We show that higher-dimensional integrable systems including the (2+1)-dimensional generalized sine-Gordon equation and the (2+1)-dimensional complex mKdV equation are associated with motions of surfaces inducedby end...We show that higher-dimensional integrable systems including the (2+1)-dimensional generalized sine-Gordon equation and the (2+1)-dimensional complex mKdV equation are associated with motions of surfaces inducedby endowing with an extra space variable to the motions of curves on S^2(R) and S^3(R).展开更多
A redundant manipulator that can online clamp pipe was developed to track along a cylinder intersection curve. With an ultrasonic transducer mounted on its end-effector, the manipulator can perform welding seam inspec...A redundant manipulator that can online clamp pipe was developed to track along a cylinder intersection curve. With an ultrasonic transducer mounted on its end-effector, the manipulator can perform welding seam inspection at pipe joint in nuclear industry. An inverse kinematics solution expressed in joint space was solved based on the combination of geometric method and D-H matrix transformation. Expression about joints variables was obtained based on the scanning parameters of pipeline. The analysis method and results can be widely applied for online trajectory planning of intersection curve scanning manipulators.展开更多
A framework is proposed to characterize and forecast the displacement trends of slow-moving landslides, defined as the reactivation stage of phenomena in rocks or fine-grained soils, with movements localized along one...A framework is proposed to characterize and forecast the displacement trends of slow-moving landslides, defined as the reactivation stage of phenomena in rocks or fine-grained soils, with movements localized along one or several existing shear surfaces. The framework is developed based on a thorough analysis of the scientific literature and with reference to significant reported case studies for which a consistent dataset of continuous displacement measurements is available. Three distinct trends of movement are defined to characterize the kinematic behavior of the active stages of slow-moving landslides in a velocity-time plot: a linear trend-type I, which is appropriate for stationary phenomena; a convex shaped trend-type II, which is associated with rapid increases in pore water pressure due to rainfall, followed by a slow decrease in the groundwater level with time; and a concave shaped trend-type III, which denotes a non-stationary process related to the presence of new boundary conditions such as those associated with the development of a newly formed local slip surface that connects with the main existing slip surface. Within the proposed framework, a model is developed to forecast future displacements for active stages of trend-type II based on displacement measurements at the beginning of the stage. The proposed model is validated by application to two case studies.展开更多
It is shown that the Pinney equation, Ermakov systems, and their higher-order generalizations describeself-similar solutions of plane curve motions in centro-affine and affine geometries.
This paper introduces realization method of kinematics analysis for the planar four bar mechanism based on the MFC. A mathematicat model is established by a simple and effective method, using the computer simulation t...This paper introduces realization method of kinematics analysis for the planar four bar mechanism based on the MFC. A mathematicat model is established by a simple and effective method, using the computer simulation technology can the dynamic demonstration mechanism taotion and automatic drawing trajectory curve of arbitrary point on the connecting rod, and can output various motion displacement, speed and acceleration diagram. The paper provides a simple way for motion analysis of planar four link.展开更多
This paper is concerned with the kinematic nonlinearity measure of parallel kinematic machine tool (PKM), which depends upon differential geometry curvalure. The nonlinearity can be described by the curve of the solut...This paper is concerned with the kinematic nonlinearity measure of parallel kinematic machine tool (PKM), which depends upon differential geometry curvalure. The nonlinearity can be described by the curve of the solution locus and the equal interval input of joints mapping into inequable interval output of the end-effectors. Such curing and inequation can be measured by BW curvature. So the curvature can measure the nonlinearity of PKM indirectly. Then the distribution of BW curvature in the local area and the whole workspace are also discussed. An example of application to the interpolation accuracy analysis of PKM is given to illustrate the effectiveness of this approach.展开更多
Following Jacobi＇s geometrization of Lagrange＇s least action principle, trajectories of classical mechanics can be characterized as geodesics on the configuration space M with respect to a suitable metric which is t...Following Jacobi＇s geometrization of Lagrange＇s least action principle, trajectories of classical mechanics can be characterized as geodesics on the configuration space M with respect to a suitable metric which is the conformal modification of the kinematic metric by the factor （U ＋ h）, where U and h are the potential function and the total energy, respectively. In the special case of 3-body motions with zero angular momentum, the global geometry of such trajectories can be reduced to that of their moduli curves, which record the change of size and shape, in the moduli space of oriented m-triangles, whose kinematic metric is, in fact, a Riemannian cone over the shape space M^＊≌S^2 （1/2）. In this paper, it is shown that the moduli curve of such a motion is uniquely determined by its shape curve （which only records the change of shape） in the case of h≠0, while in the special case of h = 0 it is uniquely determined up to scaling. Thus, the study of the global geometry of such motions can be further reduced to that of the shape curves, which are time-parametrized curves on the 2-sphere characterized by a third order ODE. Moreover, these curves have two remarkable properties, namely the uniqueness of parametrization and the monotonieity, that constitute a solid foundation for a systematic study of their global geometry and naturally lead to the formulation of some pertinent problems.展开更多
基金National Natural Science Foundation of China under Grant No.10671156the Program for New Century Excellent Talents in Universities under Grant No.NCET-04-0968
文摘We show that higher-dimensional integrable systems including the (2+1)-dimensional generalized sine-Gordon equation and the (2+1)-dimensional complex mKdV equation are associated with motions of surfaces inducedby endowing with an extra space variable to the motions of curves on S^2(R) and S^3(R).
