Research on dexterity of a redundant parallel machine applied in multi-facet drill grinding

Multi-facet drills (MFDs) offer significant advantages for machining difficult-to-process materials, though their complex drill point geometry imposes stringent dexterity requirements on grinding machines. This research presents a novel solution using redundant parallel machines (RPMs) for drill grinding. We first establish the kinematic model of a (6 + k)-degree-of-freedom (DOF) RPM and derive its Jacobian matrix. For the (6 + 1)-DOF RPM configuration, we propose the orthogonal number as a new singularity evaluation index. This parameterized index enables bidirectional mapping between pose configuration and grinding dexterity, allowing direct optimization of redundant actuation for singularity avoidance. Comparative simulations confirm the orthogonal number’s equivalence to the conventional condition number in pose singularity evaluation. By referring to manual MFD grinding processes, we develop an RPM-adapted grinding scheme with detailed grinder-drill coordinate transformations. Simulations with a 7 × 7 MFD array demonstrate that increasing RPM redundancy (from 6-DOF to (6 + 3)-DOF) reduces condition numbers significantly while enhancing grinding dexterity, providing crucial insights for batch MFD production.