🤖 AI Summary
This work proposes a novel seven-point interpolation method based on cubic quaternion Bézier curves for the kinematic synthesis of single-degree-of-freedom spatial linkages, such as 4R and 6R mechanisms. The approach generates rational motions that are inherently factorizable, enabling the exact realization of spatial six-bar linkages passing through seven prescribed 3D poses. For the first time, rational motion design is integrated with factorization techniques to ensure the resulting motion can be decomposed into mechanical linkages. The method has been implemented in an open-source CAD tool developed by the authors, facilitating efficient visual evaluation and practical engineering applications. This integration significantly enhances the automation and usability of spatial mechanism synthesis, offering a robust framework for precision motion generation in spatial linkage design.
📝 Abstract
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.