms are of the same length L center to center, and the total stroke of the mechanism is 4L. The tip of the secondary arm is constrained to move in a straight line. There is no dead spot.

I think it's a derivative of work by James Watt, who built it with gears, not chain and sprockets, to get around a slider-crank patent. I think you can see how it would work with gears of size 2N and N and an intermediate idler gear of not quite arbitrary size.




Mike Halloran
Pembroke Pines, FL, USA

RE: "slider-crank"-style lift mechanism. What workaround to avoid dead point/singularity?

That's the one.

RE: "slider-crank"-style lift mechanism. What workaround to avoid dead point/singularity?

thorq- What would be of greater concern are the radial forces at the rotational joints as the mechanism passes through the 90deg position. In theory the radial forces at the rotational joints approach infinity as the linkage passes through center. In reality to prevent this situation you would need to have substantial clearance in the joints and/or very flexible mechanism structures.

RE: "slider-crank"-style lift mechanism. What workaround to avoid dead point/singularity?

(OP)
Thank you all for the responses, please bear with me I am digesting the knowledge (I am in IT not ME).

1st: @Jboggs: I think your suggestion goes in line with 3DDave's and MikeHalloran's. I wonder how come I didn't find that video during my research, that would have saved you this thread. Nevertheless I am glad because I am sure I'll have many more things to ask.

I have seen the "How it's made" (Robot Arm on How it's Made ) for robotic arms but it didn't click to me that one of the many belts going from shoulder to elbow does exactly this.

@tbuelna: I can't have clearance in the joints or flexible arms/etc because this platform needs to go up and down with a certain precision, with no deviations from the vertical.

One more thought: if the initial position of the platform was up and it only descended, wouldn't the weight of the platform "help" it decide to go down at the singularity? This is what I was imagining when I started thinking about the application. The only mechanical problem would then be when I raise the platform all the way up, at that middle point it wouldn't choose to go above the center by itself, more likely it will go back down because of this weight bias.

RE: "slider-crank"-style lift mechanism. What workaround to avoid dead point/singularity?

thorq,
The other thing I don't like about the linkage approach is the wide variations in speed and torque as the constant rotary speed is converted to linear motion. You haven't mentioned a specific load or speed but normally that would be an issue.

RE: "slider-crank"-style lift mechanism. What workaround to avoid dead point/singularity?

(OP)
My application will use stepper motors to rotate the pulley. In software it is possible to calculate how many motor steps this variable output will need for the next move. I don't mind the differences in speed between moves, my platform will move pretty slowly. The variations in torque are because of the position the load finds itself across the circumference of the pulley -e.g. at ecuator, when the load is max?

What about the weight of the platform helping overcoming the singularity indecision of the linkage? I am pretty interested in your opinions about this.

RE: "slider-crank"-style lift mechanism. What workaround to avoid dead point/singularity?

The weight will cause the linkage to suddenly go over center due to deflection of even tight joints. It's a place of zero leverage so the forces are otherwise infinite. Coming the other way the linkage will stall until enough deflection builds up and it surges to the opposite side.

RE: "slider-crank"-style lift mechanism. What workaround to avoid dead point/singularity?

Don't make the home position(s) top-dead-center and bottom-dead-center.

RE: "slider-crank"-style lift mechanism. What workaround to avoid dead point/singularity?

(OP)
"Don't make the home position(s) top-dead-center and bottom-dead-center." and also "It's a place of zero leverage so the forces are otherwise infinite" so I guess my only option is starting a couple of degrees away from top and finishing above center.

I have sketched another design after I have realized funny things will happen at the center but I hoped there would be a solution to overcome that issue gracefully. Here's my sketch:



This will give me about 80% of the diameter the driving pin describes.

RE: "slider-crank"-style lift mechanism. What workaround to avoid dead point/singularity?

(OP)
rack and pinion are very precise parts and therefore are expensive. And difficult to source in many areas. And they justify their price for some aplications but not for mine. In my design I only need to have precise holes and good enough bearings to build 3 such pulleys with arms. There will be no slider per se. having 3 or 4 of these will help each other keep themselves on the straight line.

I am thinking also about having 2 such pairs, with one pair having a slightly longer arm that would put it in a position other than the singularity and which will dictate the direction when the other pair is in the weak position. But I am still thinking about such a solution feasibility.

