Sequenced Bone Movement with IK yet another IK question....
I'm working on an animation project where I have an accordion wall segment that needs to extend outwards, one fold at a time. When I create the the IK bone setup and pull the outermost bone, all of the bones move at once which is not the desired affect. I have played around with animating stiffness values and IK constraints, but nothing is yielding the results I'm looking for. 

Again, the desired affect is that when the accordion unfolds, only one segment will completely unfold at a time, and only when the extended accordion folds are all planar will it pull out another segment. (Bottom image, not top)

Thank you in advance!

 

Thank you AJCDFIN for the awesome help, I though I could take it from where you left it but I cannot.
Here is my solution (Some description): I have 4 horizontal bones(small red one IK_Target), they all have a 'Limit Distance' constraint to each other. Moving IK_TRGT causes the bones to come out one at a time - that gets the action you require. The rest is just 2 sets of bones parented to each other(yellow to purple), yellow bones have IK targeting the purple bone in front of it which is parented to its corresponding larger horizontal bone. I have them all stacked on top each other when built, that can be fixed last to get some offset.Forgot to mention if this rig is going to traverse the Scene it will need a ParentBone to avoid unwanted transforms.
 

DISCLAIMER: This file created in v2.76 - If using 2.7x it will open fine,, If using 2.8x 'APPEND' the objects from the 'Object' folder.