This paper deals with the design and kinematic analysis of a novel mechanism for the elbow joint of an upper-limb exoskeleton, with the aim of helping operators, in terms of effort and physical resistance, in carrying out heavy operations. In particular, the proposed eight-bar elbow joint exoskeleton mechanism consists of a motorized Watt I six-bar linkage and a suitable RP dyad, which connects mechanically the external parts of the human arm with the corresponding forearm by hook and loop velcro, thus helping their closing relative motion for lifting objects during repetitive and heavy operations. This relative motion is not a pure rotation, and thus the upper part of the exoskeleton is fastened to the arm, while the lower part is not rigidly connected to the forearm but through a prismatic pair that allows both rotation and sliding along the forearm axis. Instead, the human arm is sketched by means of a crossed four-bar linkage, which coupler link is considered as attached to the glyph of the prismatic pair, which is fastened to the forearm. Therefore, the kinematic analysis of the whole ten-bar mechanism, which is obtained by joining the Watt I six-bar linkage and the RP dyad to the crossed four-bar linkage, is formulated to investigate the main kinematic performance and for design purposes. The proposed algorithm has given several numerical and graphical results. Finally, a double-parallelogram linkage, as in the particular case of the Watt I six-bar linkage, was considered in combination with the RP dyad and the crossed four-bar linkage by giving a first mechanical design and a 3D-printed prototype.