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In order to solve the problem of stable jumping of micro robot, we design a special mechanism: elastic passive joint (EPJ). EPJ can assist in achieving smooth jumping through the opening-closing process when the robot jumps. First, we introduce the composition and operation principle of EPJ, and perform a dynamic modeling of the robot's jumping process. Then, in order to verify the effectiveness of EPJ in controlling the robot's smooth jump, we design a simulation experiment based on MATLAB. Through comparative experiments, it was proved that EPJ can greatly adjust the angular velocity of the robot and increase the jump distance of the robot. Finally, we analyze each parameter in EPJ and performs parameter optimization. After optimization, EPJ achieves a completely flip-free jump of the robot, laying an important foundation for improving the mobility of micro-robot.

The dependence of stellar magnetic activity on stellar parameters would be inspired by the chromospheric activity studies based on the large-scale spectroscopic surveys. The Ca II H and K lines are employed to construct indicators for assessing and studying the chromospheric activity of solar-like stars. We investigate the widely used bolometric and photospheric calibrated chromospheric activity index $R'_{\rm HK}$, derived from the method in the classic literature ($R'_{\rm HK,classic}$) and the method based on the PHOENIX model ($R'_{\rm HK,PHOENIX}$). Since the detailed stellar atmospheric parameters, effective temperature ($T_{\rm eff}$), surface gravity ($\log\,g$), and metallicity ([Fe/H]), are available for LAMOST, we estimate the chromospheric activity index $R'_{\rm HK,PHOENIX}$, along with the corresponding bolometric calibrated index $R_{\rm HK,PHOENIX}$, taking these parameters into account. We provide the database of the derived chromospheric activity parameters for 1,122,495 LAMOST LRS spectra of solar-like stars. Our calculations show that $\log\,R'_{\rm HK,PHOENIX}$ is approximately linearly correlated with $\log\,R'_{\rm HK,classic}$. The results based on our extensive archive support the view that the dynamo mechanism of solar-like stars is generally consistent with the Sun; and the value of solar chromospheric activity index is located at the midpoint of the solar-like star sample. We further investigate the proportions of solar-like stars with different chromospheric activity levels (very active, active, inactive and very inactive). The investigation indicates that the occurrence rate of high levels of chromospheric activity is lower among the stars with effective temperatures between $5600$ and $5900 \,{\rm K}$., Comment: 18 pages, 20 figures, accepted for publication in A&A

The distribution of stellar $\mathrm{H}\alpha$ chromospheric activity with respect to stellar atmospheric parameters (effective temperature $T_\mathrm{eff}$, surface gravity $\log\,g$, and metallicity $\mathrm{[Fe/H]}$) and main-sequence/giant categories is investigated for the F-, G-, and K-type stars observed by the LAMOST Medium-Resolution Spectroscopic Survey (MRS). A total of 329,294 MRS spectra from LAMOST DR8 are utilized in the analysis. The $\mathrm{H}\alpha$ activity index ($I_{\mathrm{H}{\alpha}}$) and the $\mathrm{H}\alpha$ $R$-index ($R_{\mathrm{H}{\alpha}}$) are evaluated for the MRS spectra. The $\mathrm{H}\alpha$ chromospheric activity distributions with individual stellar parameters as well as in the $T_\mathrm{eff}$ -- $\log\,g$ and $T_\mathrm{eff}$ -- $\mathrm{[Fe/H]}$ parameter spaces are analyzed based on the $R_{\mathrm{H}{\alpha}}$ index data. It is found that: (1) for the main-sequence sample, the $R_{\mathrm{H}{\alpha}}$ distribution with $T_\mathrm{eff}$ has a bowl-shaped lower envelope with a minimum at about 6200 K, a hill-shaped middle envelope with a maximum at about 5600 K, and an upper envelope continuing to increase from hotter to cooler stars; (2) for the giant sample, the middle and upper envelopes of the $R_{\mathrm{H}{\alpha}}$ distribution first increase with a decrease of $T_\mathrm{eff}$ and then drop to a lower activity level at about 4300 K, revealing different activity characteristics at different stages of stellar evolution; (3) for both the main-sequence and giant samples, the upper envelope of the $R_{\mathrm{H}{\alpha}}$ distribution with metallicity is higher for stars with $\mathrm{[Fe/H]}$ greater than about $-1.0$, and the lowest-metallicity stars hardly exhibit high $\mathrm{H}\alpha$ indices. A dataset of $\mathrm{H}\alpha$ activity indices for the LAMOST MRS spectra analyzed is provided with this paper., Comment: 32 pages, 12 figures, 1 table, accepted for publication in Astrophysics and Space Science

$\require{mediawiki-texvc}$A stellar chromospheric activity database of solar-like stars is constructed based on the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) Low-Resolution Spectroscopic Survey (LRS). The database contains spectral bandpass fluxes and indexes of Ca II H&K lines derived from 1,330,654 high-quality LRS spectra of solar-like stars. We measure the mean fluxes at line cores of the Ca II H&K lines using a 1 ${\AA}$ rectangular bandpass as well as a 1.09 ${\AA}$ full width at half maximum (FWHM) triangular bandpass, and the mean fluxes of two 20 ${\AA}$ pseudo-continuum bands on the two sides of the lines. Three activity indexes, $S_{\rm rec}$ based on the 1 ${\AA}$ rectangular bandpass, and $S_{\rm tri}$ and $S_L$ based on the 1.09 ${\AA}$ FWHM triangular bandpass, are evaluated from the measured fluxes to quantitatively indicate the chromospheric activity level. The uncertainties of all the obtained parameters are estimated. We also produce spectrum diagrams of Ca II H&K lines for all the spectra in the database. The entity of the database is composed of a catalog of spectral sample and activity parameters, and a library of spectrum diagrams. Statistics reveal that the solar-like stars with high level of chromospheric activity ($S_{\rm rec}>0.6$) tend to appear in the parameter range of $T_{\rm eff}\text{ (effective temperature)}<5500\,{\rm K}$, $4.3<\log\,g\text{ (surface gravity)}<4.6$, and $-0.2<[{\rm Fe/H}]\text{ (metallicity)}<0.3$. This database with more than one million high-quality LAMOST LRS spectra of Ca II H&K lines and basal chromospheric activity parameters can be further used for investigating activity characteristics of solar-like stars and solar-stellar connection., Comment: 26 pages, 15 figures, accepted for publication in ApJS