vuforia how do I force objects into a 2D plane

vuforia how do I force objects into a 2D plane

I'm working on a game in which cards are placed on a table and then rendered in augmented reality. These objects have 3D physics attached to them which doesn't work as well if they are either rotated or if the system mistakes them for being higher or lower then they really are. 
Is there a good method to force Vuforia/Unity to place all items in the same 2D plane and keep all of them upright compared to that plane? 
I currently have the following code:
using UnityEngine;
using System.Collections;

public class projectioncode : MonoBehaviour {
    Vector3 p1;
    Vector3 p2;
    Vector3 p3;
    Vector3 v1;
    Vector3 v2;
    Vector3 normal;    

     *use a plane with the following 3 coordinates 
    public void setPlaneByPoints(Vector3 point1,Vector3 point2, Vector3 point3){
        p1 = point1;
        p2 = point2;
        p3 = point3;


    public Transform projectTransform(Transform input){
        input.position = projectPoint (input.position);
        return input;
     *  projects a 3d point into space; 
    Vector3 projectPoint(Vector3 point){
        Vector3 vOToPoint = point - p1;//vector between origin and point 
        float dist = Vector3.Dot (vOToPoint, normal); //distance plane to point 
        return point - dist * normal;

     * caclulates the normal of 2 vectors
    Vector3 getNormal(Vector3 v1,Vector3 v2){
        Vector3 res= (Vector3.Cross (v1, v2));
        return res;

This seems to project objects onto a plane but the results tend to be inaccurate and result in weird movements, particularly when moving the camera around. 
This is what it looks like: 


Answer 1:

I manage to get this to work by separating the target and the model so that the model is NOT a child of the target in the scene. I let Vuforia handle the calculation of where the target is located, and then created a script to calculate the transform of the model based upon the transform of the target. In this script, I forced the y-position, x-rotation, and z-rotation to zero.

Note: This script assumes the xz-plane is aligned with the tabletop. You could also determine this by placing a “stationary target” on the tabletop and setting everything in the scene relative to the x and z components of the stationary target’s transform.

using UnityEngine;
using System.Collections;

public class VuforiaFixToPlane : MonoBehaviour  {
    public Transform target;

    private Rigidbody rb;

    void Start()  {
        rb = GetComponent<Rigidbody>();

    void FixedUpdate()  {
        Vector3 positionInPlane = target.position;
        positionInPlane.y = 0.0f;
        rb.position = positionInPlane;

        Vector3 rotInPlane = target.rotation.eulerAngles;
        rotInPlane.x = 0.0f;
        rotInPlane.z = 0.0f;
        rb.rotation = Quaternion.Euler(rotInPlane);

Answer 2:

you can “lock” the axis for a rigidbody so it cannot move/rotate/whatever around/along specific axis. Check the inspector options for the rigidbody component.