The invention relates to a joint variable-rigidity mechanism, in particular to a variable-rigidity mechanism based on geometrical features. The variable-rigidity mechanism aims to solve the problems that an existing variable-rigidity mechanism is complex in structure and poor in linearity, gaps and friction exist between the mechanism and a rod when the mechanism moves through a fulcrum, and consequently the position precision is low. The variable-rigidity mechanism comprises an output rod, a rigidity adjusting inner gear ring, a fulcrum gear, a fulcrum frame, a fulcrum bar, a middle rod, a spring, a shaft sleeve and two sliding blocks, wherein the sliding blocks are arranged at the two ends of the middle rod correspondingly, the spring is arranged on the middle rod located between the two sliding blocks in a sleeving mode, the shaft sleeve is arranged between the sliding blocks and the middle rod in a sleeving mode, and the shaft sleeve is axially positioned through bearing end covers arranged on the sliding blocks; and the fulcrum gear is engaged with the rigidity adjusting inner gear ring, and the fulcrum gear is arranged below the fulcrum frame and detachably connected with the fulcrum frame. The variable-rigidity mechanism is applied to a robot elbow joint.