Closed form solution for direct kinematics of a 4PUS + 1PS parallel manipulator

This paper presents the direct kinematics solution of a 4PUS + 1PS parallel manipulator. The mechanism consists of a fixed base and moving platform connected by five serial chains. The solution of its direct kinematics yields an eighth-degree polynomial in a single variable, which indicates that there may be up to eight different configurations for the moving platform for a given set of joint variables. A numerical example with eight real solutions is included. Therefore, the polynomial is minimal.