A machine for machining workpieces, comprising: a first column and a second column , the first column and the second column being arranged facing each other according to a first horizontal axis (Z); a guide system for guided displacement (Z1, Z2) of at least one of the first column and the second column in parallel with the first horizontal axis (Z); a first tool unit (11; 11A) adapted for supporting and driving a first rotatable tool (12; 12A), the first tool unit (11; 11A) being arranged on the first column for controlled displacement (X1; Y1) in relation to the first column in parallel with a second axis (X; Y) perpendicular to the first horizontal axis (Z); a first workpiece holding device arranged on the first column , the first workpiece holding device being arranged for controlled displacement (Z3) in relation to the first column in parallel with the first horizontal axis (Z); a second workpiece holding device arranged on the second column ; wherein the first workpiece holding device and the second workpiece holding device are arranged for supporting a workpiece between them and for controlled rotation (C1, C2) of the workpiece around a workpiece axis parallel with the first horizontal axis (Z); and wherein the machine comprises a drive system for: - controlled positioning of the first column in relation to the second column , in parallel with the first horizontal axis (Z), and - controlled positioning of the first workpiece holding device in relation to the first column , in parallel with the first horizontal axis (Z). a first column and a second column , the first column and the second column being arranged facing each other according to a first horizontal axis (Z); a guide system for guided displacement (Z1, Z2) of at least one of the first column and the second column in parallel with the first horizontal axis (Z); a first tool unit (11; 11A) adapted for supporting and driving a first rotatable tool (12; 12A), the first tool unit (11; 11A) being arranged on the first column for controlled displacement (X1; Y1) in relation to the first column in parallel with a second axis (X; Y) perpendicular to the first horizontal axis (Z); a first workpiece holding device arranged on the first column , the first workpiece holding device being arranged for controlled displacement (Z3) in relation to the first column in parallel with the first horizontal axis (Z); a second workpiece holding device arranged on the second column ; wherein the first workpiece holding device and the second workpiece holding device are arranged for supporting a workpiece between them and for controlled rotation (C1, C2) of the workpiece around a workpiece axis parallel with the first horizontal axis (Z); and wherein the machine comprises a drive system for: - controlled positioning of the first column in relation to the second column , in parallel with the first horizontal axis (Z), and - controlled positioning of the first workpiece holding device in relation to the first column , in parallel with the first horizontal axis (Z). - controlled positioning of the first column in relation to the second column , in parallel with the first horizontal axis (Z), and - controlled positioning of the first workpiece holding device in relation to the first column , in parallel with the first horizontal axis (Z). <EOS>