Abstract: Based on the Lie group and Lie algebra theory, type synthesis for 3-DOF translational parallel mechanisms is investigated systematically. Twist systems representing the subalgebra of displacement subgroup of T and X(w) are proposed. Several limb kinematic chains which can produce the displacement subgroup of X(w) are obtained through linear combination of the twists. According to the geometrical condition that guar-antees the intersection of several displacement subgroups of X(w) is the displacement subgroup of T, several novel 3-DOF translational parallel mechanisms are constructed, which testifi-es the results of type synthesis obtained before by structural constraint method.

Key words: Design theory, Lie algebra, Lie group, Parallel mechanism