Relationship Between Number of Polar Scissor Units and the angle Needed to Close System


I’m trying to design a script which will enable me to study deployable scissor mechanisms, I am using a definition by @Joseph_Oster as a starting point (requires Anenome). I have studied a few papers describing the geometry of SSM’s but am currently having a hard time trying to figure out how reverse engineer to close the system to allow me to blend between a fully open and fully deployed structure. Any help would be appreciated - I think i’m just lacking the required mathematical knowledge to reverse engineer the initial set up.

File attached, thanks for any help. (21.9 KB)

Here is another attempt however the result is incorrect due to the fact that I have not set up the input angle inputs in a way that they are influenced correctly by changing the parameter t - and therefore as the system closes the point of intersection of the initial members also changes. (27.8 KB)

Are you still stuck with this?

Some thought from me… :thinking:

This is a single, symmetric module:

Note that yellow is the bisector line of blue and black. The angle “B” from that bisector to the vertical (Y axis) is the same to the “B” to the left, wich is half of a “module”.

Angle “C” should be always smaller than 90° otherwise your structure will “stuck” in the “dead centre” once is reached. (or deadlock or standstill… see here )
C=90° is achievable, but you will have to “push” the joins, because near C=90° the movement is no longer reversible.

Once C exceed 90°, B will start to decrease again folding back the structure.
And you should know B= total angle to cover / (number of modules *2) …

C=90° is when B is at his maximum.

I think that one point of to start with is to “fix” the range of C.
C would likely be zero (or almost) for an undeveloped structure.
Its maximum? 90°?

Another point to reason on is: should purple be equal to black and green equal to black?
I’ve found no reason to them not be so; I haven’t found any utility for an asymmetric module… There is some?
You tell me.