In the simulation below, the blue blobs in the bottom left corner correspond to the X and Y coordinate or the cutter relative to the centre of the machining area of the table. The blue blobs can be dragged to change the coordinates. The black rectangle represents the workpiece and the cross within the circle represents the cutter.
As you drag the blue blobs you will notice that the two rotary tables turn in such a way that the workpiece is moved so that the correct coordinate is underneath the cutter. The easiest way to start to understand what is happening is to drag one of the blue blobs so that the edge of the rectangle is underneath the cutter. Then drag the other blue blob and see how both tables move to make the edge of the workpiece move in a straight line underneath the cutter.
It is interesting to note how much the smaller table has to swing when X has a small value and Y is moved through 0. Note that phi is the angle of the small table and theta the angle of the large one.
The Rotary table provides the X and Y axes for us, but we still need to come up with and elegant Z axis. Tony Cheal has found a linkage which provides straight line movement and might be useful for our purposes. Click here for a simulation.
Andy Goldasz has come up with a simpler solution based on a modified parallel motion linkage. Click here for a simulation.
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