I working on a horizontal industrial robot with a three links and all joints are rotational Joints. As a result of that there are some coupling parts to connect between the joints. My question about the inertia of these parts usually how I can calculate them and then is these inertia added to the inertia of the previous link or in the next link, because I'd like to find the dynamical equations for the robot and I must calculate the inertia for each joint in the center of gravity.
Inertia is calculated with respect to a certain axis. If there are two long cylindrical joints (like a human hand), both cylinders will have the same MOI with respect the joint next to them BUT before adding them you must add an additional part coming from the fact that the second cylinder is displaced and is also rotating with respect to an axis far from its own axis of rotation. Parallel and Perpendicular axes theorems help you in calculating them. Check any dynamics text or wikipedia for details.
Traditionally the way this is handled is by obtaining the minimal (aka base) inertial parameters as opposed to the standard inertial parameters.
There are 10 standard inertial parameters for a single free body, and they include mass (1), center of mass (3), and the second moment of inertia (6). For two bodies connected by a joint, there would be 20 standard inertia parameters. However, the joint causes these inertia parameters to be coupled, and as a result it is impossible to measure all 20 standard inertia parameters through outside measurements without disconnecting the two bodies.
Instead, you can compute the minimal/base inertial parameters through sensor measurement, and these base parameters are sufficient to compute the entire manipulator's dynamics. There are many methods for computing base inertial parameters; I would recommend using Google Scholar to find some articles about it. For a 3-link arm, I would recommend symbolic methods, especially if you have the arm represented in terms of D-H parameters.
For the 2nd part of your question regarding which link does the coupling belong to, this depends on which link the coupling is rigidly attached with.
If my understanding of your question is correct, you have a coupling between a motor shaft and a link shaft. That mass of coupling will rotate rigidly with only one of the two links. This is probably the 'next link' if your motor is mounted rigidly on the 'previous link'. Even if you have a passive manipulator (not actuated), the coupling will still rotate rigidly with only one of the link. The dynamics of a link should include anything that is rigidly attached to it.
All the best.
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