Back and forth rail mechanism

Hello, I am looking to move forward with an idea I have to help me out with my current job. I do need to assemble it and Im looking to get a prototype made as I can not find it in stores. I am not a very experienced fellow when it comes to DIY projects and the terminology with it which has made it difficult to find what I am looking for, but ill give it my best. I appreciate the help and I will be as descriptive as possible. Also looking for the Cheapest (since its a prototype). So if some of the features and functions I am asking for cost a lot more then it doesn't need to be added (If mentioned that it inst a must). I am open to change from others creativity/versions as It may/probably is better. Lol.....

So I am looking for a, what I like to call, a "back and forth" mechanism. I do need this mechanism to be automatic. Whether it is a switch or a remote control. I need the power of it to be at a semi slow pace ( like rocking a baby). Not a must, but would be cool to be able to change up the speed/direction. I need the system to be strong enough to where if the attachment brushes against something, It will continue in its direction and not stop. As seen in the diagram, for the part/tip that is moving back and forth I would like to be able to have a hole/clip/attachment piece where I can put different veriations of other parts on there (attachment pieces are not heavy at all). I would like the back and forth rail to be about 2-3 ft. Long.

Also, Here is the second Diagram. This is the top/Outside view of it. I want to be able to have it standing up and not have weight distribution be an issue. I am not sure how heavy the rail system is going to come out to be. But as seen in Diagram #2 with the base holding it up. I do need to to be able to support it while on. ( Maybe I can figure out myself how to find something to hold it up.) Not a must, but it would be cool, if the base/arm in diagram two is able to collapse taller or shorter.

So it is a pretty basic gantry system. I do think it does seem like I am looking for a CNC type machine (someone on reddit reccomended) but would like it "dummied" down. But hopefully this makes as much sense to get the job done. Is anyone with me or do I sound like a crazy man on crack? Thanks for all the help/criticism!!