The rotating asteroid can use as the space sling "quite easily"

Asteroid "Bennu"
(Image I)

The rotating asteroid can use as the space sling "quite easily"

If we think of the asteroids like Bennu, what is rotating quite fast, that asteroid can use as the space sling. The spacecraft that uses the catapult or sling must just connect the long cable to the surface of the asteroid by using the docking station.

This docking station is the screw that is drilled into the asteroid. When the cable is docked to the sling station the asteroid will start to rotate by using the rocket engines, which are connected to it, and then the craft will release at the right moment. 

Image I https://en.wikipedia.org/wiki/101955_Bennu

Lagrange points by NASA
(Image II)

What if the asteroid would anchor in Lagrange point?

The asteroid that is near earth would offer a place where the interplanetary probes will pull at the first, and then the probe will connect to sling. An asteroid that is a couple of hundred meters in size might anchor at the Lagrange-point L-1  what is at the range between Earth and Moon, and you can see the location of that point in the diagram. Or L-2 point behind the Moon. 

The L-3 point is just behind the sun which makes it hard to reach. In the image II  the Lagrange points are portrayed.  And when the sling is needed the asteroid would put to rotating movement, which gives the centrifugal punch to the spacecraft. 

The miniature robot space shuttle could fly quite far away from Earth, and bring the samples from the asteroid belt. Also, the asteroid base sling would give the other unmanned probes more speed, when they are traveling to Mars or the giant gas planets. The catapult sling would make small-size space systems more capacity, and that thing saves fuel, what is required also for the operations at the asteroid belt and the moon-system of the giant gas planets. 

What are Lagrange points: https://solarsystem.nasa.gov/faq/88/what-are-lagrange-points/