For example, maker community builds a machine implying/related to technologies/concepts under patent, and licenses these under GPL.
What are the consequences?
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I've answered this in the context of US patent law, but similar principles apply elsewhere in the world.
As stated in 35 USC 271, "whoever without authority makes, uses, offers to sell, or sells any patented invention, within the United States or imports into the United States any patented invention during the term of the patent therefor, infringes the patent". Thus, a patent provides the patent owner with the right to exclude others from performing these actions, and the right to sue anyone who does perform these actions (both to stop them from infringing the patent, and to collect monetary damages for their infringement).
Creating an infringing product and then licensing it under the GPL (or any other scheme) does not change the fact that it infringes a patent.
35 USC 271 also states that "Whoever actively induces infringement of a patent shall be liable as an infringer". This means that, even if the creator of the infringing product does not perform any infringing acts in the US, the act of offering it for free use could be construed as induced infringement of the patent, and they could still be sued for that infringement.