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This paper presents a non-smooth multibody dynamic formulation and error analysis of an antenna pointing mechanism including frictional spatial revolute joints (FSRJs) with small clearance in the framework of the special Euclidian group SE(3). The formulation leads to an inertial frame-invariant, a compact and unified description for rigid bodies and spatial revolute joints (SRJs). The geometric constraint of the bearing is covered by four open semi-cylinders, which can be treated as bilateral constraints assuming that the impact effects are negligible. The frictional contact problem is formulated as a horizontal linear complementary problem (HLCP), which is embedded in the Lie-group integration scheme. Error of the antenna pointing mechanism is modeled by means of the adjoint transformation and POE-based formula. The evolution of errors is obtained through the solution of non-smooth dynamics. The obtained numerical results illustrate the influences of FSRJs in dynamics modeling and error analysis of the antenna pointing mechanism.

Accuracy of the fitted surface is of great importance to the performance of deployable antennas utilized in space. This paper proposes a stiffness analysis based fitting accuracy optimization method for achieving the optimal parameters of the parabolic cylindrical deployable antenna mechanism. The stiffness matrix of the proposed cylindrical antenna mechanism is established by assembling the stiffness of beams and tension cables. Structural deformations of the mechanism are calculated where the tensioned cable is substituted by a 2-node truss element and an equivalent force acting on the joint. Consideration of the tensity of tension cables, namely tensioned or slack, is transformed into a typical linear complementarity problem. Comparison between structural deformations of the mechanism fixed at different points is performed. Sensitivities of the geometric and structural parameters on fitting accuracy are investigated. Influence of force of the driven cable on structural deformations of antenna operated in different orbits is conducted. A fitting optimization method is proposed to minimize the structural deformations subject to constraints on volume and mass. Simulation result shows that the fitting accuracy of the antenna mechanism is improved significantly through the optimization. The proposed method can be utilized for the optimal design of other deployable mechanisms constructed by joining rigid links.

In extreme ultraviolet (EUV) sources, small tin droplets are scattered into the tin mist/disk under the irradiation of the pulsed laser to produce the EUV light. Small droplet size and large droplet spacing are required to suppress debris production to protect expensive collector mirrors. To this end, a tin-droplet generator with a capillary glass nozzle was designed and built to produce uniform tin-droplet streams with the droplet diameter less than 50 μm. Meanwhile, a forced perturbation, generated by a sandwich piezoelectric transducer, was loaded into a liquid tin jet to manipulate the droplet spacing through a stepped rod. The mono-sized tin-droplet streams with an average diameter of 42 μm were successfully produced in both the Rayleigh and the forced jet breakup regimes. A two-dimensional (2D) axisymmetric model was proposed to reveal the influence of the velocity perturbation amplitude on jet breakup patterns at different wavelengths. An F*– λ* (The dimensionless perturbation velocity amplitude F*–The dimensionless wavenumber l*) map was built, and five different droplet breakup patterns were identified based on simulations. Numerical simulations indicated that the droplet spacing could be increased by providing extra momentum to droplets from the forced velocity perturbation. Finally, by increasing the velocity perturbation amplitude, the droplet spacing was increased from ∼9 Dd (droplet diameter) to ∼19 Dd without significantly increasing the droplet size. This work provides a novel approach to obtaining small mono-sized tin-droplet streams with manipulable droplet spacing.