Snake head should be followed by tail like classic snake game

I have made one script but problem is that snake move like rope, i want to make it move like Classic Snake Game. I have used hing joint to attach tail to snake head.

Here is my script:

using UnityEngine;
using System.Collections;

public class snakeHeadMovement : MonoBehaviour 
{
    public float MovementSpeed =5.0f;
    public float TurnSpeed = 20.0f;
    public GameObject TailPrefab, ApplePrefab;
    private GameObject lastChain=null;
    private float moveSpeed = 1.7f;
    private int counter = 0;
    public int Score = 0, Lives = 3;

    void snake_addTail() 
    {

       if(lastChain == null)
       lastChain = gameObject;

        GameObject newChain  = (GameObject) Instantiate(TailPrefab, lastChain.transform.position - lastChain.transform.forward, Quaternion.identity); 
       newChain.transform.rotation = lastChain.transform.rotation;
       HingeJoint hingeJoint = (HingeJoint) newChain.GetComponent<HingeJoint>();

       if(hingeJoint != null) 
       {
       hingeJoint.connectedBody = lastChain.rigidbody;
       lastChain = newChain;
       }
       counter++;
       rigidbody.mass++; // make the head weight greater so it can carry it's tail... lol
       moveSpeed += 0.05f;
    }
// Use this for initialization
    void Start () 
    {
        snake_addTail();
    }

    void OnGUI()
    {
       GUI.color = Color.magenta;
       GUI.Label(new Rect(410, 20, 100, 20), "Score: " + Score);
       GUI.Label(new Rect(490, 20, 100, 20), "Lives: " + Lives);
    }

    void OnCollisionEnter(Collision collision) 
    {

    if(collision.gameObject.name == "apple" || collision.gameObject.name == "applePrefab(Clone)" ) 
    {
       Destroy(collision.gameObject);
       Score++;  
        snake_addTail();
        return;
    }  
    if((collision.gameObject.tag == "boundry")||(collision.gameObject.name=="tailPrefab(Clone)"))

    {
        Lives--;
    }
    }

// Update is called once per frame

    void Update () 
    {
       transform.Translate(Vector3.forward * MovementSpeed * Time.deltaTime);


       if(Input.GetKey(KeyCode.UpArrow))
       {
         transform.Translate ( new Vector3(1,0,1) );
           transform.Rotate(0,180,0);
         transform.Translate ( new Vector3(0,0,1) );
       } 

       if(Input.GetKey(KeyCode.RightArrow))
       {
           //transform.Rotate(new Vector3(0,90,0));

       }

       if(Input.GetKey(KeyCode.LeftArrow))
       {
//       transform.Rotate(new Vector3(0,-90,0));

       }

       if(Input.GetKey(KeyCode.DownArrow))
       {    
         transform.Translate ( new Vector3(1,0,1) );
         transform.Rotate(0,180,0);
         transform.Translate ( new Vector3(0,0,-1) );  
       } 



       float r = Random.Range(0, 100);
       if(r > 90 && GameObject.FindWithTag("apple") == null)  
       {
       float range = 5.0f;
       Vector3 pos = new Vector3(Random.Range(-range,range), 0, Random.Range(-range,range));
       Instantiate(ApplePrefab, pos, Quaternion.identity);
       }
    }
}

the old snake games are basically a grid with each part of the snake occupying a position in the grid.

you can use a 2 or 3 dimensional array to create an arbitrarily sized playing field and then in the array simply store a vector3. thats the position in space occupied by the array.

You move from one part of the array to the next based on input. Try first to simply get a sphere to move along it. Once you have that you can focus on attaching new spheres and then having the having the array store a structure. That struct will have both a position AND a direction.

If the head which is a special part moves it will go to the next position in the array BUT it will also modify the direction of the previous position it was at so that it points toward the new one. Basically when an object moves it will move from where it is to direction. every object will move from where it is to direction except the head. The head will move from where it is to player input and will set direction.