Type synthesis of lower-mobility parallel mechanisms is a hot and frontier topic in international academic and industrial field. Based on the Lie group theory, a displacement manifold synthesis method is proposed. For all the nine kinds of lower-mobility parallel mechanisms, the mechanism displacement manifold, limb displacement manifold and the geometrical conditions which guarantee that the intersection of the limb displacement manifold is the desired mechanism displacement manifold are enumerated. Various limb kinematic chains can be obtained using the product closure of displacement subgroup. Parallel mechanisms can be constructed with these limbs while obeying the geometrical conditions. Hence, all the nine kinds of lower-mobility parallel mechanisms can be synthesized using this method. Since displacement manifold deals with finite motion, the result mechanism of synthesis have full-cycle mobility. Novel architectures of lower-mobility parallel mechanisms can be obtained using this method.
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