Rewinding machine and method for producing rolls of web material

A continuous automatic peripheral rewinding machine for producing rolls of web material wound around winding cores, comprising:

• a first winding cradle formed between a first winding roller, a second winding roller, and a third winding roller;
• a second winding cradle, formed between the first winding roller, the second winding roller and a fourth winding roller, wherein the first winding roller and the second winding roller define a nip through which the winding cores, around which the web material is found, pass and the web material is fed towards a roll being formed in the second winding cradle,
• a movable severing member acting on the web material between a winding core and a roll which is being formed in the second winding cradle to sever the web material and generate a tail edge of a completed roll and a leading edge of a new roll to be wound;
• and
• wherein the severing member comprises a pressing member controlled to selectively pinch the web material against the third winding roller to sever said web material.