基金Foundation Program Conducted by Science&Technology Committee of National Defence ( T0 12 0 0 1A0 0 1)
文摘A redundant manipulator that can online clamp pipe was developed to track along a cylinder intersection curve. With an ultrasonic transducer mounted on its end-effector, the manipulator can perform welding seam inspection at pipe joint in nuclear industry. An inverse kinematics solution expressed in joint space was solved based on the combination of geometric method and D-H matrix transformation. Expression about joints variables was obtained based on the scanning parameters of pipeline. The analysis method and results can be widely applied for online trajectory planning of intersection curve scanning manipulators.
基金partially supported by the University of Salerno (Italy) through the Civil and Environmental Engineering Ph.D. programme and FARB research funding
文摘A framework is proposed to characterize and forecast the displacement trends of slow-moving landslides, defined as the reactivation stage of phenomena in rocks or fine-grained soils, with movements localized along one or several existing shear surfaces. The framework is developed based on a thorough analysis of the scientific literature and with reference to significant reported case studies for which a consistent dataset of continuous displacement measurements is available. Three distinct trends of movement are defined to characterize the kinematic behavior of the active stages of slow-moving landslides in a velocity-time plot: a linear trend-type I, which is appropriate for stationary phenomena; a convex shaped trend-type II, which is associated with rapid increases in pore water pressure due to rainfall, followed by a slow decrease in the groundwater level with time; and a concave shaped trend-type III, which denotes a non-stationary process related to the presence of new boundary conditions such as those associated with the development of a newly formed local slip surface that connects with the main existing slip surface. Within the proposed framework, a model is developed to forecast future displacements for active stages of trend-type II based on displacement measurements at the beginning of the stage. The proposed model is validated by application to two case studies.
文摘It is shown that the Pinney equation, Ermakov systems, and their higher-order generalizations describeself-similar solutions of plane curve motions in centro-affine and affine geometries.
文摘This paper introduces realization method of kinematics analysis for the planar four bar mechanism based on the MFC. A mathematicat model is established by a simple and effective method, using the computer simulation technology can the dynamic demonstration mechanism taotion and automatic drawing trajectory curve of arbitrary point on the connecting rod, and can output various motion displacement, speed and acceleration diagram. The paper provides a simple way for motion analysis of planar four link.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 59805011) the National 973 Program (G1998030607) the National 863 High-Tech Development Program (863-511-943-001).
文摘This paper is concerned with the kinematic nonlinearity measure of parallel kinematic machine tool (PKM), which depends upon differential geometry curvalure. The nonlinearity can be described by the curve of the solution locus and the equal interval input of joints mapping into inequable interval output of the end-effectors. Such curing and inequation can be measured by BW curvature. So the curvature can measure the nonlinearity of PKM indirectly. Then the distribution of BW curvature in the local area and the whole workspace are also discussed. An example of application to the interpolation accuracy analysis of PKM is given to illustrate the effectiveness of this approach.
文摘Following Jacobi＇s geometrization of Lagrange＇s least action principle, trajectories of classical mechanics can be characterized as geodesics on the configuration space M with respect to a suitable metric which is the conformal modification of the kinematic metric by the factor （U ＋ h）, where U and h are the potential function and the total energy, respectively. In the special case of 3-body motions with zero angular momentum, the global geometry of such trajectories can be reduced to that of their moduli curves, which record the change of size and shape, in the moduli space of oriented m-triangles, whose kinematic metric is, in fact, a Riemannian cone over the shape space M^＊≌S^2 （1/2）. In this paper, it is shown that the moduli curve of such a motion is uniquely determined by its shape curve （which only records the change of shape） in the case of h≠0, while in the special case of h = 0 it is uniquely determined up to scaling. Thus, the study of the global geometry of such motions can be further reduced to that of the shape curves, which are time-parametrized curves on the 2-sphere characterized by a third order ODE. Moreover, these curves have two remarkable properties, namely the uniqueness of parametrization and the monotonieity, that constitute a solid foundation for a systematic study of their global geometry and naturally lead to the formulation of some pertinent problems.
