The invention relates to a fewer-degree-of-freedom robot mechanism. The aim of the invention is to provide a mechanism which has the characteristic of improved rigidity and bearing capacity. The invention adopts a technical scheme that the high-rigidity redundantly-actuated three-degree-of-freedom parallel mechanism comprises a dynamic platform, a machine frame, a first branch, a second branch and a third branch, wherein each of the first branch and the second branch is connected with a first single-degree-of-freedom kinematic pair, a second single-degree-of-freedom kinematic pair and a universal hinge in turn. The fewer-degree-of-freedom robot mechanism is characterized in that: the third branch is divided into two parallel branch chains; each branch chain is connected with the first single-degree-of-freedom kinematic pair, the second single-degree-of-freedom kinematic pair and a rotation pair in turn; the first rotation axis line of the universal hinge of the first branch and the first rotation axis line of the universal hinge of the second branch are in the same line and pass through the central point of the T-shaped hinge of the third branch; and the first rotation axis line of the T-shaped hinge of the third branch is vertical or parallel to the rotation axis line of the universal hinge of the first branch and the rotation axial line of the universal hinge of the second branch.