Is this derailleur pivot point suppose to side-to-side move this much?
 

I'm have a 6 speed ebike and having trouble shifting from 5th to 6th and 6th to 5th. I've already done all the adjusting of the H/L limit screws and indexing the gears with the barrel adjuster. This part of the derailleur has what I think is a lot of lateral movement https://i.imgur.com/PgmMiAfl.jpg. I'm hoping if someone can tell me if this is normal or needs replaced.

Here is a brief video https://i.imgur.com/1TUSQs7.mp4 (I hope this is viewable or let me know how else I can post a video/gif). The movement you see is completely from that pivot point circled in the 1st picture. It is not the result of pushing on the derailleur springs.

Some clarification is needed. Is the body of the derailleur moving in and out with respect to the hanger which is attached to the frame?

Or
is the hanger itself moving because it's not securely attached to the frame?

The first one if I'm understanding you correctly. The hanger is secure and straight. The derailleur body is what's moving away from the red circle, which should only rotate up and down but not side to side I don't think. Here's another angle of that pivot point I'm talking about. The bolt next to it is what connects to the hanger, which feels solid, although that plastic washer/spacer looks broken.
https://i.imgur.com/hT8Ybsrl.jpg

https://i.imgur.com/raWzd9Bl.jpg

It may be normal for that derailer or not, but it's hard to say without a video or other evidence. That is a very low-end derailer from Shimano and it could be that that model just does have a lot of "play" in the mounting hardware. An upgrade to an Altus RD-M310 or Acera RD-M360 would be a good move if you do determine this one to have too much lateral movement.

Oh I guess the original link to the video didn't work. Can you see if this works? https://i.imgur.com/1TUSQs7.mp4

It works.

I wouldn't invest much into the bike that derailleur is pretty much designed to be as cheap as possible and if it came spec'd on the bike from a factory you can imagine the rest of the bike is lacking. More than likely the play is pretty normal for that derailleur all the similar odd ball tourney derailleurs tend have a lot of play and slop but you do get what you pay for on that front. Saving a buck or two in the short term tends to cost more in the long term.

Derailers aren’t supposed to move that much. That derailer is going to move that much because it is a really poor design and poorly built. If you haven’t purchased the bike yet, run away!!! If you have purchased the bike, do yourself a favor and find an Altus rear derailer. It’ll be the best $25 you can spend on that bike.

Maybe it is, maybe it isn't supposed to move that much. But if it isn't causing you any issues why worry? Wait till it starts causing issues and just keep an eye on it. Unless you find out there is some way to snug it up.

From the first sentence of his first post:

Might not be the cause of the shifting issues. Might just be the first thing that seemed odd and they stopped investigating.

Maybe. Looks pretty sloppy to me, but often times that slop is built in.

The slop in Tourney derailers is a very large contributor to the problem. They just can’t be tuned properly because they move too much.

That might be true. However in the video the bike was moving so much every time the OP pulled and pushed on the DR that I couldn't tell if the joint was moving or just the bike. And if the OP was having to use enough force to move the bike that much then it may have made even the entire DR flex some.

You can see the derailleur moving relative to the bike, even if the bike is moving too.

You can clearly see the B knuckle (or what passes for the B knuckle in this derailer) move in and out as JohnSnoh pulls on it. This is a very common problem with the Tourney derailers. That part should not have any lateral movement at all. Since it does in the Tourneys, they can’t really be adjusted to the level of precision needed for indexed shifting.

Oddly, there are different levels of Tourney. The OEM ones are the ones to have this kind of movement. The $15 aftermarket ones are stiffer. I wouldn’t use one nor would I leave one on a bike that I’m refurbishing but at least they shift better.

I didn't clearly see it. For me there was too much other movement going on.

But I do agree in general with your statements on the DR and it's OEM version if there is such.

Look at the area that JohnSnoh marked in red in post 3. Try to ignore the bike moving. With a proper derailer, the only movement you should see is the frame moving. The derailer body will be rock solid.

I don't mean to offend you, but why do you feel you have to prove this to me?

I'm just offering a different viewpoint and it's up to the OP do decide if any replies here are useful for the problem they have. I don't think that we all have to agree.

I did get a good deal on the ebike so I figure I give it a shot. I have another bike with an Altus rear derailleur and there's no such lateral movements on that one so I might just as well upgrade this Tourney to an Altus if this isn't fixable. I just wasn't sure if this is normal on a budget derailleur like this.

It might seem like the frame is moving but it's only the camera that's moving since I'm holding it and having to move the derailleur at the same time. The bike frame is not moving. It is mounted on a bike stand. So the only movement you see is the derailleur. With that said, I've done as all the adjustments I can and the best I could get is a very slow shift between 5th and 6th. Otherwise, it would just not shift at all.

Not trying to “prove anything”. Just trying to offer a way to see the movement in the derailer body. I can easily see the body move even with the bike moving slightly. I’ve seen this in person before and that may be why the movement is more obvious to me.