If you really need education in math and how to properly do trigonometry I will help you solve this problem for free. Just ask me questions. I'm super nice and won't go around fraudulently espousing an expertise in math and demanding people pay me to solve trivial math problems.

Frankly you are not even qualified to solve the problem yourself or give me a recommendation.

Especially when this problem is basically impossible to solve. I'll give you 10 thousand dollars if you can give me a quaternion that doesn't have multiple yprs here on HN. Literally, give me your venmo.

>Nope. The only thing you need to specify is the order the YPR angles are applied (that more a convention than an assumption). In SolveSpace the assembly constraints would effectively encode the order of application.

The term "yaw pitch roll" ALREADY has the order of the Euler angles applied. Let me tell you that order, it's: yaw, pitch and then roll.

Ypr is different from straight up Euler angles in that ypr has order fixed; hence the term "ypr"

With the order of angles fixed you still get multiple answers for a single quaternion. Why don't you try it in 3D space in your own head. Given A rotational orientation in 3D, find at least two yprs needed to arrive there.

Here maybe this will help you: a ypr of (0,0,0) is the same as a ypr of (180, 180, 180). These two yprs can only be represented by a single quat. Think about it. Given only a quat you cannot determine which ypr was used by the physical gimbal to realize this orientation. For solve space to know it must be making assumptions or holding onto information outside of the quat.

There free education for you and I didn't even ask you for a dime.