A vertebral rod piece connecting device includes a first connecting rod having at least one end as a joining end, in which the outer side of the joining end near the rod end is substantially spheral shaped, and the rod end has a contact surface a second connecting rod having at least one end as a joining end, in which the outer side of the joining end near the rod end is substantially spheral shaped, and the rod end has a contact surface a ring gasket arranged between the first connecting rod and the second connecting rod, in which the ring gasket is respectively matcheed with the contact surface of the first connecting rod and the contact surface of the second connecting rod a first connecting cup having a connection mechanism at the cup opening edge, in which the inner side of the cup bottom is substantially spheral shaped, and the curvature of the spheral shape is slightly smaller or substantially equal to the curvature of the spheral shape of the outer side of the joining end of the first connecting rod for being universally joined with the spheral shape of the first connecting rod near the rod end, and the cup bottom has a through hole for allowing the end of the first connecting rod to penetrate outside from inside of the cup and, a second connecting cup having a connection mechanism at the cup opening edge, in which the inner side of the cup bottom is at least partially substantially spheral shaped, and the curvature of the spheral shape is slightly smaller or substantially equal to the curvature of the spheral shape of the outer side of the joining end of the second connecting rod near the rod end for being universally joined with the spheral shape of the second connecting rod near the rod end, and the cup bottom has a through hole for allowing the rod end of the second connecting rod to extend outside from inside of the cup, in which the connection mechanism at the cup opening edge of the first connecting cup and the connection mechanism at the cup opening
