Timeline for Animating a 2D MDOF system
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Jul 3, 2021 at 8:16 | comment | added | Martin Trcek | Now the animation runs smoothly. Again thanks for all your help | |
| Jul 2, 2021 at 17:54 | comment | added | Domen |
You can precompute the frames: frames = Table[Evaluate@Show[...], {t, 0, 10, .1}] and then use ListAnimate[frames]. You can also export the animation to a .gif or a movie file with Export["animation.gif", frames].
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| Jul 2, 2021 at 14:41 | comment | added | Martin Trcek | Oh okay then thats about everything. This is the exact model I've been looking for. Thank you you've been a massive help. I do have one final question though. When i run the code on my computer the program mathematica becomes extremely laggy. Would it be possible to smooth out the animation? | |
| Jul 2, 2021 at 14:39 | comment | added | Domen | As you can see in the code (and in the animation), the left end of the first beam has fixed coordinates $(x_0, y_0) = (0,0)$. This means that the first beam is rotating around the support on the left. | |
| Jul 2, 2021 at 14:28 | comment | added | Martin Trcek | Okay now almost everything is as I have imagined it. However have you drawn the first beam to revolve around its mass centre aswell? Because it should revolve around The support on the left. | |
| Jul 2, 2021 at 13:03 | comment | added | Domen | I haven't explicitly mentioned this before: as you can see, I draw the beams by providing their endpoints. That is why there is no $1/2$ in my coordinates. Your coordinates provide the positions of beam midpoints. As for the angle: if angles are measured in absolute frame (from the horizontal) as sketched in your drawing, then I think my derivation is correct. The $y$-component of the last beam has to be 0 (at the same height as the left support): $y_1+y_2+y_3=0 \implies L_1 \sin\varphi_1 + L_2 \sin\varphi_2 + L_3 \sin\varphi_3 = 0$. | |
| Jul 2, 2021 at 11:34 | comment | added | Martin Trcek | This is how the animation should look, however the coordinates are still not correct. The correct coordinates definitions are: X2 = X1 + (L2 Cos[[Phi]2[t]])/2; Y2 = Y1 + (L2 Sin[[Phi]2[t]])/2, X3 = X1+L2 Cos[[Phi]2[t]] + ((L3 Cos[[Phi]3[t]]))/2, Y3 = Y1+L2 Sin[[Phi]2[t]]+ (L3 Sin[[Phi]3[t]]))/2. Also the definition of [Phi]3 is somewhat strange to me. | |
| Jul 2, 2021 at 9:35 | comment | added | Domen | I think I have found the correct definition of $\varphi_3$ and the coordinates, so I have edited my first answer. Let me know if this is what you have been looking for. | |
| Jul 2, 2021 at 9:34 | history | edited | Domen | CC BY-SA 4.0 |
Corrected the answer.
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| Jul 1, 2021 at 16:45 | comment | added | Martin Trcek | The rotation of second and the third beam is revolving around the centre of mass of each beam so the coordinates change to X2 = X1 + (L2 Cos[[Phi]2[t]])/2; X3 = X2 + (L3 Cos[[Phi]3[t]])/2. This is likely the coordinate problem as im fairly certain the DE's are correct. | |
| Jul 1, 2021 at 16:35 | comment | added | Domen | This is the same way as I have defined the coordinates in my attempt. But as you can see, the right end of the third beam also has some vertical ($y$) movement. According to your drawing, this should not be happening, because it is constrained to horizontal movement. So, there is probably a mistake somewhere, either in the differential equations or in the definition of coordinates ... | |
| Jul 1, 2021 at 16:17 | comment | added | Martin Trcek | These are the coordinates in XY expressed with angles. They are placed where the torsion springs are. [X1(Kt1)=L1*Cos(φ1), Y1Kt1)=L1*Sin(φ1), X2(Kt2)=L1*Cos(φ1)+L2*Cos(φ2), Y2Kt1)=L1*Sin(φ1)+L2*Sin(φ2)]. | |
| Jul 1, 2021 at 16:09 | comment | added | Domen | Sure, but can you just write down first how the $x$ and $y$ coordinates of the joints are expressed by the angles $\varphi$? | |
| Jul 1, 2021 at 15:57 | comment | added | Martin Trcek | thank you this solution is very helpful. Would it also be possible to add a roller support on the right side that allows motion in X dimension olny? | |
| Jul 1, 2021 at 15:51 | history | answered | Domen | CC BY-SA 4.0 |