I want to open up a whole new thread to talk about Kinematics and its principles applied to Hexapods (Crustcrawler, Phoenix, *H3-R, etc.). This thread is aimed more mathematics and not the modeling of it in software. Although, if you want to express your point of view with software, it's ok as well...

My first question I want to throw out there, perhaps for those of you who are gurus in kinematics, can help me understand it better:

Given a successive rotation about all three of the axis in three-space, how do you truly determine which is of the 6 is the correct order to use?

For instance:

B = matrix for a successive rotation

Ay,beta = rotation matrix of angle beta about the y-axis

Ax,gamma = rotation matrix of angle g about the x-axis

Az,alpha = rotation matrix of angle alpha about the z-axis

So

B = Ay,beta * Ax,gamma * Az,alpha

Euler proved that twelve independent triple rotation can be had for any combination of alpha, beta, and gamma with any of the three axis... So essentially, there's a total of 12 different "B" matrices depending on the order of rotation...

Each of the twelve combination yields a different matrix. When do we know which order to use for say, hexapod? Perhaps I just don't understand when to use which order...

## Bookmarks