Help with stepper motor suggestions for project

Hi everyone, I am requesting assistance on a personal project of mine, and I would like some recommendations as to the items I need for said project that will be capable of handling the task I require.

Basically I am building my own mini bowling lane, and I am building a ball return I want to build it with a stepper motor capable of lifting 3-5lbs as that is the weight of the mini bowling balls. I want it to be stationary with an arm with a scoop type deal on the end that will be activated by a sensor after a short period of time when the ball comes to rest in the scoop, then the arm will swing the scoop with ball up 90 degrees to the left basically overhead of it, and I want it to stop there. I mainly need suggestions on what stepper motor would be capable of lifting that much weight, as well as what driver to use and any other bits I need. I wouldn't mind help with the code which I am sure I can make up myself as I am learning and I've done a little coding but yeah I mainly need help with the items needed for it. I believe I would need a Nema 23 Stepper motor but correct me if I'm wrong.

The required torque will be at least 5 lbs time the length of the arm from pivot point to center of the ball. That would be the torque in inch-pounds. You can convert to any other units you want.

A gear motor will be more efficient and probably higher torque.

If a gear motor would start and stop at specific positions without the assistance of end stop switches or whatever I possibly would consider one. But as such with Stepper motors being fairly strong depending on the one you get, as well as they moving from point A to point B precisely I would prefer to use a strong enough stepper motor.

So if I understand correctly, I need a motor that is capable of 5lbs per inch for a total amount of the length of the arm and the center of the ball. I found a 3N.m Stepper which converts to 21.24 In lbs, so I could lift something 4.248lbs at 5 inches max length correct or?

Yes, the math seems correct. Remember, you also need to have a strong structure to attach the motor to.

For the structure, I will be fabricating one out of steel plate that the motor will be mounted to, and that steel plate will be mounted to wood, probably a 2x4 that is connected to the lane itself. Do you know what driver I would need for a Nema 23 Stepper motor, I saw the TB6600 Would that suffice or is there a different one I would need?

Since only you know the motor specifications, you will have to decide.

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