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One important category of parallel mechanisms is the translational parallel mechanism (TPM). This paper focuses on the structural shakiness of the non overconstrained TPM. Such a structural shakiness is due to the unavoidable lack of rigidity of the real bodies, which leads to uncheckable orientation changes of the moving platform of a TPM. Using algebraic properties of displacement subsets and, especially, displacement Lie subgroup theory, we show that the structural shakiness of the non overconstrained TPM is inherently determined by the structural type of its limb chains. A structural shakiness index (SSI) for a non overconstrained TPM is introduced. When the set of feasible displacements of the end body of a 5-degree-of-freedom (DOFs) limb chain contains two infinities of parallel axes of rotation, we have SSI = 2; when the displacement set of the end body of a 5-DOF limb chain contains only one infinity of parallel axes of rotation, we have SSI = 1. It is proven that non over con stained TPMs constructed with limb chains with SSI = 1 are much less prone to orientation changes than those constructed with limb chains with SSI = 2. Based on the SSI, we enumerate limb kinematic chains and construct 21 non overconstrained TPMs with less shakiness.