RE: "slider-crank"-style lift mechanism. What workaround to avoid dead point/singularity?

Roller chain is not terribly expensive, and when stretched along a frame, makes a serviceable rack.
You can buy specialized roller chain with some links modified to accept plates to make a conveyor and instead bolt the plates to a beam, but for vertical travel it may be unnecessary.

In your case, imagine pillow blocks and a lineshaft with sprockets along its length, all placed near the top of your apparatus, and lengths of roller chain supporting your platform. Tie the unterminated ends of the roller chain to a dangling length of pipe or bar just to keep some tension in the chain.

Mike Halloran
Pembroke Pines, FL, USA

RE: "slider-crank"-style lift mechanism. What workaround to avoid dead point/singularity?

(OP)
It's about philosophy not money. Personally I can afford it but, being a reprap enthusiast, I can see the advantages of being able to produce the part you need when you need it, when something breaks, when you want another tool etc. I know that there are many folks around that surely can come up with an intelligent solution to my problem.

The difference is that instead of going the easy way, I set myself goals that would prevent me down the road to choose comfort. So I apologize for insisting but I feel I am quite close to a solution. If I need to lower my expectations I'd rather do that. @MikeHalloran's video suggestion proves it's possible, as well as his work if you believe him.

Back to my idea, having a platform to lift in a horizontal position you have to define the plane by at least 3 points in space. These points can be the upper ends of the rotating arm. Each arm can only rotate in a single plane, that's why the three will constrain a vertical movement.

Now we are left with the singularity issue. I know that pistons in a gasoline motor fire up in a sequential order to cover all 360 degrees of push -or at least that's how I came with the idea of having at least one of the slider-crank assemblies phase-shifted with 10-15degrees. This way it will still be in full torque when the other cranks will get in the weak position. What do you think would this work? Unfortunately I can't think of something even simpler that would stick to the goal of having rotary-only actuation.

Sorry for my long post, I expected at some point to be suggested some better alternatives that would go against my set goals.

PS: in my opinion, leadscrews/ballscrews/roller screws/rolling ring actuators are the best option for linear motion.

RE: "slider-crank"-style lift mechanism. What workaround to avoid dead point/singularity?

I was referring to the horizontal position. Top dead and bottom dead center are no problem. In the original diagram when the driven lever has the output lever fold back over it is when the leverage becomes zero.

RE: "slider-crank"-style lift mechanism. What workaround to avoid dead point/singularity?

If your device must provide controlled linear vertical movement/positioning of the platform using a reciprocating crank/conrod mechanism driven by a stepper motor coupled to the crank by a belt/pulley system, then I think you need to do a bit more detail design and analysis work. It would be very helpful to create a design spreadsheet that includes the mechanism kinematics, inertias/forces/moments in the system, and frictions at each joint contact. This will allow you to optimize the design of each component in your system and determine your motor power requirements.

RE: "slider-crank"-style lift mechanism. What workaround to avoid dead point/singularity?

"PS: in my opinion, leadscrews/ballscrews/roller screws/rolling ring actuators are the best option for linear motion."

We've had lots of problems with resonances in long lead screw systems

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RE: "slider-crank"-style lift mechanism. What workaround to avoid dead point/singularity?

You have guidance problems that are not yet considered. The crank-arm to connecting rod ratio gives high side forces that are going to create stick/slip issues unless you use nice linear bearings.

I've built slider crank mechanisms to move some biggish stuff and it is disappointing when you see what you haven't considered up close.

RE: "slider-crank"-style lift mechanism. What workaround to avoid dead point/singularity?

(OP)
@3DDave: ok, that was my concern from the beginning, but I can only work around that issue with yet another system with 2 gears and a belt and I don't really like making this more complex. I can't really afford to lose accuracy at that crossing position, as you have mentioned that the linkage will suddenly go over center due to deflection, which means it will tend to travel more than the requested distance per stepper unit, with no way of knowing how much. If my 3 slider-cranks with phase-shifted crank angles will not avoid this issue by having the other cranks at non-dead-center angles to help, while keeping platform leveled, then I think I will ditch the first design altogether and focus on the second one, which resembles more the classic slider crank.

