I am planning to make a robot that looks somewhat like this:
How would I calculate the necessary gear ratio to put at each of the motors in order to make the horizontal scissors able to both expand and retract? What gear ratio would you guys recommend using?
having a 1:7 on 100 RPM is probably a safe bet
Make it geared torque first, then speed up the gears to see what you can pull off without working the motors too hard.
if u are building a wall bot i would make a ditaching wall like “wall-e”
One of the important things to consider would be the center of gravity of the expanding wall.
In your design, when you expand, everything moves up and, therefore, it will require extra force from the motor. When you retract the wall, COG moves down making it easier on the motor.
You can use strategically placed rubber bands to counteract the force of gravity for the most part or attach the motors to the top bar.
Finally, as an alternative, you can take a look at one of the linkages from TEN FOLD Engineering that were optimized for horizontal expansion:
As for the gear ratio, you have to try it first and then adjust if nesessary.
I might be dumb but is the force of gravity even a factor when expanding horizontally? My thinking is that gravity acts vertically/is what pulls the arm down but doesn’t affect horizontal movement
Not gravity, the center of gravity. There is a difference.
Correct me if I’m wrong, but doesn’t the motor have to slide in order to push the scissors outwards.
Also if you get the vex speaker please would you be so kind as to make the bot say wall-e like in the movie every time the wall deploys?
That would be lit
The motor doesn’t slide, the other side of the wall slides passively. Here’s a diagram:
And if we make it to worlds with a wallbot and stay with the wallbot we will get a speaker and put the wall-e sound effects or something similar whenever we expand. 
Pushing the linear slide up and down involves gravity.
Dont quote me though I’m not super good with scissor lifts
I’m building a wallbot with a clamp on a dr4b. staying in 18 by 18 by 18 is really tough, but it’s doable.i just detatch the wall and then i can go stack. Targeting small goal and alliance tower. ima do what they did, expand it then tip it to gain more strength. It’s actually surprising how sturdy the wall is. You can ram into it with 4 motor drive and litterally no damage. I just put tons of rubber bands on my wall so it deploys automatically after i drop it.
It’s mounted horizontally so gravity is not acting against the wall’s motion(unless I’m missing something). My drawing made it a bit confusing but it’s like a bird’s eye view of the wall if that makes sense.
You could make an anti wall mechanism on your bot that you deploy when the match starts. It would just be a piece of plastic or something on one side and mesh or something on the other side to give it grip. Then if they attempt to put a wall down you could pull it out.
That, or you could have just a torqued up arm that can lift it out of the way. Lol
intake the wall into your tray and stack it
i was talking about the robot named walle but okay