Describing robot with Denavit-Hartenberg parameters

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Hi there,

Consider a robot with to revolute joints. The first one is oriented as a regular coordinate system {X1,Y1,Z1}, while the other is translated by 4 in the Z1 direction and then rotated around X2 by -pi/2. As I can read in different litterature, this corresponds to the DH-parameters alpha1 = -pi/2 and d2 = 4. This gives the transformation matrix T^1_2

1 0 0 0
0 0 1 4
0 -1 0 0
0 0 0 1

but there is no translation in this matrix in the Z1 direction. Just by intuition the matrix must be

1 0 0 0
0 0 1 0
0 -1 0 4
0 0 0 1

The difference is caused by the alpha1 angle, which is affecting the sin(alpha1) and cos(alpha1) in the changing entries. Can anyone tell what is wrong?

Thanks
 
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