A circular knitting machine for knitwear or hosiery, comprising: - a bearing structure; - at least a needle-bearing organ or needle cylinder rotatably mounted in the bearing structure and rotatable selectively, by means of rotation means of the cylinder, about a rotation axis of the needle-bearing cylinder; - a plurality of needles supported by the needle cylinder and mobile parallel to a rotation axis of the needle cylinder so as to produce a knitted fabric; - a dial group arranged above the needle cylinder and comprising: - a support ring solidly constrained to the bearing structure and coaxial to the needle cylinder; - a hook support organ, or hook plate, bearing a plurality of hooks, the hook plate being rotatably mounted to the support plate in such a way as to rotate about a respective rotation axis coinciding with the rotation axis of the needle cylinder; - a thread transport and cutting organ, or cutter, mounted externally of the support plate and solidly constrained to the hook plate, in such a way as to rotate together with the plate; the knitting machine further comprising rotation transmission means, housed in the bearing structure and operatively interposed between the needle cylinder and the dial group, configured for transmitting a rotation, generated by said rotation means of the cylinder, synchronously to the hook plate, such that a determined rotation of the hook plate corresponds to a same rotation of the needle cylinder, the rotation transmission means comprising: - a drive pulley receiving a rotary motion from the cylinder rotation means and rotating, synchronously with respect to the needle cylinder, about a first rotation axis; - a hook plate shaft, coaxially mounted to the hook plate and configured so as to transmit a rotation to the hook plate; - a flange, configured so as to transmit a rotary motion to the shaft of the hook plate, operatively interposed between the pulley and the hook shaft and positioned at the pulley, the flange being able to rotate about the first rotation axis; the knitting machine being characterized in that the rotation transmission means comprises an engaging mechanism operatively interposed between the pulley and the flange and configured for selectively operating at least between an engaged configuration, in which it constrains the pulley and the flange to one another, determining a synchronous transmission of the rotary drive of the pulley to the flange and from the flange to the hook plate shaft, and a disengaged configuration, in which the flange is free from constraints with respect to the pulley and the rotary motion of the pulley is not transmitted to the flange, wherein the engaging mechanism comprises at least an engaging organ movable, between the pulley and the flange, in a direction which is parallel to, or transversally or perpendicularly intersecting, the first rotation axis of the pulley and the flange, between at least an engaged position and a disengaged position so as to determine passage of the engaged mechanism respectively between the engaged position and the disengaged position, and wherein the engaging mechanism comprises actuating means operatively active on the engaging organ and configured for enabling the passage of the engaging mechanism from the engaged configuration to the disengaged configuration in any angular position assumed by the flange or the pulley, and for determining the passage of the engaging mechanism from the disengaged configuration to the engaged configuration exclusively with the engaging organ positioned at a predetermined and limited number of angular engaging and disengaging positions defined on the flange or the pulley. - a bearing structure; - at least a needle-bearing organ or needle cylinder rotatably mounted in the bearing structure and rotatable selectively, by means of rotation means of the cylinder, about a rotation axis of the needle-bearing cylinder; - a plurality of needles supported by the needle cylinder and mobile parallel to a rotation axis of the needle cylinder so as to produce a knitted fabric; - a dial group arranged above the needle cylinder and comprising: - a support ring solidly constrained to the bearing structure and coaxial to the needle cylinder; - a hook support organ, or hook plate, bearing a plurality of hooks, the hook plate being rotatably mounted to the support plate in such a way as to rotate about a respective rotation axis coinciding with the rotation axis of the needle cylinder; - a thread transport and cutting organ, or cutter, mounted externally of the support plate and solidly constrained to the hook plate, in such a way as to rotate together with the plate; the knitting machine further comprising rotation transmission means, housed in the bearing structure and operatively interposed between the needle cylinder and the dial group, configured for transmitting a rotation, generated by said rotation means of the cylinder, synchronously to the hook plate, such that a determined rotation of the hook plate corresponds to a same rotation of the needle cylinder, - a drive pulley receiving a rotary motion from the cylinder rotation means and rotating, synchronously with respect to the needle cylinder, about a first rotation axis; - a hook plate shaft, coaxially mounted to the hook plate and configured so as to transmit a rotation to the hook plate; - a flange, configured so as to transmit a rotary motion to the shaft of the hook plate, operatively interposed between the pulley and the hook shaft and positioned at the pulley, the flange being able to rotate about the first rotation axis;