# Rack and Pinion / Cascade Lift power

I was wondering how much a cascade lift or a rack and pinion elevator could lift - I’m trying to find something that can lift the entire bot. Which option is more reliable / compact?

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I made this recently, but I decided not to use it on my bot. I was going to add a claw to it and use it for both climbing and acorns, but the robot easily tips when it is fully extended (the whole thing is on a pivot so I could extend it out and grab match loads). The lift itself works really well, though. I used two 100rpm motors and 12T gears that rotated on the rack gears.

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Since there is no robot hight limit, a cascade lift would be more reliable. A good idea to use that might be able to be incorporated in the cascade lift is rubber banding. Here is a video Building Tips Every Vex Team Should Know - YouTube, start at 3:03. I don’t know if you could incorporate it, but if so, it could carry pretty heavy stuff.

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You can determine this reasonably easily by using physics. Figure out the torque output of your motor, (note that this torque is usually the stalling torque where the motor stops spinning, the actual available torque is a bit less.), then figure out what the torque output after any gear ratios is. Now that you have your torque, you can figure out how long your lever arm is… We did this in tipping point to figure out if our 6-bar lift would work.

Another thing to note, this kind of thing looks reallly good in a notebook!

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Completely agree, but you should be aware that higher torque ratios will impact speed. A vex motor could lift a ton, but it would be woefully slow. Any mechanism mush be possible to execute in 5 or 6 seconds tops.

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How are gear ratios calculated for a rack and pinion mechanism? Is it based off of the length of the rail or how much the gear moves on it? Also - will carrying the weight of the robot strip the gear?

Thank you so much for your help

Usually, it is given in something like cm/rotation or in/rotation.

Correct. More specifically, the radius of the driving gear would be your ‘lever arm’. In the case of a 36 Tooth gear, the lever arm is about 0.75"

(It appears as 0.003" larger in my CAD, but I am pretty sure this is simply an artifact due to how I determined the contact point between the rack and pinion. )

Regardless, Lets assume you are directly driving the 36T gear with a V5 11W Smart motor with a torque gear cartridge.

If we consult the Vex Knowledge Base we can determine that the stalling torque of our motor is 2.1Nm. For our purposes, lets convert this to pound feet:

According to some random website:

• One pound-foot is equal to 1.356 newton-meters. To convert your Nm figure to lb-ft, simply divide it by 1.356.

This would give us a torque of about 1.55 lb-ft.

to determine exactly how much force (in pounds) the rack is transmitting, we can use algebra!

we know that the formula for torque is this:

• Torque = Distance(lever-arm) * Force

We can substitute our torque, and lever arm distance in right away (don’t forget to convert inches to feet!):

• 1.55 lb-ft = 0.0625’ * Force

And we can isolate Force by dividing both sides by our lever arm (0.0625’), this will cancel out the lever arm on the right side of the equation:

• 1.55 lb-ft / 0.0625 ft = Force

A quick combining of like terms, and simplification of units gives us our result:

• 24.8 lbs = Force

Keep in mind this is the stalling force of the rack. This also doesn’t account for any efficiency losses in your mechanism.

Another thing, I used a 36Tooth gear and a torque motor simply as an example, and, surprisingly, it seems to be a plausible option to lift up your robot. Keeping your robot under 25 pounds is very reasonable in Vex. It is harder, but not impossible to make a robot as light as 15 or even 12 pounds.

I don’t know for sure, but I think this is a possibility. Maybe consider using at least a pair of HS pinions and racks. Always a good idea to design redundancy into your robot.

Anyway, good luck with your engineering @26annaw !

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It isn’t always the best idea to “try it and SEE” without doing any research beforehand.
In the design process, building doesn’t come before… literally almost everything else: