It might seem obvious that a true uni-pivot arm has only one pivot point. In one sense that is true, as an arm may have one pivot when it is floating with no vertical tracking force (VTF), but in use the arm cartridge combination has two pivots because the stylus is the other one. So the arm is really a uni-axis system, pivoting along the line joining the pivot and stylus. This axis can move freely in all planes. However, uni-pivot is what we are stuck with.
And that's when things get more complicated because a lot of people would prefer a uni-pivot to be a bit more like a "normal" tonearm. While usually admitting the freedom of movement is great and the stylus can then do its thing, the freedom for the axis to rotate makes people edgy for various reasons, mainly that "normal" tonearms don't do that.
Adding anti-skate at anywhere not on the stylus/pivot axis will reduce the rotational tendency, by providing a contraint on movement. And adding a device in the form of an auxiliary bearing or a sliding surface will do the same, as will adding damping. Some uni-pivots have filaments to constrain movement in the rotational frame, and some have the pivot point at an angle or even horizontal with devices to retain them in place.
None of these are uni-pivots. In reality they are constrained bearing designs like "normal" tonearms, able to move only in the horizontal or vertical plane. They use various methods to allow that movement while controlling (that is, constraining) rotational movement.
In other words, just like any gimbal arm does, often using similar types of cup and cone bearing to the traditional uni-pivot. If a traditional gimbal bearing arm had an an extra set of bearings to allow rotation of the armtube and cartridge, it would be a unipivot if all the bearing axes coincided.
The bottom line is: if a uni-pivot can't rotate on its stylus to pivot axis, it's not a uni-pivot. It actually has a number of extra bearing surfaces, sometimes four or more. But as long as there's a big and obvious sharp point that's usually enough for the publicity material.
