# Sack Attack Scissor Lift Torque Requirements (theory)

Below is a copy of a blog post I made today:

Assume that we have a scissor lift that we use to lift W lb of sacks to a height of 36 inches.

Also assume that the lift is actuated by a center pin torque with gearing ratio GR that is the output torque/motor torque.

A N stage scissor lift requires a center torque = N*(W_lb + W_lift/2)Lcos(phi) where phi is the interior angle between the arm and the base (see this scissor theory post).

The max torque occurs when phi = 0 or when the lift is at its lowest point. At this point the total torque = M* m_torq where M is the number of motors and m_torq = max motor torque set by the PTC limits.

m_torqM = N(W+W_lift/2)*L/GR or

W = GRm_torqM/L/N – W_lift/2

Lets put in some typical numbers: L = 6 in, W_lift = 1 lb, N = 4 , GR = 7:1, m_torq = 6 in lbs (the 6 in lbs is set by alloting 3.5 amps per two 393′s driven by half a cortex or power expander.)

W = 1.75*M – .5 lbs

M motors => lbs (sacks)

1 => 1.25 lbs (2.5 sacks)

2 => 3 lbs ( 6 sacks)

3 => 4.75 (9.5 sacks)

4 => 6.5 lbs ( 13 sacks)

Focusing on the 4 motor case, lets see what happens when elastic is added that pulls with an upward force on the center pivot. In this case, when the robot is picking up sacks, the motors would be holding the lift down against the elastic. When the lift goes up the elastic and motor are working together. If we add just enough elastic that the motor can still hold the lift down then this is equivalent to doubling the motor torque when the lift is down. So

Elastic +4 => 13.5lbs (27 sacks)

Or we could also up the gearing ratio by x3 factor…. the lift would be 3 times slower but here you would be making one large dump and speed is not required.

3x gear + 4 => 20.5 lbs(41 sacks)

Ok now we are talking…. 41 sacks !! But in Mythbusters style…. more is better so how about 6 motors.

3x gear + 6 => 31 lbs (62 sacks)

Ok… enough for me. Not sure how you would stack 62 sacks on the upper goal. These numbers are of course rough cuts and ignore friction etc but elastic can be use to make the theory come true.

So in summary, looks like we should be able to lift 13 sacks to a 36 in height with 4 393′s working through a 7:1 gearing ratio. Adding elastic can increase this to 27 sacks or using a 21:1 gearing we can get to 41 sacks or with a 21:1 gearing and 6 motors we can lift 61 sacks.

Thats neat. My team used some math to work out how much our lift could handle before stalling, and it turns out hte lift could carry 10 sacks off of 1 393 motor.

You can bump N down to 3. A 4-stack scissor-lift is very unnecessary. For Gateway, our 3-stack scissor lift compacted to 16" and expanded to 42". If you only need 36" of height from your lift, edging a 3-stack lift under 15" should be no problem for you.

Be careful in building your scissor-lift. Ours used 4 269s with a 21:1 torque ratio, plus elastic, and initially it had a lot of trouble lifting 3 barrels. It took us most of the season to perfect it. The Asian teams make it look easy, but scissor lifts are very hard to perfect and you should be very nit-picky during your build process.

Motors can lift alot of built well. My teams Round-Up robot was able to lift itself up the ladder in 2 stages. One was on the lift with only 2 3-wire motors geared at 72:1 or so, and the second was 2 3 wires on a rack and pinion. The robot was 25 pounds or so.

Sure…it really depends on the product N*L. I based N on the assumption that the lift delta height = 9 in per stage. This is typical of a stage that uses 12 in legs (L=6) built from 1 x 25 beams. My requirement was to have a delta height of 36 inches not an absolute height. If I read your post correctly, the lift moves from 16 in to 42 in or a delta of 26 in. This would come out to be about 9 in per stage which is similar to my assumption. So your lift could not bring a sack from the mat to 36ins unless it had a manipulator that raised the sack to an initial height of 10 in. Maybe you could post a picture of your robot.

I agree with your second comment. If you are new to scissor lifts it can be tricky especially if you are not very careful with the joint friction. I watched 1508b team spend most of the season getting their scissor lift working since they wanted to do it without my help. To their credit , they got it going for one meet and later decided to dump the design in favor of a 4 bar.

Here’s are pics:

In the first picture, the top of the lift is 42" from the surface of the table, and the bottom of the intake is 32" high. We made ours out of 15" slotted angles. If you’re designing your lift to score sacks in the high goal, this height should be sufficient.

In the second picture, the lift is at 16", and it’s not fully compacted. A well-built scissor-lift should be able to compact to the point where there’s no space between the bars, that wasn’t necessary for us, so we didn’t work to give it that ability. If it had compacted fully, its compacted height probably would’ve been closer to 6", giving it a delta height of 36".

