Help with little idea

I am hoping to create something that will speed me up a bit in my very niche business (sadly no commercial value) and am stuck as to what I would need to do this. I’m wondering if anyone out there might be able to help. Basically I have a 16cm length that I need to bring a hook across in timed intervals. So, it would move 2cm every 20 seconds or I could change it to move every 30 seconds. I’m picturing some sort of pulley with the hook attached that is connected to a motor that moves the pulley via a timer of sort. Any chance anyone knows what I need to be searching for in order to make this? Or better still if someone knows something similar that’s already out there that I could just adapt?

there are many ways to do what you want to do
please watch the video its called linear actuator it has maximum 200mm length you can make it stop at 16 cm and limit speed to 1 cm per 10 sec . that’s it .

you will need a small programmed to drive and control this actuator.

massage me if you need more help .

stepper motor driving a gear on a rack and pinion?