Without knowing the details of the system in question, it is difficult to provide specific advise. However, you do have some choices in the replacement of the two bend pulleys and take-up pulley that are typical with a gravity take-up system.
The belt (if it is to be left in place) must be clamped in position -- one clamp on either side of the take-up system-- to prevent belt from moving away from the take-up area. The gravity weight must be secured and disconnected from the take-up trolley.
Once this is done, the take-up pulley can be unbolted and lifted from the belt; and the new pulley positioned. The take-up pulley can then be lifted (crane, chainfall, etc.) so that there is slack in the take-up. Once you have sufficient slack, lift the belt off one of the two bend pulleys and support it, so that the bend pulley can rotate freely. This bend pulley can then be unbolted and swung/slid out from under the belt. The replacement pulley can then be positioned and bolted in pace. Lower the belt so that it is supported by the new pulley and repaet the procedure for the other bend pulley.
Depending on the type of splice, the weight involved, the amount of available belt, and other considerations, it may be preferable to open the belt near the take-up, do the pulley changeouts, rethread the belt, and resplice it. System specifics will dictate which method is most viable.
Although the above sounds easy, you are correct in stating that it can be a rigging nightmare. Too often, system designers or the plant itself make part replacement maintenance difficult by not providing sufficient room to work.
If you have any specific questions, please contact me.
Good luck with your project.
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