This paper presents a new method for analyzing the limb singularities of lower-mobility parallel manipulators using the superbracket of Grassmann-Cayley algebra. For lower-mobility limbs, the limb twist system does not form a 6 × 6 matrix. The proposed method allows forming a Jacobian matrix, and thus, a superbracket for any lower-mobility limb by adding twists that correspond to the limb's constrained motion(s). The method is applied to four-and five-degrees of freedom limbs.