How to make player climb a physics-driven chain?

I have a chain which is made of several 2D rigidbodies stitched together with hinge joints (as shown below). I want to make it so the player can climb this rope up and down, but also stay attached to it if it starts swinging back and forth. Does anyone know the best way to go about doing this?

Thanks for the help!

(I wasn't sure if this should go in 2D or scripting, so I just posted in both)

 

pos.y = Mathf.Lerp(prevLink.y, nextLink.y, climbPos);

When climbPos>1 and going up, change prev and next link then set climbPos = 0.
When climbPos<1 and going down, change prev and next link then set climbPos = 1.

And for x:

pos.x = Mathf.Lerp(prevLink.x, nextLink.x, 0.5f);


Something like that. This way, no matter how violent the motion, the player is always averaged between two segments in the rope, and the player's climbing is controlled by adding or subtracting climbPos. For example: climbPos += GetAxis("Vertical");

In any case, this is just one approach you can think about and learn from - using tweening or lerping to go between two points in a reliable manner. It's reliable because you're not relying on physics or collisions, but on a single number - climbPos.