We intend to study a modified version of the planar Circular Restricted Three-Body Problem(CRTBP) by incorporating several perturbing parameters. We consider the bigger primary as an oblate spheroid and emitting radia...We intend to study a modified version of the planar Circular Restricted Three-Body Problem(CRTBP) by incorporating several perturbing parameters. We consider the bigger primary as an oblate spheroid and emitting radiation while the small primary has an elongated body. We also consider the perturbation from a disk-like structure encompassing this three-body system. First, we develop a mathematical model of this modified CRTBP.We have found there exist five equilibrium points in this modified CRTBP model, where three of them are collinear and the other two are non-collinear. Second, we apply our modified CRTBP model to the Sun–Haumea system by considering several values of each perturbing parameter. Through our numerical investigation, we have discovered that the incorporation of perturbing parameters has resulted in a shift in the equilibrium point positions of the Sun–Haumea system compared to their positions in the classical CRTBP. The stability of equilibrium points is investigated. We have shown that the collinear equilibrium points are unstable and the stability of non-collinear equilibrium points depends on the mass parameter μ of the system. Unlike the classical case, non-collinear equilibrium points have both a maximum and minimum limit of μ for achieving stability. We remark that the stability range of μ in non-collinear equilibrium points depends on the perturbing parameters. In the context of the Sun–Haumea system, we have found that the non-collinear equilibrium points are stable.展开更多
This paper presents a calibration method for parallel manipulators using a measurement system specially installed on an external fixed frame. The external fixed frame is important as an error reference for calibration...This paper presents a calibration method for parallel manipulators using a measurement system specially installed on an external fixed frame. The external fixed frame is important as an error reference for calibration in certain operations, such as in the configuration of a parallel manip- ulator functioning as a machine tool where the workpiece is fixed to a worktable. The pose of the end-effector is mea- sured using three digital indicators installed on the external fixed frame. To enable measurement, the end-effector is assumed to be a plane large enough that all digital indicators could touch. The error is defined as the difference between the theoretical and actual readings of the digital indicators. The geometric parameters of the parallel manipulator are optimized to minimize this error. This calibration method is low cost and feasible for compensating geometric parameter errors for a parallel manipulator. Optimal pose selection for the calibration is achieved using a swarm intelligence search algorithm. The method is implemented on a prototype of a six degrees-of-freedom （DOFs） Gough-Stewart platform constructed to function as a machine tool.展开更多
基金funded partially by BRIN’s research grant Rumah Program AIBDTK 2023。
文摘We intend to study a modified version of the planar Circular Restricted Three-Body Problem(CRTBP) by incorporating several perturbing parameters. We consider the bigger primary as an oblate spheroid and emitting radiation while the small primary has an elongated body. We also consider the perturbation from a disk-like structure encompassing this three-body system. First, we develop a mathematical model of this modified CRTBP.We have found there exist five equilibrium points in this modified CRTBP model, where three of them are collinear and the other two are non-collinear. Second, we apply our modified CRTBP model to the Sun–Haumea system by considering several values of each perturbing parameter. Through our numerical investigation, we have discovered that the incorporation of perturbing parameters has resulted in a shift in the equilibrium point positions of the Sun–Haumea system compared to their positions in the classical CRTBP. The stability of equilibrium points is investigated. We have shown that the collinear equilibrium points are unstable and the stability of non-collinear equilibrium points depends on the mass parameter μ of the system. Unlike the classical case, non-collinear equilibrium points have both a maximum and minimum limit of μ for achieving stability. We remark that the stability range of μ in non-collinear equilibrium points depends on the perturbing parameters. In the context of the Sun–Haumea system, we have found that the non-collinear equilibrium points are stable.
文摘This paper presents a calibration method for parallel manipulators using a measurement system specially installed on an external fixed frame. The external fixed frame is important as an error reference for calibration in certain operations, such as in the configuration of a parallel manip- ulator functioning as a machine tool where the workpiece is fixed to a worktable. The pose of the end-effector is mea- sured using three digital indicators installed on the external fixed frame. To enable measurement, the end-effector is assumed to be a plane large enough that all digital indicators could touch. The error is defined as the difference between the theoretical and actual readings of the digital indicators. The geometric parameters of the parallel manipulator are optimized to minimize this error. This calibration method is low cost and feasible for compensating geometric parameter errors for a parallel manipulator. Optimal pose selection for the calibration is achieved using a swarm intelligence search algorithm. The method is implemented on a prototype of a six degrees-of-freedom （DOFs） Gough-Stewart platform constructed to function as a machine tool.
