Based on the ecological footprint (EF) model, the dynamic changes in the per capita EF and per capita ecological carrying capacity (EC) in Qinghai Province from 2007 to 2017 were quantitatively analysed. The grey GM(1,1) prediction model was used to predict the per capita EF, per capita EC, and EF of ten thousand yuan of GDP. Additionally, the spatial change characteristics of the sustainable development status of the study area in four time periods were analysed using GIS technology. The results showed the following. (1) In the 11-year study period, Qinghai Province’s EF per capita grew gradually, increasing from 2.3027 hm2 in 2007 to 2.9837 hm2 in 2017. (2) The EC per capita in Qinghai Province remained a slight linear upward trend. (3) The environmental sustainability in Qinghai Province deteriorated over time. (4) According to the spatial characteristics, the overall sustainable development state changed markedly in the eastern region but was stable in the central and western regions. This paper proposes some countermeasures and suggestions to help Qinghai Province work towards sustainable development, such as controlling the population, adjusting the industrial structure, developing a low-carbon circular economy, and implementing ecological engineering.
Dynamic modeling and frequency characteristic analysis of a novel 3-PSS (three-prismatic-spherical-spherical) flexible parallel micro-manipulator with three translational DOF in space were investigated in this paper. Firstly, the kinematics analysis was developed based on the pseudo-rigid body model. The Jacobian matrix and the relationship between the micro angular deformation of the flexible spherical hinge and the end pose of mobile platform were respectively obtained by employing vector closed-loop method and coordinate transformation method. Then, taking into account the elastic strain energy of the flexible spherical hinge, dynamic model of this mechanism was established via Lagrange equations, and the expression of natural frequency was further derived. Combined with a set of given parameters, natural frequencies of the system were calculated by using MATLAB software. For the comparison purpose, a simulated modal analysis of the mechanism with the same parameters was also performed by employing finite element ANSYS software. Results from numerical calculation and finite element simulation indicated that maximum error of their natural frequencies was 2.71%, which verified the correctness of the theoretical dynamic model. Finally, variations of natural frequencies with changes of the basic parameters were analyzed. Analysis results show that natural frequencies increase with the increase of the bending stiffness kbm of flexible spherical hinge and the difference in radius Er between static platform and mobile platform, while decrease with the increase of the length l of the link rod and the masses of the main components of mechanism. Besides, it can be further drawn from these obtained results that the natural frequencies increase with the increase of the angle θl between the link rod and the z axis of reference coordinate system. Considering that the increase of the stiffness kbm and the angle θl will reduce the scope of working space, it is recommended in designing the structure to choose a set of larger stiffness kbm and angle θl as much as possible under the premise of satisfying the working space.
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