@WhitewaterWoman
The "spoked" fitting in my sink looks like
@Outdated 's except that there's a large screw on the center which is used to tighten/loosen it.
These systems are homeowner-friendly, but you need to have practiced a little so you can figure out the particular system you're working with "on sight". It only takes one small project to get that skill, but you're in the middle of your first one and it may still feel difficult.
Some things to think about for "under-sink" work:
* Those big plastic pipes are all very low pressure OFC - the water won't go uphill (unless you use a hose with some pressure to clean it /lol). That's why the open pipe from the dishwasher doesn't have to be capped.
* Drains smell bad - the "U- and S-shaped" parts (which "always" have water in them) stop the smell coming back up from the drains. If you remove/replace one, have something ready to block the drain side (easy to improvise)
* Screw threads leak (**) but they're very effective and reliable for holding things together. So seals are achieved via some form of compression between suitable surfaces. This is why there sometimes seem to be one or two extra parts in the joints.
* Pay attention to where the gaskets (if any) were when you disassemble. You can figure it out later OFC, but the first time it's easier to take pictures. It will all make sense when you reassemble, so you probably won't have to take pix next time you do this.
Here's how it works, so you can figure yours out:
* There are different ways to achieve a seal at the top (between the sink and the pipe). Those I've seen are based on sealing between the layers by drawing the "spoked" part in the sink and the top of the pipe together - i.e. something is needed to apply force vertically from above the sink to below the sink, with the sink itself a stationary "framework".
* The natural way to do this is via a "nut and bolt" kind of setup, but I'm sure there are others.
* Gaskets (rubber, plastic, etc) are soft enough to fill the gaps when they're squeezed, and also mean you don't need precision-.manufactured parts. They're not always needed though (see below).
* There's more than one way to do this - mine isn't the same as
@Outdated's, and yours may be different to both.
* The other plastic-to-plastic connections in the pipe system use the same principles, but what's applying force are big plastic rings with inner threads. They grip the pipe (e.g. press on an integrated collar) and squeeze the end of the pipe against a gasket to seal the joint.
* You can see which short pipe sections have threaded ends and which have collars in your picture by the direction of the threaded rings.
I took my kitchen sink apart (only 5 min - I have a suitable screwdriver in the kitchen), and it works like this:
* The "spoked part" in the sink and the sink itself have exactly matching "conic section" shapes where they touch
* There's a special pipe-to-sink connector part on top of the pipe. The part in contact with the sink has the same/matching shape
* It seals by pulling the pipe part up to the "spoked" metal part in the sink via a screw (the "bolt") that's integrated into the "spoked sink part"
* There's a threaded metal element integrated into the "top-of-pipe" connector (inner thread, so it works like a nut).
* The seal doesn't need a gasket - all three parts are matched in shape and size, and the plastic can deform a little so make the seal tight.
* NB: screw threads are like a ramp wrapped around a cylinder - you get a lot of leverage from a fine thread.
The downside of my system is the need for standardized parts (three components must match
exactly: sink, spoked part, top of the pipe). The upside is that you don't need gaskets so it's faster and easier to work with. Not so good if you can't replace all the parts though - at that point, one failure and you need a new sink.
A more generic system (where the only hard standard is the approximate size of the (unthreaded) hole in the sink) would use one or two gaskets.
(**)
Just for completeness, it's possible to seal screw threads if you need to, and there may be modern uses for this method. It's a PITA though: you have to wrap special thread (thin line) around the screw thread, and it's probably tricky to tighten the screw. Gaskets and O-rings are much easier.