[en] This paper deals with the counterweight optimization of an asymmetrical hybrid machine tool based on dynamic isotropy. The dynamic model is derived and the dynamic manipulability ellipsoid is studied. Based on dynamic manipulability ellipsoid, the dynamic isotropy is defined. Counterweight block and fluid counterweight are presented to balance the weight of moving parts. The mass of the counterweight block is optimized to obtain the maximum dynamic isotropy in the workspace. The dynamic isotropy of the machine tool after counterweight optimization is compared with that before counterweight optimization. Furthermore, the dynamic isotropy of the machine tool with fluid counterweight is investigated and compared with that of the machine tool with counterweight block.

[en] This paper presents the dynamic analysis of a flexure-based compliant stage. The dynamic model is first obtained, after which the equivalent masses of the flexure hinge, including the axial equivalent mass, the bending equivalent mass, and the shear equivalent mass, are derived. According to this method, the equivalent mass components of the proposed stage are derived by accumulating those of the output platform, input platform, and flexure hinges. Finally, to verify the validity of the proposed method, the first two resonant frequencies and the corresponding mode shapes are analyzed by using finite element analysis (FEA). An experimental platform is fabricated, and experimental results and FEA values appear to be in accordance with the theoretical calculations. This result demonstrates that the dynamic model and equivalent mass are accurate. The dynamic model provides an effective method for calculating equivalent masses, and dynamic characteristics can be precisely estimated from the corresponding analytical models.