Pentapod CNC joints

Hi guys! 
I've been studying pentapod kinematics recently and I have probably a very stupid question, sorry.
I watched these two videos and it looks like both of these are using the following scheme. There are five gimbals (aka universal joints) attached to a fixed upper frame, then there are five linear joints followed by two revolute joints (also like universal joint). Except for the lower strut -- it has only one revolute joint. 
But watching these videos it looks like the struts are rotating around their own axes themselves! Does it mean that the upper joints are actually spherical? With three rotating degrees of freedom? 
And if they are not spherical, how the tool can actually make all those movements then? Can it really be 5DoF without allowing the struts to rotate around their axes? I've read some research papers about pentapods -- most of them say that pentapods are SPU. But I've also seen a patent that states that their pentapod is UPU.
There's really a mess in my head now. Any help or reading suggestions appreciated. 
Thanks!

These are the videos I've been talking about:

I think I just got it. Seems like the trick here is the usage of non-captive linear actuators mounted to the two-axis gimbals. In such actuators if the strut is not restrained externally then it will just rotate with the motor's nut without linear motion.
So returning to the pentapod -- such external restraint for the struts is the spindle, which actually needs to be moving (and the joints through which the struts are connected to the spindle are also freely rotating around the spindle).
So if the strut must rotate around itself during the positioning of the spindle, it will actually kinda "twist" with the ballnut, rotating and sliding simultaneously to achieve the correct position and orientation around the spindle.
So the upper joint assemblies are actually not pure "spherical", but they allow 3-axis rotations as a side-effect of the usage of non-captive actuators.