Computer-Aided Design of Rational Motions for 4R and 6R Spatial Mechanism Synthesis

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.