data-in/data-out. Mostly switches/relays of some sort, and sensors.. A simple concept is flip a light switch "on" and the light bulb gets power and lights up. Flip it off and the light goes off. Apply that to kinky devices and you get something on and off. Then think of a dimmer switch, it still does on and off, but also adds variable voltage levels so the bulb isn't just fully on or off, but somewhere in between. Apply that, and you could control the speed of a vibe, the stroke of a fucking machine or the intensity of an e-stim application. SO, the controller would need to apply power to a servo/motor to draw it back to it's limit (a limit switch or just held at its max capable draw/pull) and hold it there until the power is switched off, resulting in the swing of the spanking apparatus. The cycle would need to be set as well as how many times the cycle is repeated.
Arduino programming should be able to do the cycle part as well as tripping the relay to engage the servo
The rest is coming up with the hardware to use. A power supply, the servo, then how it attaches to things so it's not simply flopping around on the floor, then the 'device' that will be swinging and how it attaches to the servo, then as
@droptokon pointed out, what causes the swing, like a spring.
I'm sure I could find some 'common gadgets' to start with, I would just need to know what 'gizmos' this Arduino involves and start putting something together