Parent Constraints not working on animated Robotic Arm

I implemented a robotic arm assembly scenario, in which user has to collaborate with robot. Now I have animated my robotic arm, in animation robotic has to pick up different small parts and place them on a bigger part. Both robotic arm and other objects are contained under a parent object “Working Cell”, the problem I am facing is that I want that robotic arm should move the objects as if its gripper has held them and for this I have applied the parent constraint on smaller object lets say bearing which has to be assembled, so now in animation robotic arm moves, first the object on which constraints are applied is in active not to show it that it is moving, but as soon as it moves over the part I make object active(mind that during all this parent constraint on the object is always active). When object has to be placed on the bigger part it snaps there. Now problem is sometimes it follows parent constraints accurately sometimes not, sometimes the object follow parent constraints correctly but doesn’t snap instead start flying in the environment, (both is kinematic and gravity is on for rigid body). Attached is the image how my hierarchy looks like. what can be the reason of such unexpected behaviour.