A linear mechanical transmission comprising: - a containment structure; - a roto-translational element extending along an axis of rotation and comprising a first threaded portion and a second threaded portion, said roto-translational element being configured to translate along said axis and simultaneously rotate about said axis; - a rotary element connected or connectable to a drive unit to define a mechanical power input unit and equipped with a first thread designed to engage rotatably with said first threaded portion of said roto-translational element, in particular by means of a lead nut and screw or recirculating ball or roller coupling, in such a way as to define a first threaded connection (3, 8); - a fixed guide, in particular forming part of said containment structure, having a second thread designed to engage with said second threaded portion of said roto-translational element in such a way as to define a second threaded connection (4, 14); - a translating element, translating along said axis and defining a power output unit, said translating element being connected to the roto-translational element for translating at the same linear speed as the roto-translational element; wherein said roto-translational element is simultaneously coupled to the rotary element and to the fixed guide, respectively, by means of said first and second threaded connections (3, 8; 4, 14) and wherein said first and second threaded connections (3, 8; 4, 14) have different pitches in such a way as to vary the angular speed between the roto-translational element and the rotary element; characterized in that the translating element is connected to the roto-translational element by one or more ball bearings or by one or more circumferential rows of balls or by one or more roller bearings for achieving a free rotation, and at the same time an axial connection, between the translating element and the roto-translational element. - a containment structure; - a roto-translational element extending along an axis of rotation and comprising a first threaded portion and a second threaded portion, said roto-translational element being configured to translate along said axis and simultaneously rotate about said axis; - a rotary element connected or connectable to a drive unit to define a mechanical power input unit and equipped with a first thread designed to engage rotatably with said first threaded portion of said roto-translational element, in particular by means of a lead nut and screw or recirculating ball or roller coupling, in such a way as to define a first threaded connection (3, 8); - a fixed guide, in particular forming part of said containment structure, having a second thread designed to engage with said second threaded portion of said roto-translational element in such a way as to define a second threaded connection (4, 14); - a translating element, translating along said axis and defining a power output unit, said translating element being connected to the roto-translational element for translating at the same linear speed as the roto-translational element; wherein said roto-translational element is simultaneously coupled to the rotary element and to the fixed guide, respectively, by means of said first and second threaded connections (3, 8; 4, 14) and wherein said first and second threaded connections (3, 8; 4, 14) have different pitches in such a way as to vary the angular speed between the roto-translational element and the rotary element; characterized in that the translating element is connected to the roto-translational element by one or more ball bearings or by one or more circumferential rows of balls or by one or more roller bearings for achieving a free rotation, and at the same time an axial connection, between the translating element and the roto-translational element.