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enter image description here

The figure shows an articulated arm kinematic model having 3 degrees of 
freedom.**Theta** represents **joint angle**, **d** represents **joint 
distance**, **alpha** represents **link twist angle** and **a** represents 
**link length**
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There is no unique DH parametrization but a couple of variations of DH parametrization out there in textbooks. Basically they all agree on the systematic way to describe the "center" of robots but diverge on the way the base and end-effector are treated. This is because often the the simplest mathematical representation of the representation (i.e. with the less frame and parameters) is not matching the more intuitive one for the user/application.

For you given example, I think you got confused as of where the frames for the DH parametrization are lying on the robot. Based on your table the center point of frame 0 and 1 are the same (which do not appear in your drawing). Then in your drawing you seem to have chosen to put the frame 3 at the end-effector, which makes logically the distance a3 appear, another solution would have been to have the center of frame 3 located on joint 3, then a3 should not appear in your DH table. The later solution is valid but less intuitive in my view (e.g. if you start to think about reaching location in space with your robot it's more intuitive to consider the end-effector than the joint 3 position to describe it)

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