Fasciculus:Chronogrammes loi sinusoidale par partie en vitesse.svg

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Summarium

Descriptio
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).
Datum
Fons Opus proprium
Auctor 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)

Potestas usoris

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His condicionibus:
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recentissima10:50, 14 Februarii 2014Minutum speculum redactionis 10:50, 14 Februarii 2014 factae610 × 814 (111 chiliocteti)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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