Machining device for workpiece machining, comprising: a machining head for machining a workpiece at a machining point, a main body on which the machining head is mounted, and three connecting devices (18, 19, 20) for connecting the main body to the machining head, said connecting devices (18, 19, 20) each being connected to the main body in a pivotable manner about mutually parallel first pivot axes via first articulated joints (21a,b, 22a,b, 23a,b) and each being connected to the machining head in a pivotable manner about second pivot axes, parallel to the first pivot axes, via second articulated joints (24a,b, 25a,b, 26a,b), wherein, in order to position the machining head at a defined angle of rotation (α) with respect to an axis of rotation that is parallel to the first and second pivot axes (S1, S2) and contains the machining point, the positions of the second articulated joints (24a,b, 25a,b, 26a,b) are settable in a plane (X Z, Z Z) perpendicular to the axis of rotation, wherein each connecting device (18, 19, 20) has two rod-like connecting elements (18a,b 19a,b, 20a,b) which are each attached to the main body via a first articulated joint in the form of a first ball joint or universal joint (21a, 21b; 22a, 22b; 23a, 23b) and which are each attached to the machining head via a second articulated joint (24a,b, 25a,b, 26a,b) in the form of a second ball joint or universal joint (24a, 24b, 25a, 25b, 26a, 26b), characterized in that, for the parallel displacement of the machining head in the direction of the axis of rotation, the positions of the first ball joints or universal joints (22a, 22b) of the rod-like connecting elements (19a, 19b) of one of the connecting devices are settable independently of one another. a machining head for machining a workpiece at a machining point, a main body on which the machining head is mounted, and three connecting devices (18, 19, 20) for connecting the main body to the machining head, said connecting devices (18, 19, 20) each being connected to the main body in a pivotable manner about mutually parallel first pivot axes via first articulated joints (21a,b, 22a,b, 23a,b) and each being connected to the machining head in a pivotable manner about second pivot axes, parallel to the first pivot axes, via second articulated joints (24a,b, 25a,b, 26a,b), wherein, in order to position the machining head at a defined angle of rotation (α) with respect to an axis of rotation that is parallel to the first and second pivot axes (S1, S2) and contains the machining point, the positions of the second articulated joints (24a,b, 25a,b, 26a,b) are settable in a plane (X Z, Z Z) perpendicular to the axis of rotation, wherein each connecting device (18, 19, 20) has two rod-like connecting elements (18a,b 19a,b, 20a,b) which are each attached to the main body via a first articulated joint in the form of a first ball joint or universal joint (21a, 21b; 22a, 22b; 23a, 23b) and which are each attached to the machining head via a second articulated joint (24a,b, 25a,b, 26a,b) in the form of a second ball joint or universal joint (24a, 24b, 25a, 25b, 26a, 26b), characterized in that, for the parallel displacement of the machining head in the direction of the axis of rotation, the positions of the first ball joints or universal joints (22a, 22b) of the rod-like connecting elements (19a, 19b) of one of the connecting devices are settable independently of one another.