Rich,
By the looks of it you got somewhat confused, and mixed up the techniques of ‘shaken by the head’ and ‘pulled by the tail’. That’s obvious the reason why you get the feeling your “ joints keep falling apart”.
In the model you send me the position of the pivots of all the objects is perfectly fitted for them to function I a ‘pulled by the tail’ structure. On the other hand is the top to bottom structure of the chain suited for a ‘shaken by the head’.
Your device is clearly a basic Inverse Kinematic structure, similar to a robot arm. Such is by default a ‘pulled by the tail’ system.
So in the model “Delivery Unit And Arms 001.3dm” I reversed the entire Hierarchy hence making “Tray Point” the end (the tail) of the chain instead of the head. No pivots were relocated, no joints redefined. For “Tray” the Simple Constraint was omitted since no constraint was defined.

The objects “Chair Post Point”, “Chair Arm Connector Point”, “DU Arm Connector Point” and “DU Tray point “ are superfluous – they were simply deleted.
Then I made “Chair Post” a Hing Z, and IK-constrained “Tray Point” to “Path Point”… and bingo, no more joints falling apart.
Remains the matter of “DU Arm”. I guess it is not the intention to let it rotate along its Y axis?
Its shape suggests that the link is meant to shift up and down, hence allowing the tray to follow the variation in height of its path. And I suppose the same goes for “DU Connector”.
So by means of illustration, in model 002 both objects are made a Telescopic Joint Z. Apparently the height of the tray varies too much for the arm to deal with?!
Both models are available at https://we.tl/t-lSJXg5hawU
Luc
PS.
- The topic of ‘shaken by the head’ versus ‘pulled by the tail’ is explained in my video Whys of IK in Bongo 2.0 - YouTube (minute 6:25 till 10:40). Here are the concerning models Haeds and tails.3dm (517.2 KB) Why 05 end.3dm (184.6 KB) .
- I’ll deal with your Cone, Tube and Filter issue later
:.