Type synthesis of deployable and symmetrical single-loop mechanisms for constructing aerospace platforms

This paper presents a general synthesis method for 1-DOF single-loop mechanisms (SLMs). This method divides an SLM into two portions: one is a revolute pair and another is a branch chain consisting of several kinematic pairs. The core idea is to design several kinematic pairs in the branch chain without constraining the rotation of the revolute pair. First, the constraint line graph of this revolute pair is drawn. The constraints of the branch chain are classified according to the equivalent constraint line graph of this revolute pair. Subsequently, the synthesis schemes corresponding to these constraints are formulated. Deployable and symmetrical SLMs are constructed, which include not only novel SLMs such as R_S1P₁R_S3R_S2P₂R, and R_c1R_c2PR_c2′R_c1′, but also classical SLMs such as Bennett and Bricard SLMs. It verifies the feasibility and effectiveness of the method. Finally, based on the overconstrained SLMs, another approach for obtaining more deployable non-overconstrained SLMs is proposed. By this approach, some non-overconstrained 7R SLMs are also obtained. Three examples are given to illustrate the potential applications of the obtained SLMs.