It called a Table Wobble Saw which the groove is adjustable by changing the position of the wobble saw washers (wedge type).I think the groove in the wood can go up to 2".If you want 4" then you have to run it over twice by adjusting the side width runner.I don't think you can get them in the UK anymore but not sure because of safety laws and regs (perhaps the earlier UK model was dangerous) but you can in USA.
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