This paper presents a new method for analysing 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.