Move Player smoothly on animated model?

So I’ve got a building model which is attached with a weld constraint to a platform underneath. The platform is being moved by a prismatic constraint. The player can walk around smoothly on models that are welded to the platform, however, if a building model has been set up for animation, where basically the building falls over, then the players on that building tend to stutter a bit when they are on it and walking on it.
So generally if a player is on a model that has been rigged for animation, can they ride on it smoothly without stutter or not?

the only way I can think is by renderstepped, move the player only on the x and z axis (unless the platforms going up) to the moving platform, although I just woke up and I can’t think straight lol