提出了少自由度并联机构基于李群理论的位移流形综合理论.给出了全部9类少自由度并联机构的机构位移流形,分支位移流形和保证所有分支位移流形之交集为期望机构位移流形的几何条件.利用位移子群乘法运算的封闭性,可得到不同结构的分支运动链.使用这些分支运动链,满足相应几何条件即可构建出具有期望自由度的并联机构,并且其优点是无需判别机构的瞬时性,依据此原理可以进一步根据多方面的实际需要综合新的机型. A synthesis theory of displacement manifolds based on Lie group theory is proposed for less-degree-of-freedom parallel mechanism. The displacement manifolds, branch displacement manifolds and intersection of all branch displacement manifolds for all nine degrees of freedom DOFs are given The geometrical conditions of the displacement manifold of the mechanism can be obtained by using the closure of the multiplication of displacement subgroups, Its advantage is no need to judge the instantaneous mechanism, according to this principle can be further based on the actual needs of many new models.