Ci Si

-Si Ci
 i i


Rz (ei) =


 2. Translation the matrix

 1 0
 Trz(di) =


0 0 0 0


0 0 1 0 0 0 0 1


of di units along axis zi-1 described by


0 0 0 1 0 0


0 0 1 d 0 0 0 1


 3. Translation of homogeneous transform


Trx (ai) =


ai units along axis xi, with


1 0 0 ai

0 1 0 0 0 0 1 0 0 0 0 1


4. Rotation about xi of angle ai,


Rx(a i) =


1 0 0 0


0 7i -Ci
 0 ai i 0 a1 r


0 0 0 1


 The matrix A1 of Eq. (2.1) is obtained by the product (Paul, 1981),


(2.3)


(2.4)


(2.5)


(2.6)

..