S形加减速

时间：2025-03-28 20:39:04

加加速度、加速度、速度、位移随时间的变化函数：

tk(k=0,1,...7) ：表示各个阶段的过渡点时刻；

τk(k=0,1,...7) ：局部时间坐标，表示以各个阶段的起始点作为时间零点的时间表示，

τk=tk−tk−1(k=1,...7) ;

Tk(k=1,...7) ：各个阶段的持续运行时间。

j (t) = ⎧ ⎩ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ j m a x 0 - j m a x 0 - j m a x 0 j m a x 0 \leq t \leq t 1 t 1 \leq t \leq t 2 t 2 \leq t \leq t 3 t 3 \leq t \leq t 4 t 4 \leq t \leq t 5 t 5 \leq t \leq t 6 t 6 \leq t \leq t 7

a (t) = ⎧ ⎩ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ j m a x τ 1 a m a x a m a x - j m a x τ 3 0 - j m a x τ 5 - a m a x - a m a x + j m a x τ 7 0 \leq t \leq t 1 t 1 \leq t \leq t 2 t 2 \leq t \leq t 3 t 3 \leq t \leq t 4 t 4 \leq t \leq t 5 t 5 \leq t \leq t 6 t 6 \leq t \leq t 7 t = t 1 时 ， a m a x = j m a x T 1

v (t) = ⎧ ⎩ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ v s + 1 2 j m a x τ 21 v 1 + a m a x τ 2 v 2 + a m a x τ 3 - 1 2 j m a x τ 23 v 3 v 4 - 1 2 j m a x τ 25 v 5 - a m a x τ 6 v 6 - a m a x τ 7 + 1 2 j m a x τ 27 0 \leq t \leq t 1 t 1 \leq t \leq t 2 t 2 \leq t \leq t 3 t 3 \leq t \leq t 4 t 4 \leq t \leq t 5 t 5 \leq t \leq t 6 t 6 \leq t \leq t 7 v 1 = v s + 1 2 j m a x T 21 v 2 = v 1 + a m a x T 2 v 3 = v 2 + 1 2 j m a x T 21 v 3 = v 4 v 5 = v 4 - 1 2 j m a x T 25 v 6 = v 5 - a m a x T 6 v 7 = v 6 - 1 2 j m a x T 25

S (t) = ⎧ ⎩ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ v s τ 1 + 1 6 j m a x τ 31 S 1 + v 1 τ 2 + 1 2 j m a x T 1 τ 22 S 2 + v 2 τ 3 + 1 2 j m a x T 1 τ 23 - 1 6 j m a x τ 33 S 3 + v 3 τ 4 S 4 + v 4 τ 5 - 1 6 j m a x τ 35 S 5 + v 5 τ 6 - 1 2 j m a x T 5 τ 26 S 6 + v 6 τ 7 - 1 2 j m a x T 5 τ 27 + 1 6 j m a x τ 37 0 \leq t \leq t 1 t 1 \leq t \leq t 2 t 2 \leq t \leq t 3 t 3 \leq t \leq t 4 t 4 \leq t \leq t 5 t 5 \leq t \leq t 6 t 6 \leq t \leq t 7 t = t 1 时, S 1 = v s T 1 + 1 6 j m a x T 31 t = t 2 时, S 2 = S 1 + v 1 T 2 + 1 2 j m a x T 1 T 22 t = t 3 时, S 3 = S 2 + v 2 T 1 + 1 3 j m a x T 31 t = t 4 时, S 4 = S 3 + v 3 T 4 t = t 5 时, S 5 = S 4 + v 4 T 5 - 1 6 j m a x T 35 t = t 6 时, S 6 = S 5 + v 5 T 6 - 1 2 j m a x T 5 T 26 t = t 7 时, S 7 = S 6 + v 6 T 5 - 1 3 j m a x T 35

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