The radially engaging systems includes a housing having at least one guide channel formed therein. At least one sliding member is slidably received in the guide channel to selectively extend or retract therein in order to connect and lock mechanical components together. Each sliding member is provided with an elongate follower. A rotator is operatively mounted to the housing. The rotator includes at least one guide curve based upon an Archimedian spiral. The follower rides inside the guide curve. Selective rotation of the rotator converts the rotation into linear movement of the connected sliding member. Conversely, selective linear movement of the sliding member converts the same into rotation of the rotator.