a3=a3 cosa sin a 0a1 SIna cos ot0‖a 2 a 0 01人a3 =Rz(a)川a2 a3
3 3 a ′ = a ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ = − ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ ′ ′ ′ 3 2 1 3 2 1 a a a 0 0 1 sin cos 0 cos sin 0 a a a α α α α ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ = 3 2 1 z a a a R ( α )
类似地,绕y轴转角β则有 cos阝0-sinβ a2 01 0 2 Sinβ0cos 3 a Ry(β)a2 13
类似地，绕 y轴转角 ，则有 β ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ = ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ − = ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ ′ ′ ′ 3 2 1 3 2 1 a a a sin 0 cos 0 1 0 cos 0 sin a a a β β β β ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ = 3 2 1 y a a a R ( β )
普遍而言,先绕2转0,再绕新y转β (即N轴),再绕新z轴(即z)转y, 这时 a2=Rz (YRN()r(a)a2 a3 事实上, Rz2(y)=RN(β)Rz()Rz()Rz(c)RN(β)
普遍而言，先绕 z 转 ，再绕新 y 转 (即N轴)，再绕新z轴(即 )转 ， 这时 事实上， α β z′ γ ⎟⎟⎟⎠⎞ ⎜⎜⎜⎝⎛ =⎟⎟⎟⎠⎞ ⎜⎜⎜⎝⎛ ′′′ ′ 321 z N z 321 aaa R ( )R ( )R ( ) aaa γ β α R ( ) R ( )R ( )R ( )R ( )R ( ) 1N 1 z γ N β z α z γ z α β − − ′ =
(a) (b) (C)
而RN(β)=Rz(a)R√(β)Rz(a) a2=[Rz(a) Ry(sri(a]Rz(aRe(YRZ (aRN(B)RN(B)Rz(a)a2 a3 3 a Rz(a)RY(B)R2(Y) a2 a 3 而且可以看到
而 而且可以看到 R ( ) R ( ) R ( ) R ( ) 1 N β z α y β z α − = ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ = ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ ′ ′ ′ − − − 3 2 1 N z 1 N 1 z z z 1 z y z 3 2 1 a a a [ R ( ) R ( ) R ( )] R ( ) R ( ) R ( ) R ( ) R ( ) R ( ) a a a α β α α γ α β β α y 3 z 1 z 2 a R ( a a )R ( )R ( ) ⎛ ⎞ ⎜ ⎟ = ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ αβγ