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I could imagine a set of counterweights to offset the weight of the assembly as its moving up/down (say Y axis is moving in a vertical fashion). Simple pulley and adjustable weight system, so you can dial in the EOAT weight. Do the machine/Control. It would then seem as normal.
X asis would need testing and not so simple to compensate as the weight would then pull “off” the conduit. Vs pushing down on them.
Z axis would be recommended to mount as to “capture” the weight, meaning the EOAT would be mounted facing up, with the load pressing down into the holder.