# Math Help - how to find roll, pitch yaw....

1. ## how to find roll, pitch yaw....

given an x,y,z position for the end of an robot arm(end effector), is there any way to find the roll, pitch and yaw for it...Given access to entire history of x-y-z positions. I'll be using IK then to evaluate whether these values are possible or not. All I need to find is just some 'correct' value for them....

any pointers for how to compute the roll-pitch-yaw values....

2. $(x,y,z)$ in cartesian co-ordinates is $(\rho\sin\phi\cos\theta,\rho\sin\phi\sin\theta,\rh o\cos\phi)$ in spherical co-ordinates.

where $\rho$ is the distance of the end of the arm from the origin, $\phi$ is the pitch, and $\theta$ is the yaw. This is assuming your arm is a single straight line pivoting about a fixed origin, in which case, there would be no way to find roll, since a change in roll does not cause a change in (x,y,z) position...the arm just rotates about its central axis, leaving the endpoint in the same position.

What exactly is the setup of your arm? I guess it's more complicated than a single straight line, and you have joints in it.