Why would you want to design your own u-joints? These are standard parts widely available. Like rolling element bearings, they are comodities. Unless you are designing something really big, such as propshafts for 100 ton mine haul trucks.
I don't have so much knowledge about designing of cardan shafts. When an engineer are responsible for initial designing or choosing the right pieces like diameter of shaft tube or universal joint, i think there should be some mathematical correlations and theoretical aspects. I just want to learn the basic principles. When a customer come to me and say I design a new truck, a new differential, new motor ? should be able to do design the new complete cardan shaft.
I recommend a book from F. Duditza "Cardan joints". Originally written in roumenian, a french translation has been published also by Eyrolles. It's classical and excellent source for people seriously involved in the design of cardan joints. If you are interested in equations and modeling, fatigue analysis you may wish to download the following paper:
Hi, you may find useful the following links. Manuals on the design of cardan joints are scarce. I recommend the book of Wagner (Published by SAE) and a book by Duditza. This last book was originally written in roumenian, but there is a french translation by Eyrolles. Although little known by American engineers, it's an outstanding contribution to the design of Cardan joints.
Sincerely,
Ettore