In this article, our recent work on a kind of 2-degree-of-freedom lower-mobility parallel mechanism, which has one rotation degree of freedom and one translational degree of freedom, used in multilayer garage is presented. It has the following characteristics: lower-mobility, non-symmetric structure but can realize symmetric movement and a good compatibility for different kinds of lifting work. Kinematic performance should be considered in the first of designing a new kind of mechanism, the optimal kinematic design and analysis of this lower-mobility parallel mechanism are primarily investigated. In process of study, the global conditioning index over workspace is adopted, we establish a new evaluation method for the lower-mobility parallel mechanism, called global symmetry index and simulation results are shown. In addition, the flexible workspace of this lower-mobility parallel mechanism is also proposed. The evaluation index can be also applied on other lower-mobility parallel mechanism, which needs steady and symmetric movement.