Determination of displacements in cross-sections of four-bar mechanism links from distributed dynamic loads and their animation using MAPLE

  • М. U. Utenov al-Farabi Kazakh National University, Almaty, Republic of Kazakhstan
  • S. К. Zhilkibayeva al-Farabi Kazakh National University, Almaty, Republic of Kazakhstan
  • Zh. Zh. Baygunchekov K.I. Satpaev Kazakh National Research Technical University, Almaty, Kazakhstan


The links of high-speed mechanisms and manipulators are deformed under the action of inertiaforces and external loads. These deformations have significantly influence on the accuracy of executionof the required law of motion by the operating point of the mechanism and the positioning ofthe manipulator grip. Accordingly, longitudinal and transverse displacements, angles of rotation ofcross-sections of links under the action of distributed dynamic and external loads are investigatedin this paper. The developed technique allows defining deformations of links of mechanisms andmanipulators 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 elasticline of the beam, to determine the longitudinal displacements of the points of the links – Hooke’slaw and the boundary conditions of the computed scheme of the investigated linkages for elasticcomputation are used. The bending moment in the basic differential equation of the elastic line ofthe beam and the longitudinal force in Hooke’s law were determined by the theory developed bythe authors of the analytical definition of internal forces in the links of planar linkages with staticallydeterminate structures, taking into account the distributed dynamic loads from the massesof 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 arereceived, with the construction on the links the diagrams of transverse, longitudinal displacementsand angles of rotation of the link cross-sections. The developed analytical technique for determiningdeformations in the cross-sections of links is used to calculate the strength and stiffness ofelements of movable linkages.


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How to Cite
UTENOV, М. U.; ZHILKIBAYEVA, S. К.; BAYGUNCHEKOV, Zh. Zh.. Determination of displacements in cross-sections of four-bar mechanism links from distributed dynamic loads and their animation using MAPLE. Journal of Mathematics, Mechanics and Computer Science, [S.l.], v. 98, n. 2, p. 45-56, aug. 2018. ISSN 1563-0277. Available at: <>. Date accessed: 20 feb. 2019. doi:
Keywords Mechanisms, movable linkages, displacements, distributed dynamic loads