Link Coordinates

The 2 slides above introduces the 2 D-H parameters, namely the joint distance $d_k$ and joint angle, ${\theta }_k$. Understanding the diagram, we have a center joint $k$, that connects 2 links ($k$ and $k-1$). The joint'a axis, $z_{k-1}$ is defined, along with the link's own axes, $x_{k-1}$ and $x_k$.

Moreover, the D-H parameters, $d_k$ and ${\theta }_k$, behave differently when we have different types of joint. If joint $k$ is a prismatic joint, where the links $k-1$ and $k$ moves in the direction of $z_{k-1}$, joint distance $k$ is variable and the joint angle ${\theta }_k$ is fixed. If the joint $k$ is revolute, then the distance $k$ is fixed since there is no straight line movement along the joint $k$'s axis $z_{k-1}$, but the joint angle ${\theta }_k$ is variable, since we can rotate the links $k-1$ and $k$.

This above slide introduces another few D-H parameters, namely link twist angle, ${\alpha }_k$ and link length, $a_k$.

What the new perspective illustrates is the center link $k$ that has joints $k$ and $k+1$. Joints have their $z_{k-1}$ and $z_k$ axes drawn.