In the case of reverse drag of normal faulting, the displacement and horizontal extension are determined based on the established equations for the three mechanisms: rigid body, vertical shear and inclined shear. Ther...In the case of reverse drag of normal faulting, the displacement and horizontal extension are determined based on the established equations for the three mechanisms: rigid body, vertical shear and inclined shear. There are three sub-cases of basal detachment for the rigid body model: horizontal detachment, antithetic detachment and synthetic detachment. For the rigid body model, the established equations indicate that the total displacement on the synthetic base (D<sub>t2</sub>) is the largest, that on the horizontal base (D<sub>t1</sub>) is moderate, and that on the antithetic base (D<sub>t3</sub>) is the smallest. On the other hand, the value of (D<sub>t1</sub>) is larger than the displacement for the vertical shear (D<sub>t4</sub>). The value of (D<sub>t1</sub>) is larger than or less than the displacement for the inclined shear (D<sub>t5</sub>) depending on the original fault dip δ<sub>0</sub>, bedding angle θ, and the angle of shear direction β. For all original parameters, the value of D<sub>t5</sub> is less than the value of D<sub>t4</sub>. Also, by comparing three rotation mechanisms, we find that the inclined shear produces largest extension, the rigid body model with horizontal detachment produces the smallest extension, and the vertical shear model produces moderate extension.展开更多
The solution for the forward displacement analysis（FDA） of the general 6-6 Stewart mechanism（i.e., the connection points of the moving and fixed platforms are not restricted to lying in a plane） has been extensive...The solution for the forward displacement analysis（FDA） of the general 6-6 Stewart mechanism（i.e., the connection points of the moving and fixed platforms are not restricted to lying in a plane） has been extensively studied, but the efficiency of the solution remains to be effectively addressed. To this end, an algebraic elimination method is proposed for the FDA of the general 6-6 Stewart mechanism. The kinematic constraint equations are built using conformal geometric algebra（CGA）. The kinematic constraint equations are transformed by a substitution of variables into seven equations with seven unknown variables. According to the characteristic of anti-symmetric matrices, the aforementioned seven equations can be further transformed into seven equations with four unknown variables by a substitution of variables using the Grobner basis. Its elimination weight is increased through changing the degree of one variable, and sixteen equations with four unknown variables can be obtained using the Grobner basis. A 40th-degree univariate polynomial equation is derived by constructing a relatively small-sized 9 × 9 Sylvester resultant matrix. Finally, two numerical examples are employed to verify the proposed method. The results indicate that the proposed method can effectively improve the efficiency of solution and reduce the computational burden because of the small-sized resultant matrix.展开更多
A special form of the Stewart platform is presented in which the top platform and base platform are similar and corresponding vertices are connected by six prismatic joints.A closed-from solution for the forward displ...A special form of the Stewart platform is presented in which the top platform and base platform are similar and corresponding vertices are connected by six prismatic joints.A closed-from solution for the forward displacement analysis of this mechanism is developed.When the six vertices of the top platform are in a quadratic curve,this mechanism becomes singular.This new theoretical result is confirmed with a numerical example.展开更多
The characteristics of the inelastic response of structures affected by hanging wall and forward directivity in the 1999 Chi-Chi earthquake are investigated. Inelastic displacement ratios （IDRs） for ground motions i...The characteristics of the inelastic response of structures affected by hanging wall and forward directivity in the 1999 Chi-Chi earthquake are investigated. Inelastic displacement ratios （IDRs） for ground motions impacted by these nearfield effects are evaluated and comprehensively compared to far-field ground motions. In addition, the inelastic displacement responses to hanging wall and footwall ground motions are compared. It is concluded that the inelastic displacement response is significantly affected in the short period range by hanging wall and in the long period range by footwall. Although high peak ground acceleration was observed at hanging wall stations, the IDRs for structures on hanging wall sites are only larger than footwall sites in the very long period range. Forward directivity effects result in larger IDRs for periods longer than about 0.5s. Adopting statistical relationships for IDRs established using far-field ground motions may lead to either overestimation or underestimation in the seismic evaluation of existing structures located in near-field regions, depending on their fundamental vibration periods.展开更多
This paper presents the forward displacement analysis of an 8-PSS(prismatic-spherical-spherical)redundant parallel manipulator whose moving platform is linked to the base platform by eight kinemtic chains consisting o...This paper presents the forward displacement analysis of an 8-PSS(prismatic-spherical-spherical)redundant parallel manipulator whose moving platform is linked to the base platform by eight kinemtic chains consisting of a PSS joint and a strut with fixed length.A general approximation algorithm is used to solve the problem.To avoid the extraction of root in the approximation process,the forward displacement analysis of the 8-PSS redundant parallel manipulator is transformed into another equivalent problem on the assumption that the strut is extensible while the slider is fixed.The problem is solved by a modified approximation algorithm which predicates that the manipulator will move along a pose vector to reduce the difference between the desired configuration and an instantaneous one,and the best movement should be with minimum norm and least quadratic sum.The characteristic of this modified algorithm is that its convergence domain is larger than that of the general approximation algorithm.Simulation results show that the modelified algorithm is general and can be used for the forward displacement analysis of the redundant parallel manipulator actuated by a revolute joint.展开更多
文摘In the case of reverse drag of normal faulting, the displacement and horizontal extension are determined based on the established equations for the three mechanisms: rigid body, vertical shear and inclined shear. There are three sub-cases of basal detachment for the rigid body model: horizontal detachment, antithetic detachment and synthetic detachment. For the rigid body model, the established equations indicate that the total displacement on the synthetic base (D<sub>t2</sub>) is the largest, that on the horizontal base (D<sub>t1</sub>) is moderate, and that on the antithetic base (D<sub>t3</sub>) is the smallest. On the other hand, the value of (D<sub>t1</sub>) is larger than the displacement for the vertical shear (D<sub>t4</sub>). The value of (D<sub>t1</sub>) is larger than or less than the displacement for the inclined shear (D<sub>t5</sub>) depending on the original fault dip δ<sub>0</sub>, bedding angle θ, and the angle of shear direction β. For all original parameters, the value of D<sub>t5</sub> is less than the value of D<sub>t4</sub>. Also, by comparing three rotation mechanisms, we find that the inclined shear produces largest extension, the rigid body model with horizontal detachment produces the smallest extension, and the vertical shear model produces moderate extension.
