What´s the best tool to make the corners of planks rounded:
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Now that is has been clarified that you mean the corners (not the edges or arrises) my Answer needs to be completely revised. It still depends on the radius you want.
Very small radii
If you want to just round your corners slightly, say to a radius of 1-3mm arguably the easiest and simplest method is just to sand them (or by filing if you use files). You have to be careful if you want a very uniform result regardless of the method used but in general you can do this successfully by eye.
It's fairly easy to do this sanding by hand sanding using a block to back the abrasive paper. You can also do this by rotating the piece against a disk sander (one of the most common uses for this tool). This is also possible using a belt sander but much more care needs to be taken as it's very easy to remove more wood than intended, or to end up with an asymmetrical curve which looks terrible.
If you want a larger radius it's a very good idea to mark the workpiece to give you lines to work towards, unless you're using a method (e.g. a router template) that automatically creates a radius of a fixed size. Woodworkers are rather famous for just grabbing something round in the workshop and drawing around it, washers, bottle tops and spraycan caps all being favoured for this purpose.
For these larger radii many methods are available. You can still remove the wood entirely by sanding if you want, but this is only really practical using power sanding. Even doing a sizeable radius many owners of disk sanders or horizontal belt sanders will remove all the wood by sanding it off.
In the absence of a power sander the most common method today would be using a router and a template of some kind. Templates can be made in the shop but there are numerous commercial versions, and as you can see they can be used on the router table or using a handheld router:
Note the Woodpeckers template shown isn't for a fixed radius, it has replaceable inserts that cover a wide range of radii. This template is retired however, but a version of it returns to production periodically. So it may or may not be available when you read this!
This is a lot of wood to remove in one pass using a router, it wouldn't be a bad idea to cut a 45° off the corner prior to routing to ease the load on the bit. Just be careful not to cut too much off!
A bandsaw or jig saw are also possibilities for cutting round corners, but there's often a definite limit on the safe size of the workpiece that can be tackled on a bandsaw. You'd normally sand to refine the surface after either operation.
Using hand tools, the traditional method for removing the wood is to chisel down vertically, see image in this previous Answer and this is still a viable method, if a bit slow in thicker and harder woods. Your chisel needs to be very, very sharp. Although in the past the slightly faceted surface created would often have been left as it was these days it would be normal to sand to fully smooth it.
You can also rasp the bulk of the wood away (being careful initially to rasp off the edge towards the end grain, never the other way around or you'll get terrible splintering), then switch to files to complete the smoothing followed by scraping and/or sanding to create the final surface.