Introduction to virtual reality in simulink (Bouncing Ball Exemple)

How to…

Intro to Matlab-Simulink Virtual Reality on: 2016/04/29

By: Shck Rodrigue Tchamna

Objective: Show you how to simulate a mathematical system in Simulink and visually check your equation on a real-virtual system.

Watch the Video here: Youtbe link Problem Description: Let’s assume we let a ball freely falls from an initial height h0 . We want to find the equation of the motion, and then simulate it in Simulink Virtual Reality to check if our equation really drive the physical ball as expected.

r

r  1.5m

h0  20m Note: y is measured from the ground to the center of the ball.

Step 1: Equation of motion: Free Fall motion without initial velocity

Free fall motion

dy 2  g 2 dt

Collision equation dy 2 dy 2 if y  r , Fy  m 2  K 0  r  y   mg  m 2 dt dt K0 dy 2  r  y  g  2 m dt

Before collision

After collision

rx

y

ry

ry

rx  ry  rz  r

y

ry

rx

Note: There compression!

is the amount of compression

is

a

ball

rx  rz ; ry  y

Assumption: after collision, the deformation in the x and z direction are equal.

Collision equation

dy 2  if y  r , 2  K  r  y   g dt

K

K0 m

Volume conservation equation

After bouncing

Before bouncing Sphere Volume 4 3 r 3

Ellipse Volume 4  rx ry rz with ry  y 3

Let’s assume rx

 rz

4 2 4 3   rx y   r  rx  rz  3 3 Scale equations

rx  rz 

r3 ; ry  y y

r3 y

Step 2: Build this model in Simulink

dy 2  g dt 2

Free fall motion

Collision equation

Scale equations

dy 2  if y  r , 2  f  g dt

rx  rz 

f  K r  y

r3 ; ry  y y

function [f, rx, ry,rz] = fcn(y) %#codegen

% % % Before collision with the ground

% % f is the ground reaction. The compression of the ball bring about a repell force from the ground, equal to the ball compression

if y >= r f = 0; rx = r; ry = r; rz = r;

K = 500; r = 1.5;

else %% y <r After collision with the ground f = K*(r-y); rx = sqrt(r^3/y); ry = y; rz = rx;

% % To avoid division by zero if y<1e-4 y=1e-4; end end

Step 3: drag and drop the Simulink Virtual Reality Sink block from the Simulink 3D Animation Library

Step 4: Install the Virtual reality editor by typing the following command in the Matlab prompt

vrinstall -install editor

And you will have the following

Starting editor installation ...

Done.

Step 5: Double-click on the VR Sink block, then Click on New

Step 6: Right click on Add Node, then open ď&#x192; Group ď&#x192; Transform

This Transform node is for the Sphere-Ball. To rename the Transform node: 1) Right-click the Transform node. 2) Select the Edit Name menu item. 3) In the edit box to the left of the Transform node, type Ball.

Step 7: Add a Shape node Expand the Ball Transform node. Then Select the children node. Then add a Shape node, using the following sequence of menu selections:

Step 8: Expand the Children Node, then the Shape and right-click on the Appearance node in order to add an appearance under the appearance node.

Step 9: Add a Sphere Node under the Geometry Node

Step 10: Add Material under material node

Change the Ball colour if you wish

Step 11 : Change the Size of the Ball; r=1.5m

Step 12: Click on Translation and Set the ball to its initial position, at 20 m

Note: After clicking on Apply, the Ball will Vanish from the Screen. Do not Panic. Do the following to bring the ball back.

It is also advisable to save your file Now before continuing!!!

Step 13: Right click on Root and Add a Viewpoint

Note: Change the Viewpoint so as to have a good vision of the Ball. You can set different viewpoint from the above viewpoint.

Step 14: Let’s add our floor where the Ball is going to bounce. The Floor is nothing but a Box Node.

Lets copy the Ball Transform Node and make change from this Node. Right Click the Ball(Transform), Then Copy it. Then go to the Edit menu, then Paste

You should have something like this

Step 15: Refer to previous steps and rename it as “Floor”. Then expand all, Go to the Shape node and delete the Sphere, then add a Box instead.

You should have something like this

Step 16: Change the Floor size

Step 17: Then Go to Translation and bring the Floor position down

Note. You can Click on the wheel of your mouse and drag the mouse in order to slightly roatate and see The system in 3D.

Note. We can also add Background Node if we want to do so

Step 18: Close it and save it when it prompts to do so, then go back in your Simulink Model, Double-click on the VR Sink, then Browse and find the location of the file you just saved.

Step 19: Click on the View button

You should be able to see this Figure

Step 20: Now Real things Start!!! We want to link our Simulink output signals to the Virtual Reality Block. Since we are interested in the translation of the Ball, letâ&#x20AC;&#x2122;s thick the Translation checkbox of the Ball.

Note that the translation node is a 3 by 1 vector, representing the translation on the x, y and z axis. Since we only have one translation here on the y axis, we sill use a VR Signal Expander. The output width is 3 and the non-zero index is 2, meaning the value of y.

The VR Signal Expander can be found in the Simulink 3D Animation Tab

Watch the Video

Step 21: We want to see the actual deformation of the ball. It can be done using the Scale along the x, y and z axis

Step 22: we need a bus in order to make a 3 by 1 deformation vector

Watch the Video here: Youtbe link