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Summary

Description
English: Chronograms for a movement with a velocity law that is sine-like in its increase and decrease phase, 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. The maximum velocity is v0.

There are three parts which last T/3:

  1. Acceleration (cosine velocity law).
  2. Constant velocity.
  3. Braking (cosine velocity law).
Français : Chronogrammes pour un mouvement suivant une loi sinusoïdale par pattie en vitesse, afin de maîtriser l'à-coup (jerk). La vitesse maximale est notée v0.

Il y a trois partie d'une durée de T/3 :

  1. Accélération (loi de vitesse en cosinus).
  2. Mouvement uniforme (vitesse constante).
  3. Freinage (loi de vitesse en cosinus).
Date
Source Own work
Author Christophe Dang Ngoc Chan (Cdang (talk))

1.

2.

3.

Max.

Scilab source

function [t1, t2, t3] = indice(t)
    t1 = (t < 1/3);
    t2 = (t >= 1/3) & (t < 2/3);
    t3 = (t >= 2/3);
endfunction

function [j]=jerk(t)
    [t1, t2, t3] = indice(t);
    j = zeros(t);
    j(t1) = (9*%pi^2/2)*cos(3*%pi*t(t1));
    j(t2) = 0;
    j(t3) = -(9*%pi^2/2)*cos(3*%pi*t(t3));
endfunction

function [a]=acceleration(t)
    [t1, t2, t3] = indice(t);
    a = zeros(t);
    a(t1) = (3*%pi/2)*sin(3*%pi*t(t1));
    a(t2) = 0;
    a(t3) = -(3*%pi/2)*sin(3*%pi*t(t3));
    endfunction

function [v] = vitesse(t)
    [t1, t2, t3] = indice(t);
    v = zeros(t);
    v(t1) = (1/2)*(1 - cos(3*%pi*t(t1)));
    v(t2) = 1;
    v(t3) = (1/2)*(1 + cos(3*%pi*t(t3)));
endfunction

function [x] = position(t)
    [t1, t2, t3] = indice(t);
    x = zeros(t);
    x(t1) = (1/2)*(t(t1) - (1/3/%pi)*sin(3*%pi*t(t1)));
    x(t2) = t(t2) - 1/6;
    x(t3) = (1/2)*(t(t3) + (1/3/%pi)*sin(3*%pi*t(t3))) + 1/6;
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", "$x/(v_0 \mathrm{T})$")

subplot(4, 1, 2)
plot(t, v)
xtitle("vitesse", "t/T", "$v/(v_0)$")

subplot(4, 1, 3)
plot(t, a)
xtitle("accélération", "t/T", "$a\times \mathrm{T}/v_0$")

subplot(4, 1, 4)
xtitle("à-coup", "t/T", "$j \times \mathrm{T}^2/v_0$")
plot(t, j)

Licensing

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current10:50, 14 February 2014Thumbnail for version as of 10:50, 14 February 2014610 × 814 (111 KB)Cdang{{Information |Description={{en|1=Chronograms for a movement with a velocity law that is sine-like in its increase and decrease phase, in order to control the jerk. A body is moved from the position ''x'' = 0 to ''x'' = ''x''<sub>f</sub>, the duration...

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