Type synthesis of two degrees-of-freedom rotational parallel mechanisms with a fixed center-of-rotation based on a graphic approach

Mechanisms usually have to be particularly designed to meet the high-performance requirements in terms of different applications. For instance, Two degrees of freedom (DOF) rotational parallel mechanisms (RPMs) with a fixed center-of-rotation can eliminate parasitic motion and could provide the rotary stage with excellent dynamic stability, good controllability and easy operation. Therefore, this paper mainly aims at synthesizing 2-DOF RPMs with fixed center-of-rotation, a class of special RPMs with potential excellent performances. A graphic approach based on freedom and constraint spaces is introduced firstly. The constraint spaces of a class of the existing 2-DOF RPMs are illustrated, and the corresponding type synthesis patterns are summarized by comparing the geometric properties of those spaces with the mechanism characteristic. After fully decomposing the four-dimensional constraint space into sub-constraint spaces, a general type synthesis procedure is proposed based on the freedom and constraint topology. Two novel 2-DOF RPMs with fixed center-of-rotation are constructed based on the proposed method and procedure. The proposed graphic approach proves to be effective and simple to synthesizing those parallel mechanisms with some special performance.