The assembly comprises: 1) a socket subassembly having an unitary elongated body, including at one extremity a first engaging cavity, at an opposite extremity, a second engaging cavity: and incorporating an externally open, annular channel provided between the extremities of the socket subassembly: 2) a strain transducer subassembly, for measuring torsional strains on the socket subassembly, mounted in the externally open annular channel: 3) a circular cover attached to the socket subassembly for enclosing the externally open, annular channel: and 4) an electronic subassembly for converting the torsional strains on the socket subassembly to standard torque values and for determining tightening angular displacements by means of a sensor: the electronic subassembly being interconnected to the strain transducer subassembly and mounted on the circular cover to face the strain transducer subassembly.