Ok, I’m with you now.

Just for fun, lets analyze your lift and guess at your payload lifting capability, the lift extension time and the max height.

Correct me if I am wrong but it looks like you have a 7:1 gear ratio with 4 legacy motors. With N = 3 and a half leg length L of 7.5 ins the lifting capability W + W_lift/2 = GRMm_motor/L/N = 746 /7.5/3 = 7.4 lbs.
Here I assumed 3 in lbs for the steady hold torque of a legacy, but with elastic aids we can double this to 6 in lb. One stage of the structure W_lift is probably about 1 lb so that leaves about 7 lbs for the payload and manipulator. The manipulator looks heavy and includes some slides so lets give it 4 lbs.

That leaves 3 lbs for payload which is about right for the game.

We don’t need to consider friction in the calculations since it is assumed that elastic is used to compensate for this loss.

What about speed? The angle change of the legs is about 120 degs or 1/3 of a revolution. The motor turns 7 x this or 2.3 rev. The speed of the motor is nonlinear with lift height , moving slow at first. We could guess at 30 to 60 rpm as the average or .5 to 1 rev/s. This would give a lift extension time of 2.3 to 4.6 seconds depending upon load.

Checking the max delta height… the phi_max is about 70 deg and phi_min is 15 deg where phi is the angle between the horizontal and the leg. So the max delta height = NL2*[sin(phi_max) - sin(phi_min)] = 45*sin(70)-sin(15)) = 30.6 in

Anything I missed?

Are you planning to use a scissor lift in Sack attack?

Actually, we couldn’t afford much aluminum, and there was a great deal of friction in our linear slides, so we used a 21:1 ratio on the lift. We probably could’ve gotten away with 15:1 or even 9:1, but we wanted to make it very robust. Despite using such a heavy ratio, the lift was not as slow as one would expect it to be. With a load of 3 game objects, the lifting time was about 5 seconds.
See a video (Red Interaction)
In the video our alliance partner was a 2-stack scissor lift with a 5:1 ratio and 4 393s. We were the only teams in our state brave enough to try scissor lifts.

Our phi_max could have been larger if we’d needed the extra height. We used stoppers on the bottom linear slide to keep it from going higher than that.

We don’t plan to use a scissor lift again for Sack Attack. One stressful season was enough. After all the reliability problems we had, we’re switching over to a simple 4-bar. But we are keeping records of everything we’ve learned from making this scissor lift in case we ever want to use one for a different game.
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Ok, so plenty of torque so i would have estimated 1/3*21= 7 motor turns at near 90 rpm or 7/1.5= 4.7 seconds.

Looks like Team 2012 has no fear and are planning a scissor lift. I like the use of vertical linear slides to do the lifting. It avoids the 1/tan(phi) force multiplication of a horizontal actuator and the cos(phi) effect of a rotary pivot actuator. Lots of lubrication on the bottom slide will keep the friction in check but I’d rather see a roller bearing here, but its a bit tricky.

hmmmmm usage of verical linear slides like that looks awfully familiar

Construction of Coby our Gateway isolation robot:

Sliders do add friction, though, and we didn’t see any practical disadvantages in having the lift move at different speeds during different parts of lifting. Lubrication helped with our slides, but the slides at the top refused to have their friction eliminated.

One thing that decreased our friction in the bottom slides was mounting one bar of the bottom “X” to a fixed, non-moving hinge so that there was only one slider on each side instead of two.

I suppose we’ll see how things work out for 2012 one they get some weight on that lift of theirs…

@Vamfum that design utilizing vertical linear slides looks awfully familiar

A picture of Coby our isolation zone robot from Gateway:

If you have any questions feel free to message me we probably had all the mechanical difficulties you could possibly have with that robot… Including an overnight rebuild of the scissor lift replacing all steel pieces with aluminum.

Cool… This would be a great example to extend the torque requirements analysis to a vertical actuator. First, a few questions:

1. Is this a partial lift or did you only use one linear actuator with a single 269 or 393 motor in the final product??
2. Do you have a close up of the upper and lower roller guide channels?.. Looks like you are using spacers as wheels embedded in a slot made by the edge of a 1x35 and a chassis rail… but can’t really see. It is close to what I had in mind about roller bearings rather than a linear horizontal slide as a guide to reduce friction.
3)what was the maximum practical load capability and lift speed?

Once we have these, I’ll do a sample torque analysis.

The angle still comes into play unless you mount the slides completely vertical. You are most likely to find a configuration where the linear track starts out fairly horizontal and moves more vertically as it travels along. Something will typically get in the way as you move along forcing you into a different configuration.

Vamfun’s previous blog post had a link to a wonderful paper on the equations of scissor lifts.

Here’s this key paper he links in:

See section 5 of that paper for the analysis of a variety of actuator positions. Given the geometries of Vex slides, it’s most likely to be position 5 for the linear slides. You can see it still has a horizontal component to it.

