Correct Explanation of Yaw, Pitch, and Roll Euler Angles with Rotation Matrices and Python Code

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In this robotics and aerospace tutorial, we explain one very important topic for properly understanding the kinematics and dynamics of rigid bodies. We explain the concept of roll-pitch-yaw Euler angles. In particular, we explain the so-called Z-Y-X Euler angle convention. We will first graphically explain the yaw-pitch-roll Euler angles, and then we will derive the expression for rotation matrices and direction cosine matrices that are the consequence of Euler rotations. We will also present the Python code that can be used to compute the direction cosine matrix of the associated Euler rotations.