File:Chronogrammes loi trapezoidale en acceleration.svg
Original file (SVG file, nominally 507 × 820 pixels, file size: 92 KB)
Captions
Summary
[edit]DescriptionChronogrammes loi trapezoidale en acceleration.svg |
English: Chronograms for a movement with a trapezoidal acceleration law, in order to control the jerk. A body is moved from the position x = 0 to x = xf, the duration of the movement is T.
There are three parts which last T/3:
Français : Chronogrammes pour un mouvement suivant une loi trapézoïdale en accélération, afin de maîtriser l'à-coup (jerk).
Il y a trois partie d'une durée de T/3 :
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Date | |
Source | Own work |
Author | Christophe Dang Ngoc Chan (Cdang ) |
SVG development InfoField |
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Scilab source
This media was created with Scilab, a free open-source software. Here is a listing of the Scilab source used to create this file. |
function [t1, t2, t3, t4, t5, t6, t7] = indice(t)
t1 = (t < 1/9);
t2 = (t >= 1/9) & (t < 2/9);
t3 = (t >= 2/9) & (t < 1/3);
t4 = (t >= 1/3) & (t <= 2/3);
t5 = (t > 2/3) & (t <= 7/9);
t6 = (t > 7/9) & (t <=8/9);
t7 = (t > 8/9);
endfunction
function [j]=jerk(t)
[t1, t2, t3, t4, t5, t6, t7] = indice(t);
j = zeros(t);
j(t1) = 9;
j(t2) = 0;
j(t3) = -9;
j(t4) = 0;
j(t5) = -9;
j(t6) = 0;
j(t7) = 9;
endfunction
function [a]=acceleration(t)
[t1, t2, t3, t4, t5, t6, t7] = indice(t);
a = zeros(t);
a(t1) = 9*t(t1);
a(t2) = 1;
a(t3) = (3 - 9*t(t3));
a(t4) = 0;
a(t5) = 6 - 9*t(t5);
a(t6) = -1;
a(t7) = 9*t(t7) - 9;
endfunction
function [v] = vitesse(t)
[t1, t2, t3, t4, t5, t6, t7] = indice(t);
v = zeros(t);
v(t1) = 9/2*t(t1).^2;
v(t2) = t(t2) - 1/18;
v(t3) = (-9/2*t(t3) + 3).*t(t3) - 5/18;
v(t4) = 2/9;
v(t5) = (-9/2*t(t5) + 6).*t(t5) - 16/9;
v(t6) = -t(t6) + 17/18;
v(t7) = (9/2*t(t7) - 9).*t(t7) + 9/2;
endfunction
function [x] = position(t)
[t1, t2, t3, t4, t5, t6, t7] = indice(t);
x = zeros(t);
x(t1) = 3/2*t(t1).^3;
x(t2) = (0.5*t(t2) - 1/18).*t(t2) + 1/486;
x(t3) = ((-3/2*t(t3) + 3/2).*t(t3) - 5/18).*t(t3) + 1/54;
x(t4) = 1/9*(2*t(t4) - 1/3);
x(t5) = ((-3/2*t(t5) + 3).*t(t5) - 16/9).*t(t5) + 11/27;
x(t6) = (-0.5*t(t6) + 17/18).*t(t6) - 145/486;
x(t7) = ((3/2*t(t7) - 9/2).*t(t7) + 9/2).*t(t7) - 73/54;
endfunction
t = 0:0.005:1;
j = jerk(t);
a = acceleration(t);
v = vitesse(t);
x = position(t);
scf(0);
clf;
subplot(4, 1, 1)
plot(t, x)
xtitle("position", "t/T", "$x/(a_0 \mathrm{T}^2)$")
subplot(4, 1, 2)
plot(t, v)
xtitle("vitesse", "t/T", "$v/(a_0 \mathrm{T})$")
subplot(4, 1, 3)
plot(t, a)
xtitle("accélération", "t/T", "$a/a_0$")
subplot(4, 1, 4)
xtitle("à-coup", "t/T", "$j \times \mathrm{T}/a_0$")
plot(t, j)
Licensing
[edit]Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 08:23, 28 August 2018 | 507 × 820 (92 KB) | Cdang (talk | contribs) | less points (only two for a line segment) | |
16:49, 13 February 2014 | 507 × 820 (106 KB) | Cdang (talk | contribs) | {{Information |Description={{en|1=Chronograms for a movement with a trapezoidal acceleration law, in order to control the jerk.}} {{fr|1=Chronogrammes pour un mouvement suivant une loi trapézoïdale en accélération, afin de maîtriser l'à-coup ''(j... |
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Short title | chronogrammes pour une loi trapézoïdale en accélération |
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Width | 507.19229 |
Height | 819.54492 |