How to calculate the torque for motors for a Core XY movment?

I am trying to design a simple setup that follows the core XY movement shown:

I have been researching the statics behind this movement in order to calculate the minimum torque for the motor so I would select the cheapest one required to move a platform. I currently know the mass of the platform and the estimated dimensions for the platform. Everything else is up to me to design. I have reduced the system to this:

But I cannot find anywhere whether this is the correct method of doing this. Could someone please help me?

• Hi welcome to Engineering SE. Is there any specific velocity/acceleration profile, or do you just need it to go from position A to B?
– NMech
Oct 26, 2020 at 13:05
• Thank you for your reply. I just want to go from A to B Oct 26, 2020 at 13:12
• I assumed that the platform is moving on the horizontal plane (not vertical), and that you are using stepper motors, is that correct?
– NMech
Oct 26, 2020 at 13:37
• Am I the only one not understanding the mechanism? If B turns counterclockwise, the part in the middle can move right and/or downward. How is the mechanism constrained so that the required movement comes about?
– mart
Oct 26, 2020 at 16:08
• @mart, I understand what you are saying, the required movement is not just horizontal, my bad for not clearing that up. If one motor is turning, then the platform will move diagonally, yes. I reduced the system like that only to ease the calculation for the torque required to start the movement of the platform. Oct 26, 2020 at 16:27

1 Answer

Since you want to just position the platform from position A to position B (and I suspect that the motion is horizontal i.e. gravity does not get involved), then the main torque you need to overcome is due to losses on the pulleys.

However, the problem there is that the losses on the pulleys will be depended on many factors:

• load (platform + any weight on it)
• bearings used on the pulley
• correct alignment
• tension on the cable
• type of "cable" (e.g. belt, synchro belt, chain)
• ...

The bad thing about the above (with the exception of the first) is that they are very difficult to quantitatively assess.

the good thing is that if there is a proven design and assembly methodology (its deceivingly important), they won't have much an effect.

So bottom line, try to find a cost effective stepper motor with a decent torque (you don't mention sizes but for example most 3d printers use nema 17), and get a stepper motor driver that allows you to adjust the Amps to at least 2 times the nominal amps. Then even if you run into trouble with the nominal amps you can adjust the Amps.

PS: What you are trying to do is essentially load supermarket trolley and push it on a horizontal plane. If the floor is smooth enough and the wheels properly rigid and round then the pushing force to keep it moving is very small (its getting it to move that its the problem).

• Thank you for your detailed answer. That is specifically what I am trying to find out. What is required for the platform to start moving? In theory, I should be able to calculate the minimum torque required to move the platform with one motor (As showed in the second picture). Can Icalculate the torque by τ=Frsin(a) Oct 26, 2020 at 16:31
• To start moving you need to overcome static friction, cogging torque etc. if you just overcome it you will have a minuscule acceleration. But since you just want to go from place a to place B, it shouldn't really matter. I am not sure what is angle $a$ you use.
– NMech
Oct 26, 2020 at 17:51