This paper proposes the nonsingular design principle, which can completely eliminate constraint/ actuation singularity in parallel mechanism (PM), and accordingly designs a nonsingular redundant 2RPSUPU?2SPS (R: revolute joint, P: actuated prismatic joint, S: spherical joint, U: universal joint) leg mechanism with R^x R^y T^z DOF (R^x : rotational DOF around x, R^y : rotational DOF around y, T^z : translational DOF along z, DOF: degree of freedom). Aiming at the defect that the conventional Jacobian matrix cannot reveal the linear correlation/noncorrelation between the constraint screws of the PM, the determination criteria of constraint and actuation singularity are derived and the design principle of redundantly actuated PM eliminating constraint/actuation singularity is constructed according to the reciprocal screw principle. Based on this, the design process of parallel leg mechanism without singularity is put forward. Finally, by analyzing the rank of complete Jacobian matrix composed of constraint Jacobian matrix and secondary constraint Jacobian matrix, it is verified that the redundant parallel leg mechanism in this paper can completely eliminate constraint singularity and actuation singularity. The research results make a necessary positive contribution for motion planning, optimizationsolving of forward kinematics parameters, dimensional synthesis and motion control of nonsingular parallel leg mechanism.