# Help understanding decoupled inverse kinematics

I've been researching decoupled inverse kinematics with respect to industrial robots. The assumptions made in the decoupled equations greatly simply the equations, however I am having a hard time understanding how these are actually applied once a tool is attached to the robot.

According to one source, "The spherical wrist assumption makes the position of the wrist center point is independent on the end-effector orientation."

This is great since many industrial robots are built this way, but what happens once you attach a tool, say a MIG welding gun? The length of the tool creates an offset from the wrist center which then makes it such that the position of the wrist center IS influenced by the orientation of the end effector. All of the derivations of inverse kinematics using decoupled equations stop at J6 and do not include a tool frame. To me, this really causes a issue? Am I missing something here?lop

## 1 Answer

An End-Of-Arm-Tooling (EoAT) is simply a hard-coded frame transform offset form the real-robot ee. It does not change the inverse kinematics equations for the 6R robot. You just need to make sure you correctly define the transformation matrix so that you don't run into any issues. Just before you calculate the IK, you apply the inverse of the frame transform offset given by the EAoT and then you are good to go. The math does not get any more complicated than a single extra math operation.

• OK, so this is making a little more sense. You use the decoupled equations to first solve T [0->6] then you can add in a work offset frame and a EoAT frame after the fact? So then you end up with inverse kinematics that give T [work -> 0 -> 6 -> EoAT]. Aug 14, 2019 at 15:28
• Yes The IK solves T0-6 and then the EAoT frame is T6-7, which is a constant frame that you already know I suggest you try this out with Matlab it makes this sort of thing super easy to implement Aug 14, 2019 at 17:22
• First use the EoAT transformation, and task requirements, to define where the position of the wrist center needs to be. This lets you compute the first three joint angles. Use these values to find the final three joint angles. Aug 14, 2019 at 18:30