# Finding the relative pose of a robot gripper

I have a robot arm with a gripper. I know the gripper pose (relative to the robot base coordinate system) at any moment. At startup, I record the pose of the gripper and set this as the original pose `O`

. Then, the gripper moves to its new pose `N`

, again in the robot base coordinate system. What I want to calculate, is `R`

, the relative pose of the gripper *in the coordinate system of the original pose* `O`

, rather than in the coordinate system of the robot base, which would just be `N`

.

So, `O`

= original pose, `N`

= new pose, `R`

= relative pose

From my calculations:

`O`

* `R`

= `N`

Therefore:

`R`

= `O^-1`

* `N`

However, from my observations, `R`

is the pose of the hand relative to the original pose, but in the coordinate system of the robot base. I want it to be in the coordinate system of the original pose. How do I get this?