Systematic Elastostatic Stiffness Model of Over-Constrained Parallel Manipulators Without Additional Constraint Equations

The establishment of an elastostatic stiffness model for over constrained parallel manipulators(PMs),particularly those with over constrained subclosed loops,poses a challenge while ensuring numerical stability.This study addresses this issue by proposing a systematic elastostatic stiffness model based on matrix structural analysis(MSA)and independent displacement coordinates(IDCs)extraction techniques.To begin,the closed-loop PM is transformed into an open-loop PM by eliminating constraints.A subassembly element is then introduced,which considers the flexibility of both rods and joints.This approach helps circumvent the numerical instability typically encountered with traditional constraint equations.The IDCs and analytical constraint equations of nodes constrained by various joints are summarized in the appendix,utilizing multipoint constraint theory and singularity analysis,all unified within a single coordinate frame.Subsequently,the open-loop mechanism is efficiently closed by referencing the constraint equations presented in the appendix,alongside its elastostatic model.The proposed method proves to be both modeling and computationally efficient due to the comprehensive summary of the constraint equations in the Appendix,eliminating the need for additional equations.An example utilizing an over constrained subclosed loops demonstrate the application of the proposed method.In conclusion,the model proposed in this study enriches the theory of elastostatic stiffness modeling of PMs and provides an effective solution for stiffness modeling challenges they present.

Free Vibration Analysis of Rectangular Plate with Cutouts under Elastic Boundary Conditions in Independent Coordinate Coupling Method

Based on Kirchhoff plate theory and the Rayleigh-Ritz method,the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved Fourier series in combination with the independent coordinate coupling method(ICCM).The effect of the cutout is taken into account by subtracting the energies of the cutouts from the total energies of the whole plate.The vibration displacement function of the hole domain is based on the coordinate system of the hole domain in this method.From the continuity condition of the vibration displacement function at the cutout,the transition matrix between the two coordinate systems is constructed,and the mass and stiffness matrices are completely obtained.As a result,the calculation is simplified and the computational efficiency of the solution is improved.In this paper,numerical examples and modal experiments are presented to validate the effectiveness of the modeling methods,and parameters related to influencing factors of the rectangular plate are analyzed to study the vibration characteristics.

Antenna system characteristics and solar radio burst observations

The Chinese Spectral Radio Heliograph（CSRH） is an advanced aperture synthesis solar radio heliograph, independently developed by National Astronomical Observatories, Chinese Academy of Sciences. It consists of 100 reflector antennas,which are grouped into two antenna arrays（CSRH-I and CSRH-II） for low and high frequency bands respectively. The frequency band of CSRH-I is 0.4–2 GHz and that for CSRH-II is 2–15 GHz. In the antenna and feed system, CSRH uses eleven feeds to receive signals coming from the Sun. The radiation pattern has a lower side lobe and the back lobe of the feed is well illuminated. The characteristics of gain G and antenna noise temperature T affect the quality of solar radio imaging. For CSRH, the measured G is larger than 60 d Bi and T is less than 120 K. After CSRH-I was established, we successfully captured a solar radio burst between 1.2–1.6 GHz on 2010 November12 using this instrument and this event was confirmed through observations with the Solar Broadband Radio Spectrometer at 2.84 GHz and the Geostationary Operational Environmental Satellite. In addition, an image obtained from CSRH-I clearly revealed the profile of the solar radio burst. The other observational work involved the imaging the Fengyun-2E geosynchronous satellite which is assumed to be a point source.Results indicate that the data processing method applied in this study for deleting errors in a noisy image could be used for processing images from other sources.