Imagine a central axis that contains the machinery that powers the ride. A number of spokes (say, four for the purpose of this thread) emanate out from the central axis. At then end of each spoke is another central axis around which the ride vehicles spin. So as the ride moves, riders are spun in smaller circles within a bigger one. Also, the spokes move up and down vertically.
What is this called?
A Jump and Smile?
The Cyclone variant of the Scrambler?
Or an Octopus?
I know the same basic concept under the name of Breakdance, but there the axes for the smaller circles sit on a rotating plate rather than arms.
I think the Scrambler is closest to what I’m thinking of.
Circles within circles could be the teacups:
Worked carnivals in the past, and very few rides have ever had only one name.
I rode one of those at a state fair. It was the Black Widow. It had appropriate paint and decoration.
Man I hated that thing. Dreamed about it for weeks, afterwards.
Scramblers I have ridden do not have arms that move up and down. Octopus/Monster like in @hogarth ’s post does have arms that move up and down but also have cars that spin on their axes. They also have to be loaded/unloaded in two stages, since when half the arms are in the bottom position the other half are in the top position.
This is key to the last time I rode one of the torture devices. Mrs. Martian (well before she was Mrs. Martian) had a summer job at Dorney Park. I went to see her and, since the park was slow, they gave her the afternoon off and a couple of all-day ride passes. When we got on the monster, the operator (who of course knew Mrs. Martian) would not let us off for at least six or seven rides. Seemed like an hour. Haven’t been on one since. I’ll do any roller coaster in the world, but no more circle rides.
My experience on the Octopus:
I went with a friend to the local fair (on a hot day) and we went extra early to get an “early bird” price on entry. Since there weren’t many customers, the operator of the Octopus “treated” us to an extra-long version of the ride. By the time I got off, I felt nauseous and my extremities felt numb; I’m guessing it was sunstroke combined with being spun around and around. Fun times!
It lacks what I’d call spokes but the Zipper has the spin within the spin. The cars are are free to rotate and a coordinated team could rock it into a spin while the ride was otherwise off for loading.
At Kennywood Park in Pittsburgh it was called the Monongahela Monster but I’ve also heard it called the Spider.
Me in a nutshell!
I’ve seen that ride! Better be a pretty large nutshell. 
A similar but slightly tamer ride is the Tilt-a-Whirl.
That’s the name that I know those types of rides as.
I’ll take the octopus over the scrambler or tilt-a-whirl any time. The latter two jerk me around too much; the movement of octopi I’ve ridden has been much smoother.
We call them generically “The Hurler”.
[Insert barfy emoji]