Abstract. This paper presents the output decoupling property of planar flexure-based compliant mechanisms with symmetric configuration. Compliance/stiffness modeling methods for flexure serial structures and flexure parallel structures are first derived according to the matrix method. Analytical model of mechanisms with symmetric configuration is then developed to analyze the output decoupling property. The proposed analytical model shows that mechanisms are output decoupled when they are symmetry about two perpendicular axes or when they are composed of either three or an even number of identical fundamental forms distributed evenly around the center. Finally, output compliances of RRR and 4-RRR compliant micro-motion stages are derived from the analytical model and finite element analysis (FEA). The comparisons indicate that the results obtained from the proposed analytical model are in good agreement with those derived from FEA, which validates the proposed analytical model.

We report the evolution of the X-ray pulsations of EXO 2030+375 during its 2021 outburst using the observations from Insight-HXMT. Based on the accretion torque model, we study the correlation between the spin frequency derivatives and the luminosity. Pulsations can be detected in the energy band of 1-160 keV. The pulse profile evolves significantly with luminosity during the outburst, leading to that the whole outburst can be divided into several parts with different characteristics. The evolution of the pulse profile reveals the transition between the super-critical (fan-beam dominated) and the sub-critical accretion (pencil-beam dominated) mode. From the accretion torque model and the critical luminosity model, based on a distance of 7.1 kpc, the inferred magnetic fields are (0.41 − 0.74) × 10 12 G and (3.48 − 3.96) × 10 12 G, respectively, or based on a distance of 3.6 kpc, the estimated magnetic fields are (2.4 − 4.3) × 10 13 G and (0.98 − 1.11) × 10 12 G, respectively. Two different sets of magnetic fields both support the presence of multipole magnetic fields of the NS.