Linear motion of pink object along longitudinal axis and its rotary motion around vertical axis are controlled by two grounded blue motors. Two worms are identical.
When the motors rotate in the same direction at the same velocity, the object moves linearly only.
When the motors rotate in different directions at the same velocity the object rotates only.
Linear displacement L = S.(n1 + n2)/2
Angular displacement in degrees: A = 180. k.(N1 – N2)/Z
S: lead of the worms of k starts
n1, n2: worms revolutions. They are of same sign (+ or -) if the worms rotate in the same direction and vice versa.
Z: tooth number of the pink gear.
Advantage: self-locking feature. So after getting desired position of the pink object there is no need to supply the motors further with the electricity.

Thank you cargueconcuidado for showing me this conception.