Determination of displacements in cross-sections of four-bar mechanism links from distributed dynamic loads and their animation using MAPLE
The links of high-speed mechanisms and manipulators are deformed under the action of inertia forces and external loads. These deformations have significantly influence on the accuracy of execution of the required law of motion by the operating point of the mechanism and the positioning of the man...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Al-Farabi Kazakh National University
2018-08-01
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| Series: | Вестник КазНУ. Серия математика, механика, информатика |
| Subjects: | |
| Online Access: | https://bm.kaznu.kz/index.php/kaznu/article/view/393/401 |
| Summary: | The links of high-speed mechanisms and manipulators are deformed under the action of inertia
forces and external loads. These deformations have significantly influence on the accuracy of execution
of the required law of motion by the operating point of the mechanism and the positioning of
the manipulator grip. Accordingly, longitudinal and transverse displacements, angles of rotation of
cross-sections of links under the action of distributed dynamic and external loads are investigated
in this paper. The developed technique allows defining deformations of links of mechanisms and
manipulators and can be applied at their designing. To determine the transverse displacements,
the angles of rotation of the cross-sections of the links – the basic differential equation of the elastic
line of the beam, to determine the longitudinal displacements of the points of the links – Hooke’s
law and the boundary conditions of the computed scheme of the investigated linkages for elastic
computation are used. The bending moment in the basic differential equation of the elastic line of
the beam and the longitudinal force in Hooke’s law were determined by the theory developed by
the authors of the analytical definition of internal forces in the links of planar linkages with statically
determinate structures, taking into account the distributed dynamic loads from the masses
of links, dead weight and from the acting external loads. According to the developed technique,
programs are created in the MAPLE system and animations of the movement of mechanisms are
received, with the construction on the links the diagrams of transverse, longitudinal displacements
and angles of rotation of the link cross-sections. The developed analytical technique for determining
deformations in the cross-sections of links is used to calculate the strength and stiffness of
elements of movable linkages. |
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| ISSN: | 1563-0277 2617-4871 |