Player twitches when moving on the elevator

I have an elevator, which moves by a simple animation. When player moves on it, he are twitches like in the video on 0:22. How can I fix this?

![90040-124599-1489496795-1.jpg|1022x588](upload://6fh0n2o1ffRjJrg1ZcoJt0B8ByY.jpeg)

90041-124600-1489496915-2.jpg

When the player (or any object really) is on an elevator (or moving platform) I think one of the best practices is to parent that object to the elevator/platform.