Is it permissible to bow down to grasp one's mother's or father's hand and kiss it, and to kiss their feet?

If the bowing is for the purpose of extending the hand and grasping it, there is no objection, as it is a customary movement to take something. However, if the bowing is in the meaning of rukūʿ (prostration), then it is not permissible. It is permissible to kiss the hands and feet of parents as a sign of honor to them.