Are we still debating the validity of the sentence that says  does not require equal angles between the input shaft axis and the joint and output shaft axis and the joint to maintain constant velocity The basic geometry of the double cardan is identical with or without the centering element and is identical whether the intermediate coupling is a short shaft long shaft or yolk as in the case of the joint  the references provide sufficient information to make this clear  no more references are required  the whole point of a centering element with a DC joint is to fix the differential angle problemCorrect me if Im wrong but I gather youve have been assuming all along that the double cardan must include a centering element while I have assumed the more general case and this is why youve been challenging the validity of some aspects of the articleWhat is your view of my previous post or are we close to reaching an agreement