Scissor Lift Calculations

Hey everyone. I’ve been looking into scissor lifts and I’ve been wondering if anyone knows of speed and torque calculations that come in handy.

The specific design I’m thinking of dislike this:

(Sorry if the link doesn’t work, I’m on mobile. Try looking up vex scissor lift on youtube)

See Chris Seigert’s blog here:

For a detailed mathematical analysis of scissor lift see (pdf file):

For mathematical analysis of actutor forces in scissor lift see (pdf file):

This is a good example of use of math in robotics. Also an opportunity to engage your math/physics teacher in the project.](

If you are powering from the centre (like the video) it is the following:

Force here is the weight of your scissor plus what you are lifting, in lbs.
Distance is the total length of the levels of your scissor lift. For example, if you have three of the stages you see in the video, the distance is 3*12.5 inches (each bar is 12.5 inches long).
Theta is the angle between the scissor and the ground.

The scissor lift has 3 stages.
Each stage is 17.5 inches long.
The scissor lift and everything you are lifting weighs 5 lbs.
When it is compacted, the angle between the scissor and ground is 25 degrees.

F=5 lbs
cos(theta)=0.91 (roughly, 2 decimal places)

FDcos(theta)/2=552.50.91=236.25 inch lbs of torque.
/2= (roughly) 120 inch lbs.

A 393 stalls at around 13.5 inch lbs, but that damages the motor. However, you can quite safely load it at 10 inch lbs with elastic assist.

120/10=12 -This is the gear ratio required to lift that with a single 393 (1:12)
With two 393s, you could probably use a 1:5 with good elastics.

In my opinion, probably powering the center angle is the relatively ideal way to power a scissor lift. Pushing it up from the bottom yields a square root function curve and requires huge power at a low position. Using linear slides or chains to directly elevate the height of a joint sounds great, but actually do require some space. Directly changing the angle yields a concaving up cosine curve between motor rotation angle and lift height, but it is acceptable. Most importantly, it saves space by only requiring clearance for motors.

Seeing the number of stages required for this game’s scissor lift, I’m guessing that sliders will be worth using, if not required unless you make extensive adjustments to your robot design.

I may just be stupid, but can you give me a picture of the angle you are talking about? A diagram or picture would be nice. Thanks :slight_smile:

I’ve seen lots of good scissor lifts with a powering mechanism like this that could hang on a one to five ratio. If you’ve already got the lift built I don’t know anymore.


Also I believe the angle they are talking about with the level to the ground is the bottom bars when it is lowered.

scissor lift .1.jpg
t vex.png

With the vertical linear slide powered lift in the top picture. I’ve had a team member in my club that built one of these and it constantly shredded the rack gears. Later they even made it so that each side bad two sets of the linear slides to spread the load with the same result.

Now they might have done something wrong but it was a terrible experience for them.

Just to clarify, here’s a sketch on my team’s first toss up scissor to show what angle I was talking about in my post above.

Something else to note-as the angle changes, so does cos(theta). So while at the bottom of the lift you might need cos(25)Fd torque (if your angle is 25 degrees) somewhere near the top you would only need cos(75)Fd torque. If you check what cos(25) and cos(75) are, you find that you need significantly more torque at the bottom than the top. We utilised this fact in our six bar to get 2 motor 1:7 low hang.

Alright that’s what I thought… Just wanted to make sure :slight_smile:

What is the best way to find the angle?

A quick way is to use a protractor.

What do you mean by ‘find the angle’?
If you mean the starting angle (when designing), then you would get the length of one of the beams, sketch a triangle, where that length is the hypotenuse, and decide one of the other two sides, either the height or the base. Then use trigonometry to figure out that angle.

If your beam is 12.5 inches long, and it rises 2.5 inches at the end when compacted, it is:
So in this case:
sin(x)=2.5/12.5 =0.2
x = arcsin(0.2) =11.5 degrees

You could cad the scissor lift (or just the bottom stage if you just need a couple of measurements) and then use some of Inventor’s measuring tools to check precisely.

I am an idiot. That’s what I get for working 4AM-3PM -_-


Very true. But comparing to directly powering a lift by using horizontal slides, this is acceptable. We experimented with both last year and found that the angle changing is much better.

For a detailed mathematical analysis of scissor lift see (pdf file):

For mathematical analysis of actutor forces in scissor lift see (pdf file):

This is a good example of use of math in robotics. Also an opportunity to engage your math/physics teacher in the project.](

I strongly suggest you all peruse these as they offer a heck of a lot info on scissors and the forces needed to raise your lift based upon the style of actuator. These are excellent resources to compare the different lift types.

Pages 47-49 of the second link details some formulas of the change in height per change in angle for some popular mount points.

As you squish your scissor flat, the initial force in many of these configurations will stress the poor little motors out. However, the mount point on the edge (or center) is a constant. But that can be tricky to get working and is a constant speed. The good news about some the other mount points is that they start off slow but they get really quick as you get up there.


My team tried to build a scissor lift (twice) at the beginning of this year.

Our first iteration used four 393 motors to lift from the center, geared 1:7. We were able to make some pretty shafts by twisting them about 4-5 times, but we failed to lift the scissor lift.

Afte we destroyed these shafts, we did failure analysis and determined that the stress exposed to the shafts was greatly exceeding the steel’s ultimate yield strength.

Our second iteration used four 393 motors and a rack-&-gear system to lift. This time we were successful at destroying about 5 rack gears and causing our drive (geared 24:15) to move really slowly. One of the shafts in our drive broke the delrin bearing block and ate its way through the aluminum backing due to the huge amount of weight on the center of the chassis.

The two sides of our lift would not raise at the same speed either. Believe me, it was quite frustrating. Another issue was that if one motor burned out, the entire system was useless, and we were stuck being a very slow pushbot for the rest of the match, assuming our drive didn’t burn out within the first 30 seconds.

Of course, our scissor lift was very heavy despite being made completely of aluminum. At worlds we found some teams that brought some very well built and rugged scissor lifts that worked a lot better than ours did. (I can’t recall any team numbers now). My experience with scissor lifts is not the greatest; you can see why we switched to a 2-bar. If you are going to try to power the lift from the center, then I would recomend directly mounting the gear to the lift with standoffs. (Maybe this year’s high-strength shafts will be useful here.) My advice would be to look through all kinds of designs first and rate them with your team before going for any one design. We rated our designs, and the scissor lift was rated as number one in the beginning; after we saw its shortcomings after the first two events, we went back through our design process and decided on what would eventually go to worlds with us. (And win world design.) :slight_smile: