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I'm using modified denavit hartenberg to represent my robot end-effector. But i couldnt find equation to calculate rpy if im using mdh. Below my MDH.
I try use rpy equation for dh paramater(from Getting pitch, yaw and roll from Rotation Matrix in DH Parameter), but when i apply it doesnt seem correct. Does anyone know the correct equations? I'd be very thankful for any help.
The orientation of the end-effector is obtained by multiplying together the MDH homogeneous transformation matrices for each of the joints. There are well known algorithms and code implementations to extract roll, pitch, yaw angles from such a homogeneous transformation matrix. You need to be careful about how you define roll, pitch and yaw angles, there are multiple conventions which is frustrating and confusing to those entering the field.
It doesn't seem particularly useful to go directly from MDH parameters to RPY angles, since in general a robot has more than one joint.
However, if you did want to go this path, then just looking at the expression we see that the orientation is a rotation about the x-axis of $\alpha$ followed by a rotation about the z-axis of $\theta$. The XYZ RPY convention, often used for problems with robot manipulator arms, is defined as an SO(3) rotation $R = R_x(y) R_y( p) R_z( r)$ so it is clear that $\alpha$ is the yaw angle, $\theta$ is the roll angle, and pitch angle is always 0.