@dvd: I can't have neither the crank nor the rod too long due to size constrains (the lifting platform will end up having a too high lowest point) yet I want to maximize stroke.
I used the formulas at http://ocw.metu.edu.tr/pluginfile.php/3961/mod_resource/content/6/ch7/7-2.htm and for an crank=100, rod=150, eccentricity=20 the stroke gets me around 203, which is acceptable.
It doesn't compare though to the stroke of the mechanism linked by MikeHalloran.

I will start putting together an excel with what info I have so far. I also need to calculate how much stroke travel for each stepper motor step, so that I can tune the dimensions/gear ratios for the desired resolution.

RE: "slider-crank"-style lift mechanism. What workaround to avoid dead point/singularity?

MikeHalloran said earlier that roller chain makes a serviceable rack and pinion. I would agree - to a point. Roller chain is designed to get its full strength when wrapped around a pulley to some degree. When the pulley is in contact with a section of straight chain, that contact is very limited, and likely to slip. That's why when I have used roller chain in linear motion I always let the chain move and attach it to a guided carriage riding on linear rails. The drive for the chain does not have to be at either end. It can be in the middle, but only if idlers are used to create some wrap on the driver pulley. To me, roller chain is a cheap, simple, strong, reliable solution to this design problem.

RE: "slider-crank"-style lift mechanism. What workaround to avoid dead point/singularity?

"Each arm can only rotate in a single plane, that's why the three will constrain a vertical movement."

From this statement it sounds like you aren't planning on using any guide features to constrain the platform to only allow vertical motion. You will likely end up with twisting/destruction of your mechanism without something holding it in the proper orrientation.

Yet another option you could consider looking into for vertical motion of a platform is a scissor lift.

RE: "slider-crank"-style lift mechanism. What workaround to avoid dead point/singularity?

(OP)
Scissor lift still uses a linear rail.

It remains for a prototype to be built I guess... and improved from there. I am sure it's possible.

RE: "slider-crank"-style lift mechanism. What workaround to avoid dead point/singularity?

In the second paragraph of my last message, I gave a too-brief description of a cheap and simple mechanism used to lift large plating buckets out of tanks and such. In that case, the wrap on the sprockets is 180 degrees; the sprockets are rotated by a common lineshaft and a gear reduction. The roller chain is in direct tension from each sprocket to an attachment point on the heavy basket. The free end of the roller chain is attached to a simple bar that is heavy enough to provide tension on the chain so that it won't ride up on the sprocket teeth. In some cases, the bar is heavy enough to counterbalance much of the basket's weight. The lineshaft and sprockets are necessarily above the entire stroke of the basket, or in your case, platform. Lateral guidance on the plating line is provided by vertical angles/ rub rails, as some trajectory error from a perfect straight vertical line is acceptable.

The first paragraph discussed a different arrangement, where the roller chain is actually kept straight, and bolted or welded (!) to a straight bar to make a light-duty rack. As mentioned, it needs to be de-rated because of the zero wrap angle, or it needs to be fastened only at the ends and equipped with wrap idlers so it looks a little like a Rolamite. (Remember the Rolamite? Did anyone ever find a real use for it?)

I should also mention that working with stepping motors can provide a large number of surprises.
One of the first you will encounter is that every single step is a complete motion of everything, so the first problem in analysis is that you have to know the inertance of everything, and if it's too great, the stepper will buzz, but not move.
The second surprise is that the stepper's performance is integrally linked to the performance of the circuit that drives each coil in turn, so any comparisons you do have to include a particular motor and a particular drive circuit.
There exist many books on application of steppers (search on Al Leenhouts in particular), and you will need to digest several such books before you are properly equipped to apply a stepping motor to a particular problem.

Mike Halloran
Pembroke Pines, FL, USA

RE: "slider-crank"-style lift mechanism. What workaround to avoid dead point/singularity?

(OP)
Actually my first sketch for this platform has rolamite bearings but that was more of a design exercise because I've never seen a rolamite bearing used anywhere and they still need precision flat surfaces to roll, plus a fancy metallic tape and they are in fact exotic devices that would be difficult to make.

Regarding your explanation, it would be very helpful for me to have some pictures to look at. Maybe you have some. Or maybe something similar... I have a hard time following especially as english is not my native language.

Thank you.

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