工业机器人课件2-2

2.2.2 两杆之间位姿矩阵的建立 建立坐标系
关节轴线为z轴 长度线为x轴
确定参数 变换过程
α θ Tii−1 = Rot (x, i-1 )Trans(li−1 0 0)Trans(0 0 di ) Rot (z, i )
cosθi cosα sin θ i −1 i = sin αi−1 sin θi 0 − sin θi cosαi−1 cosθi sin αi−1 cosθi 0 0 li−1 − sin αi−1 − di sin αi−1 cosαi−1 di cosαi−1 0 1
C5 0 T54 = S 5 0
− S5 0 C5 0
0 −1 0 0 0 0 1 0
nx n 0 0 1 2 3 4 5 T6 = T1 T2 T3 T4 T5 T6 = y nz 0
ox oy oz 0
ax ay az 0
px py pz 1
Py = S1 (l2C2 + l3C23 − d4 S23 ) + d3C1
Pz = −l2 S2 − l3 S23 − d4C23
Mபைடு நூலகம்TOMAN
HP6
− S2 0 − C2 0
0 1 0 0
0 0 0 1
C3 S 2 T3 = 3 0 0
C6 0 5 T6 = − S6 0
− S3 C3 0 0
− S6 0 − C6 0
0 l2 0 0 1 d3 0 1
0 0 1 0 0 0 0 1
2.2 运动学正解方程
2.2.1 机器人杆件的几何参数及关节变量
杆件的几何参数 杆件长度——杆上两关节轴线之间的最短距离 杆件扭角——杆上两关节轴线之间的夹角 αi 两杆之间关节参数 θi 关节转角——两杆长度线之间的夹角 关节偏置量——两杆长度线之间的距离 d
i
li
zi
zi +1
zi -1 i θi i -1 αi-1 l i-1 di xi xi -1
相邻两杆间的位姿矩阵
C1 − S1 S C1 0 T1 = 1 0 0 0 0
C4 0 3 T4 = − S4 0 − S4 0 − C4 0
0 0 0 0 1 0 0 1
0 l3 1 d4 1 0 0 1
C2 0 1 T2 = − S2 0
nY = S1 [C23 (C4C5C6 − S4 S6 ) − S23S5C6 ] + C1 (S4C5C6 + C4 S6 ) nx = −S23 (C4C5C6 − S4 S6 ) − C23S5C6 ox = C1[C23 (−C4C5 S6 − S4C6 ) + S23S5 S6 ] + S1 (−S4C5 S6 + C4C6 ) ox = C1[C23 (−C4C5 S6 − S4C6 ) + S23S5 S6 ] + S1 (−S4C5 S6 + C4C6 ) oz = −S23 (−C4C5 S6 − S4C6 ) + C23S5 S6 ax = −C1 (C23C4 S5 + S23C5 ) − S1S4 S5
PUMA560
l3 z1 z0 z2 z3
d3 x0 x1 x2 l2 x3 z5
x4 x5 x6 z4 z6
参数表
i 1 2 3 4 5 6 ai-1 0 -900 0 -900 900 -900 li-1 0 0 l2 l3 0 0 di-1 0 0 d3 d4 0 0 θi θ1 θ2 θ3 θ4 θ5 θ6
nx = C1[C23 (C4C5C6 − S4S6 ) − S23S5C6 ] + S1(S4C5C6 + C4S6 )
a y = −S1 (C23C4 S5 + S23C5 ) + C1S4 S5
az = S23C4 S5 − C23C5 Px = C1 (l2C2 + l3C23 − d4 S23 ) − d3 S1