Bones parent-child relationship on different axis So I am creating this mechanical arm rig and at the tip theres this grip mechanism that consists of two parts sliding towards each other for the grip to close on something.
Now, in order to make it quicker and easier on me in the animation phase I have gone ahead and added this third bone (number 1 in the image) which controls bones number 2 and 3. 
How do I make it so when I move bone #1 on the X axis, bones #2 and #3 move on the Y axis in and out accordingly?
Hope I make myself clear enough.
Try a transformation constraint on bones 2 and 3.  Transformation constraints take the transformation of one bone and use it to apply some arbitrary transformation to a different bone.  They're sort a poor man's driver.  (This is also something you could easily do with drivers.  Plenty of other ways too.)

Let's say you want bone B to move 1 unit in the positive X local axis when you move bone A 1 unit in its positive Y local axis.  Create a transformation constraint on bone B.  You want to affect position on both bones, so use "loc" (location) for both bones.  Map Y to X.  Set it to use local space for both bones.  Finally, enter a range of values for input and output; in this case, use 0 to 1 for the source Y and 0 to 1 for the destination X.

For the other side, it's the same constraint, except you want it moving in the opposite direction-- so map the destination to 0 to -1 in the X instead.