Architectural singularity belongs to the Type II singularity,in which a parallel manipulator(PM)gains one or more degrees of freedom and becomes uncontrollable.PMs remaining permanently in a singularity are beneficial...Architectural singularity belongs to the Type II singularity,in which a parallel manipulator(PM)gains one or more degrees of freedom and becomes uncontrollable.PMs remaining permanently in a singularity are beneficial for linearto-rotary motion conversion.Griffis-Duffy(GD)platform is a mobile structure admitting a Bricard motion.In this paper,we present a coordinate-free approach to the design of generalized GD platforms,which consists in determining the shape and attachment of both the moving platform and the fixed base.The generalized GD platform is treated as a combination of six coaxial single-loop mechanisms under the same constraints.Owing to the inversion,hidden in the geometric structure of these single-loop mechanisms,the mapping from a line to a circle establishes the geometric transformation between the fixed base and the moving platform based on the center of inversion,and describes the shape and attachment of the generalized GD platform.Moreover,the center of inversion not only identifies the location of rotation axis,but also affects the shape of the platform mechanism.A graphical construction of generalized GD platforms using inversion,proposed in the paper,provides geometrically feasible solutions of the manipulator design for the requirement of the location of rotation axis.展开更多
In this paper, we got the best linear unbiased predictor of any linear function of the elements of a finite population under coordinate-free models. The optimal predictor of these quantities was obtained in an earlier...In this paper, we got the best linear unbiased predictor of any linear function of the elements of a finite population under coordinate-free models. The optimal predictor of these quantities was obtained in an earlier work considering models with a known diagonal covariance matrix. We extended this result assuming any known covariance matrix. It is shown that in the particular case of the coordinatized models, this general predictor coincides with the optimal predictor of the total population under a regression super population model with correlated observations.展开更多
After half a century research, the mechanical theorem proving in geometries has become an active research topic in the automated reasoning field. This review involves three approaches on automated generating readable ...After half a century research, the mechanical theorem proving in geometries has become an active research topic in the automated reasoning field. This review involves three approaches on automated generating readable machine proofs for geometry theorems which include search methods, coordinate-free methods, and formal logic methods. Some critical issues about these approaches are also discussed. Furthermore, the authors propose three further research directions for the readable machine proofs for geometry theorems, including geometry inequalities, intelligent geometry softwares and machine learning.展开更多
基金Supported by National Natural Science Foundation of China (Grant Nos.U1813221,52075015)Personnel Startup Project of Zhejiang A&F University Scientific Research Development Foundation of China (Grant No.2024LFR015)。
文摘Architectural singularity belongs to the Type II singularity,in which a parallel manipulator(PM)gains one or more degrees of freedom and becomes uncontrollable.PMs remaining permanently in a singularity are beneficial for linearto-rotary motion conversion.Griffis-Duffy(GD)platform is a mobile structure admitting a Bricard motion.In this paper,we present a coordinate-free approach to the design of generalized GD platforms,which consists in determining the shape and attachment of both the moving platform and the fixed base.The generalized GD platform is treated as a combination of six coaxial single-loop mechanisms under the same constraints.Owing to the inversion,hidden in the geometric structure of these single-loop mechanisms,the mapping from a line to a circle establishes the geometric transformation between the fixed base and the moving platform based on the center of inversion,and describes the shape and attachment of the generalized GD platform.Moreover,the center of inversion not only identifies the location of rotation axis,but also affects the shape of the platform mechanism.A graphical construction of generalized GD platforms using inversion,proposed in the paper,provides geometrically feasible solutions of the manipulator design for the requirement of the location of rotation axis.
文摘In this paper, we got the best linear unbiased predictor of any linear function of the elements of a finite population under coordinate-free models. The optimal predictor of these quantities was obtained in an earlier work considering models with a known diagonal covariance matrix. We extended this result assuming any known covariance matrix. It is shown that in the particular case of the coordinatized models, this general predictor coincides with the optimal predictor of the total population under a regression super population model with correlated observations.
基金supported by the Funds of the Chinese Academy of Sciences for Key Topics in Innovation Engineering under Grant No.KJCX2-YW-S02
文摘After half a century research, the mechanical theorem proving in geometries has become an active research topic in the automated reasoning field. This review involves three approaches on automated generating readable machine proofs for geometry theorems which include search methods, coordinate-free methods, and formal logic methods. Some critical issues about these approaches are also discussed. Furthermore, the authors propose three further research directions for the readable machine proofs for geometry theorems, including geometry inequalities, intelligent geometry softwares and machine learning.
