This paper proposes a 1CS-4SS spatial linkage and presents the solution region synthesis methodology for six specified positions. Firstly, synthesis equations of the SS dyads and the CS dyad are proposed, the discrete solutions of the CS dyad are obtained by Bertini numerical method. The 1CS-4SS spatial linkage are obtained by selecting four SS dyads on the solution curves of the SS dyad and one CS dyad on the discrete solutions of the CS dyad. We display all solutions of linkages in a plane, which is called the solution region. Secondly, The Jacobian matrix is deduced to determinate the defective linkages. The Bertini numerical method and Groebner basis method are used for position analysis of the linkages, and the analysis results from the two methods are compared and mutually verified. The feasible solution region can be obtained after eliminating defective linkages and linkages that fail to satisfy the other requirements from the solution region plane. Finally, the validity of the formulas and applicability of the proposed approach are illustrated by an example.

本文提出了一个1CS-4SS空间链接，并提出了六个指定位置的解决方案区域综合方法。首先，提出了SS二元组和CS二元组的合成方程，并通过Bertini数值方法得到了CS二元组的离散解。通过在SS dyad的解曲线上选择四个SS dyad和在CS dyad的离散解上选择一个CS dyad，可以获得1CS-4SS空间链接。我们在平面上显示链接的所有解，这称为解区域。其次，推导雅可比矩阵以确定有缺陷的连接。使用Bertini数值方法和Groebner基方法对连杆进行位置分析，并将两种方法的分析结果进行比较并相互验证。在从缺陷区域平面消除有缺陷的连接和不能满足其他要求的连接之后，可以获得可行的溶液区域。最后，通过一个例子说明了公式的有效性和所提出方法的适用性。