Step 1: Making the drop spindle's whorl
A couple of things to consider when designing the whorl are radius and weight. If the radius is too large the whorl may bump into things (like your leg) while you are spinning. If the whorl is too heavy it could break a fine thread, but if the whorl is too light it will stop turning quickly and you will be constantly having to flick it to keep it going.
It isn't actually the weight of the whorl that determines how long it turns -- it's the moment of inertia. Physics teaches us that if you want to maximize the moment of inertia of an object of fixed mass, that mass should be distributed as far from the center as possible. So the ideal whorl would have only thin spokes connecting a heavy rim to the center.
All of the whorls shown here work just fine.
Step 2: Attaching the spindle
You can simulate the hook with a single clip. This requires you to make a half-hitch with the thread after winding on and before resuming spinning, just like with a traditional spindle. But if you use two clips to make the double hook shown here, you'll find that you can wrap and unwrap the yarn around it much more quickly. Try it! You'll see what I mean.
The whorl has a tendency to slide down the spindle (especially if you are spinning wool "in the grease"), which is why this design is only suitable for making a bottom whorl spindle, not a top one. If it bothers you, you can add more clips or spacers to the spindle below the whorl. I just push it back up again if it gets too low.
Step 3: The Lazy Kate
Step 4: The Niddy Noddy
To use it, tie the end of your yarn to the end of a cross piece, grasp the center of the shaft in one hand and wrap the yarn around the cross pieces in the pattern shown in the first picture. After you get the hang of it, the yarn winds very quickly with the niddy noddy just rocking gently from side to side as your free hand guides the yarn to the correct place.
Step 5: A finished skein
These are fun designs that are quick to make, cheap (if you already own the K'nex), and very portable. I sometimes demonstrate spinning to children and I plan on using these spindles in the future. Many kids have K'nex at home, so I can send them home with a bit of wool knowing they'll have what they need to follow up on their first lesson.
And did I mention how pretty the colors are when the spindles are turning?