Mechanical Telescopic Cylinder

Input: red screw driven by a electric motor.
Yellow frame carries orange pulleys. Their blue cables have points fixed to grey base and to green frame.
The green frame carries pink pulleys. Their black cables have points fixed to the yellow frame and to blue frame.
The red screw – yellow nut drive makes the yellow frame goes up down.
The green frame moves two times faster than the yellow frame.
The blue frame moves four times faster than the green frame.
Front part of the mechanism is cut-off for easy understanding.