基金Supported by National Natural Science Foundation of China(Grant No.51375059)National Hi-tech Research and Development Program of China(863 Program,Grant No.2011AA040203)+1 种基金Special Fund for Agro-scientific Research in the Public Interest of China(Grant No.201313009-06)National Key Technology R&D Program of the Ministry of Science and Technology of China(Grant No.2013BAD17B06)
文摘The solution for the forward displacement analysis（FDA） of the general 6-6 Stewart mechanism（i.e., the connection points of the moving and fixed platforms are not restricted to lying in a plane） has been extensively studied, but the efficiency of the solution remains to be effectively addressed. To this end, an algebraic elimination method is proposed for the FDA of the general 6-6 Stewart mechanism. The kinematic constraint equations are built using conformal geometric algebra（CGA）. The kinematic constraint equations are transformed by a substitution of variables into seven equations with seven unknown variables. According to the characteristic of anti-symmetric matrices, the aforementioned seven equations can be further transformed into seven equations with four unknown variables by a substitution of variables using the Grobner basis. Its elimination weight is increased through changing the degree of one variable, and sixteen equations with four unknown variables can be obtained using the Grobner basis. A 40th-degree univariate polynomial equation is derived by constructing a relatively small-sized 9 × 9 Sylvester resultant matrix. Finally, two numerical examples are employed to verify the proposed method. The results indicate that the proposed method can effectively improve the efficiency of solution and reduce the computational burden because of the small-sized resultant matrix.
文摘A special form of the Stewart platform is presented in which the top platform and base platform are similar and corresponding vertices are connected by six prismatic joints.A closed-from solution for the forward displacement analysis of this mechanism is developed.When the six vertices of the top platform are in a quadratic curve,this mechanism becomes singular.This new theoretical result is confirmed with a numerical example.
基金National Natural Science Foundation of China Under Grant No. 50538050 and No. 50608024
文摘The characteristics of the inelastic response of structures affected by hanging wall and forward directivity in the 1999 Chi-Chi earthquake are investigated. Inelastic displacement ratios （IDRs） for ground motions impacted by these nearfield effects are evaluated and comprehensively compared to far-field ground motions. In addition, the inelastic displacement responses to hanging wall and footwall ground motions are compared. It is concluded that the inelastic displacement response is significantly affected in the short period range by hanging wall and in the long period range by footwall. Although high peak ground acceleration was observed at hanging wall stations, the IDRs for structures on hanging wall sites are only larger than footwall sites in the very long period range. Forward directivity effects result in larger IDRs for periods longer than about 0.5s. Adopting statistical relationships for IDRs established using far-field ground motions may lead to either overestimation or underestimation in the seismic evaluation of existing structures located in near-field regions, depending on their fundamental vibration periods.
基金Funded by the National Natural Science Foundation of China(Grant No.50905102)the China Postdoctoral Science Foundation(Grant No.200801199)the Natural Science Foundation of Guangdong Province(Grant No.8351503101000001)
文摘This paper presents the forward displacement analysis of an 8-PSS(prismatic-spherical-spherical)redundant parallel manipulator whose moving platform is linked to the base platform by eight kinemtic chains consisting of a PSS joint and a strut with fixed length.A general approximation algorithm is used to solve the problem.To avoid the extraction of root in the approximation process,the forward displacement analysis of the 8-PSS redundant parallel manipulator is transformed into another equivalent problem on the assumption that the strut is extensible while the slider is fixed.The problem is solved by a modified approximation algorithm which predicates that the manipulator will move along a pose vector to reduce the difference between the desired configuration and an instantaneous one,and the best movement should be with minimum norm and least quadratic sum.The characteristic of this modified algorithm is that its convergence domain is larger than that of the general approximation algorithm.Simulation results show that the modelified algorithm is general and can be used for the forward displacement analysis of the redundant parallel manipulator actuated by a revolute joint.
