Abstract
The article deals with the application of the "finite rotation and displacement" method (FRDM) which can find the desired values of the generalized coordinates for the control system of a parabolic antenna. The special manipulator of a sequential structure with sufficient rigidity is used to control the parabolic antenna. The rigidity of this manipulator is ensured by use of links in the form of spherical shells and bearings located along the perimeter of each shell in the rotation plane of each link. It allows to optimally place the material of the manipulator's design and to obtain sufficient rigidity with minimal weight. The manipulator consists of four links connected by fifth class kinematic pairs with an arbitrary inclination of the axes. For this task the antenna's orientation is important without taking into account the small displacement of its position during the process of its orientation. The FRDM method provides both orientation and position. It is based on determining the precise and optimal iterative steps for each degree of mobility, providing maximum approximation to the specified orientation parameters of the parabolic antenna. According to the method's algorithm, the software is developed consisting of subprograms for organizing a general solution of the inverse kinematics for an arbitrary number of links and a particular one for a manipulator in the form of source data. The initial data are the vector model of the manipulator, the values of the structural constraints of the generalized coordinates, and the characteristics of kinematic pairs by type and class
Highlights
Manipulator inverse kinematic solutions based on vector formulations and damped least-squares methods // IEEE Transactions on Systems, Man and Cybernetics. 1986
The article deals with the application of the "finite rotation and displacement" method (FRDM) which can find the desired values of the generalized coordinates for the control system of a parabolic antenna
The special manipulator of a sequential structure with sufficient rigidity is used to control the parabolic antenna. The rigidity of this manipulator is ensured by use of links in the form of spherical shells and bearings located along the perimeter of each shell in the rotation plane of each link
Summary
Для организации моделирования траекторного движения манипулятора необходимо задать начальные значения ориентации антенны с помощью углов Эйлера-Крылова: φ = 0o, ψ = 0o, θ = 0o. Моделирование траекторного движения можно осуществлять от рукоятки управления, программным заданием законов изменения ориентации антенны и любым другим способом. Полученные траектории в виде графиков изменения обобщенных координат звеньев манипулятора показаны на рисунке 6. Для представленной траектории движения записан файл визуализации движения модели манипулятора, представленный в [17]. Если звенья манипулятора обозначить указателями вращения, показанными на рисунке 7, то видно, что конфигурации звеньев манипулятора в «мертвых» точках образуются в случае одновременного совпадения направлений указателей с плоскостью дифферента. Манипулятор поворачивать по курсу относительно вектора e 1, согласно векторной модели, то Таблица 2 Сингулярные точки «мертвого» типа Если вых» точек. манипулятор поворачивать по курсу относительно вектора e 1, согласно векторной модели, то Таблица 2 Сингулярные точки «мертвого» типа
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