The graph gives you an idea of what’s going on as the angle is small on the scissor. The tangent of 0 is infinity and you can really watch the motors struggle on these lower angles.

As you try these various configurations and break the motor gears, you get to learn how to change the gears on the 393 motors real good!

So now in this configuration your calculations of torque required should add the weight of that new motor lift assembly too. There are no aluminum linear slides and the motor brackets and motors and gears start to add up. Adding rigidity means more parts too which means more weight and friction points.

The linear slide mechanism seemed much more reliable for our guys this year and that is why they switched to it after unseccessfully trying to make the central gear lift mechanism as described on the first post on this thread. One thing to watch out for on that is a slight shift from the holes means skipping gears. Our guys did not use shoulder screws on that so maybe that would have helped.

Another one of the keys to the linear slide mechanism was the attachment point to the scissor. All that lifting force is on the shaft hooked to the scissor some place. Adding an extra bracket on the slide end to give the shaft two plastic bearings to guide it helped a lot. I can post pictures if you are really interested.

Unfortunately I do not have any close up pictures as this picture came off of my cell phone and I am in Chicago for a summer internship. However I can still answer your questions.

In the final product we had 1 linear actuator on 3 sides of the robot as een in the picture. The right and left side had 393s and the rear had two 269 motors. The logic behind this was that we did not want an odd number of 393s on the drive train.

Actually we used an axle that sat in two inner trucks on the linear slides on each side of the scissor lift. We reduced friction by using a lithium lubricant.

The maximum that this lift could lift was about 6 objects plus the heavy intake that we had on it however it could not hold all 6 at once due to the rear linear slide poking up in the middle of our intake mechanism. As for the total time to max height was about 7~8 seconds. Which is what killed us at worlds since we could not compete with the speed of 6-bar mechanism.

Love to see the pictures.

PS… I actually like the other paper more because of his use of the simpler energy formulation.

I posted a blog link to an excel scissor performance calculator where I used your lift as a test case. The primary outputs were:

I_total… 6.4 amps Total current draw at speed
W… …2.6 lbs Total payload capability
rpm_motor… 60.0 rpm motor rpm during lifting
t_lift… 2.7 sec Lift extension time

As you can see, the lift extension time is much faster hence I suspect that the assumption of friction being compensated completely by elastic bands is not true for your robot. In fact as I mention in the post I suspect that your lift is moving at around 20 to 25 rpm which would draw around 12 total amps or 4 amps per power rail available if you used a power expander and distributed the motor loads properly.

Maybe I have an error somewhere but I don’t see it.

Attaching a 3 hole long of a 2x2 L angle allows you to put a delrin block to give two points of stability for the shaft as it goes from the lift to the scissor. The second picture has the other slide on the table to get another view.

They ended up liking that so much they put a delrin bearing block on both the inside and outside of the angle piece to give a really long resting point for the shaft. Put a big white nylon washer between the Delrin and the scissor. Otherwise the shaft can bend a bit as you push up.

Zoom in on the connection point here if you can. Delrins all the way across. At what point is it overkill?

80N - Nightcrawler tall view

Click on the pictures to go to Flickr…

The lift time mismatch bothered me so I rechecked my assumptions. Indeed, I should have used dh_dl = .67 rather than 2 as I noted in the post. This error occured because the lift attach point of the actuactor is on a midpoint …true but the midpoint is on the second stage so any movement of this point will cause a 2/3 movement of the bottom stage height which dh_dl is tied to.
The corrected primary outputs were:

I_total… 6.4 amps Total current draw at speed
W… …21.1 lbs Total payload capability
rpm_motor…60.0 rpm motor rpm during lifting
t_lift…8.1 sec Lift extension time

So now the lift time agrees very well…but the lift payload capability has gone up substantially. I have no explanation for this other than the manipulator was much heavier than 6 lbs.

See corrected post here:

This is a good example of the application of Spackman’s actuator force formula:

(W + W_f/2) = F_actuator/(dh_dl*N)

dh_dl is the change in height dh for an actuactor displacement dl.

This is is a energy balance equation that basically states the the energy from the actuator F_actuactor*dl must equal to the energy added to the Weight lifted = (W+W_f/2)dhN .

The N comes from the number of stages. So dh_dl must be referenced to a single stage.

Glad you posted this, I have seen it before and really appreciated the construction. Wasn’t this posted as being built by a girl team? Daughter?

Anyway, I love the use of 1x25 beams replacing C channel. It is light and yet very strong. Our 1508 team built a plain X version using this technique.

So… what was the reasoning behind the added parallel beams?

How did this robot perform relative to your other team robots?

What was the lift performance?: time to extend, min height, max height, motors used, lift frame weight with manipulator and payload capability.