Player Grab Mechanic

I was wondering if anybody had ideas to go about a grab mechanic for my game. The main mechanic will allow for the player to grab certain parts of the environment and hang/swing from them. Similar to games like little big planet 3 or human fall flat where you can basically attach your hand to a piece of the world and physics will continue as if you were part of that object (I just need the entire character to attach).

I have already programmed this in a way, but when released from the object, the character just stops all previous physics and falls straight down normally. I was not sure if something like a physics handle on a socket could attach?

If anyone has any ideas or feedback I am open to try anything. I cannot figure this out.