How to control a short "animation" with a single bone? I've never really rigged something before (not counting automatic weights ;).

I've made a simple rig of a landing gear, and I'd like to have a single control bone control the whole unfolding sequence.

I've made a simple animation mostly showing what I want to bone to do by moving it along the Z axis:



I tried to setup various transform constraints to rotate the various bones according to the Z location of the control bone, but I must be doing something 
wrong, as they don't work as I expect.

Blendfile

Is this even a good approach to rigging something like this?
Blend file
I took your blend, made a copy of the landing gear and rig and deleted the animation.
I then added Transformation Bone constraints to four of your bones; arm1, arm1.001, pad, and pad_backflip. Notice the different values of the Min and Max for the Source Z axis on the Transformation constraints. That is how I timed the different parts to happen at different times. Your Control_bone drives all of the Transformation constraints.