This paper focuses on geometric methods for generating rational motions used in the design of single-loop rational linkages, 1-degree-of-freedom mechanisms that can execute prescribed spatial tasks. Building on established rational motion synthesis methods, we introduce a new interpolation scheme for seven 3D points based on cubic quaternionic Bezier curves. The resulting motion admits factorization, i.e. the synthesis of a spatial six-bar mechanism whose tool frame passes the specified seven points. To support engineering practice, we provide open-source CAD tools that implement also the other methods and provide fast visual evaluation of motion generation and mechanism synthesis.

翻译：本文聚焦于生成有理运动的几何方法，用于设计单回路有理连杆机构——一种能够执行预定空间任务的单自由度机构。在现有有理运动综合方法的基础上，我们提出了一种基于三次四元数贝塞尔曲线的七个三维点插值新方案。所得运动允许进行因式分解，即综合出一个其工具坐标系可通过指定七个点的空间六杆机构。为支持工程实践，我们提供了开源CAD工具，该工具也实现了其他方法，并能对运动生成与机构综合进行快速可视化评估。