Number of links and joints in a linkage

[influx]

Homework Statement

Homework Equations

M = 3(L – 1) – 2J

L= number of links, J = number of joints

The Attempt at a Solution

As far as I can see, using the above L and J values for each linkage yields the correct M value. However, the L and J values lead me to think I'm missing something.

Can someone explain why L = 4 for the first and second linkages? In the first one there are only 3 links and in the second linkage there are only 2 links. Also, surely for the second one J = 3 since there are only 3 visible joints?

Similarly, why does L = 5 for the bottom left linkage when there are only 4 links and why does L = 4 and J = 3 for the bottom right linkage when there are only 2 links and only 2 joints?

 

[haruspex]

Can someone explain why L = 4 for the first and second linkages? In the first one there are only 3 links and in the second linkage there are only 2 links. Also, surely for the second one J = 3 since there are only 3 visible joints?

Similarly, why does L = 5 for the bottom left linkage when there are only 4 links and why does L = 4 and J = 3 for the bottom right linkage when there are only 2 links and only 2 joints?

In the first three, there is effectively a link between the two fixed platforms. The distance between them cannot change.
The last one has three joints: one at the base, the slider itself, and a third at the top of the slider.
I don't see a fourth link, but I know nothing of this subject so could be missing something.