# Screw based Jacobian transformation

The mechanism shown on the picture has prismatic, revolute and spherical joints in order and I derived the screw based Jacobian in local frame $$B_i$$, for the isolated leg. The isolated leg coordinate frame is located at $$B$$ and it is a copy of frame $$O$$.The leg is assumed to have a center of End-effector at $$A_i$$. Now, I suppose to transform the Jacobian to O' and O. and I am confused. Can anyone help me, please? Here is the form HMT used to drive Jacobian $$H^B_1H^1_A$$, which is from $$B_i$$ to $$A_i$$ and the $$\\ Ad_g=\begin{bmatrix}R&[P]_xR\\0&R\end{bmatrix}$$ is the matrix I used to premultiply the Jacobian. But what I make me confused is the path to transforming the given Jacobian to frame $$O$$ and $$O'$$.