How to climb up when hanging in the Female Ward chapter?

I am in the part where you have to hang down from some broken planks and move sideways, hand by hand. That itself wasn't explained in the game, I found out by accident that this is even possible.

Where I was:

I just walked through the dark room from which two club wearing cannibals come after you. The next room had completely destroyed floor, leaving only few planks to walk on. According to the walkthrough, it's the room where you lose your camera once you get through it.

What I did:

• First I thought I am supposed to walk on planks, leaning to the wall, as usual.
• When I tried that, I always fell. One time, instead of falling down I ended hanging from those planks.
• I found out that I can move in both directions while hanging down.
• I moved to desired location but couldn't get myself up

Now as I hang down, how to climb up on the platform to my left?