{"id":16135,"date":"2024-03-14T03:14:38","date_gmt":"2024-03-14T07:14:38","guid":{"rendered":"https:\/\/blogs.mathworks.com\/simulink\/?p=16135"},"modified":"2024-03-14T08:38:22","modified_gmt":"2024-03-14T12:38:22","slug":"computing-%cf%80-simscape-multibody-style","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/simulink\/2024\/03\/14\/computing-%cf%80-simscape-multibody-style\/","title":{"rendered":"Computing \u03c0… Simscape Multibody Style"},"content":{"rendered":"
On this <\/span>\u03c0<\/span> day 2024, I decided to tag along with Mike Croucher from <\/span>The MATLAB Blog<\/span><\/a> and show one way to compute <\/span>\u03c0<\/span>.<\/span><\/div>
While Mike went for advanced maneuvers involving the <\/span>MATLAB AI Chat Playground<\/span><\/a>, <\/span>Parallel Computing Toolbox<\/span><\/a>, and even <\/span>Quantum Computing<\/span><\/a>, I decided to go with the way our ancestors would have done thousands of years ago: by rolling a cylinder. See method 1 in <\/span>this WikiHow article<\/span><\/a> for more details.<\/span><\/div>

The Model<\/span><\/h2>
Using Simscape Multibody, I connected a <\/span>Planar Joint<\/span><\/a> and a <\/span>Cylinder Solid<\/span><\/a> together. I let the Cylinder fall on an <\/span>Infinite Plane<\/span><\/a> and used the <\/span>Spatial Contact Force<\/span><\/a> block to compute the contact dynamic between those two:<\/span><\/div>
mdl = <\/span>'ComputePi'<\/span>;<\/span><\/span><\/div><\/div>
open_system(mdl);<\/span><\/span><\/div><\/div><\/div>
\"\"<\/img><\/div>
I used <\/span>Motion Actuation<\/span><\/a> to roll the cylinder by 360 degrees and sensed by how much it had translated. I was then able to compute <\/span>\u03c0<\/span> using:<\/span><\/div>
\u03c0<\/mi>=<\/mo>d<\/mi><\/mrow>2<\/mn>r<\/mi><\/mrow><\/mfrac><\/mrow><\/math><\/span><\/div>
where <\/span>d<\/span> is the distance travelled and <\/span>r<\/span> is the radius of the cylinder. <\/span><\/div>
in = Simulink.SimulationInput(mdl);<\/span><\/span><\/div><\/div>
out = sim(in);<\/span><\/span><\/div><\/div>
r = 1; <\/span>% Cylinder radius;<\/span><\/span><\/div><\/div>
d = out.yout{1}.Values.Data(end); <\/span>% final distance<\/span><\/span><\/div><\/div>
pi_estimate = d\/(2*r)<\/span><\/span><\/div>
pi_estimate = 3.0956<\/div><\/div><\/div><\/div>
Because the cylinder slipped a bit on the ground, I did not get a very accurate result, but it's probably representative of the result you would get if you had tried computing <\/span>\u03c0<\/span> that way a few thousand years ago.<\/span><\/div>
Here is the <\/span>Mechanics Explorer<\/span><\/a> animation for this simulation:<\/span><\/div>
\"RollingCylinder.gif\"<\/img><\/div>

Now it's your turn<\/span><\/h2>
Hopefully, you can find more accurate ways to compute <\/span>\u03c0<\/span>. <\/span><\/div>
If you need to model cylinders rolling on the ground, try opening the model used for this blog post in <\/span>MATLAB Online<\/span><\/a> by clicking on this banner:<\/span><\/div>
\"\"<\/img><\/a><\/div>\r\n<\/div>