Creating rotating component in Template (sleeper)

Trying to create the component, which is supposed to be turned fully on curves (by cant). The component is sleeper, which has geometry, which must turn in full, not just point by point. Therefore I use Angle Distance constraint from the Left and Right rails, expecting the Rigid rotation, as it is explained in help.

However the result is rotated horizontal lines, but vertical position of points is not changed. This was the result, when I used Horizontal and Vertical constraints, or when tried Vector Offset constraints - nothing helped. So, finally, tried using Angle Distance constraint, but the result is again as in below Picture.

Here are the constraints, used for every point of each sleeper:

Is there a way to force the point to be moved to both - horizontal and vertical directions, if Parent points are moved also not just by vertical and horizontal, but by both directions?

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