Determination of displacements in cross-sections of four-bar mechanism links from distributed dynamic loads and their animation using MAPLE
DOI:
https://doi.org/10.26577/jmmcs-2018-2-393Keywords:
Mechanisms, movable linkages, displacements, distributed dynamic loadsAbstract
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.
References
[2] Stephen Timoshenko, Strength of Materials: Part I. Elementary Theory and Problems (New York: D. Van Nostrand Company Inc., 1948), 134 – 135.
[3] Anatoly Darkov and Hayman Shpiro, Strength of Materials (Moscow: High School, 1975), 289.
[4] Seetharamulu Kaveti, "Displacement Method" , in Dynamic Analysis of Skeletal Structures: Force and Displacement
Methods and Iterative Techniques (India: McGraw-Hill Education, 2014), 412.
[5] Alexander Tschiras, Structural Mechanics: Theory and Algorithms (Moscow: Stroyizdat, 1989), 111.
[6] Georgy Pisarenko et al., Strength of Materials (Kiev: Vischa shkola, 1979), 85.
[7] George N. Sandor and Imdad Imam, "A general method of kineto-elastodynamic design of high speed mechanisms" ,
Mech. Mach. Theory 8 (1973), pp. 497 – 516, doi.org/10.1016/0094-114X(73)90023-2.
[8] Akira Abe, "Trajectory planning for residual vibration suppression of a two-link rigid-flexible manipulator considering large deformation" , Mech. Mach. Theory 44 (2009), pp. 1627 – 1639, doi.org/10.1016/j.mechmachtheory.2009.01.009.
[9] Ling Mingxiang et al., "Kinetostatic modeling of complex compliant mechanisms with serial-parallel
substructures: a semi-analytical matrix displacement method" , Mech. Mach. Theory In Press 2018,
doi.org/10.1016/j.mechmachtheory.2018.03.014.
[10] David V. Hutton, Fundamentals of finite element analysis (New Delhi: Tata McGraw-Hill Publishing Company, 2007), 387.
[11] Nitin S. Gokhale, Practical Finite Element Analysis (India: Finite To Infinite, 2008), 416.
[12] Hejun Du and Shihfu Ling, "A nonlinear dynamic model for Three-Dimensional Flexible Linkages" , Computers and Structures 56 (1995), doi.org/10.1016/0045-7949(94)00529-C.
[13] H. El-Absy and Ahmed A. Shabana, "Geometric stiffness and stability of rigid body modes" , Journal of Sound and Vibration 207 (1997), doi.org/10.1006/jsvi.1997.1051.
[14] Ding Zhaocai, "Analysis of dynamic stress and fatigue property of flexible robot" , (paper presented at the IEEE International Conference on Robotics and Biometrics, Kunming, China, December 17-20, 2006).
[15] Shigang Yue, Shiu Kit Tso, Weiliang Xu, "Maximum-dynamic-payload trajectory for flexible robot manipulators with kinematic redundancy" , Mech. Mach. Theory 36 (2001), doi.org/10.1016/S0094-114X(00)00059-8.
[16] Moharam H. Korayem, Mohammad Haghpanahi, Hamidreza Heidari, "Maximum allowable dynamic load
of flexible manipulators undergoing large deformation" , Transaction B: Mechanical Engineering 17 (2010),
https://pdfs.semanticscholar.org/c481/b62788e8b3ffbc6ba3a1af07b05e849439d8.pdf .
[17] Muratulla Utenov et. al. "Computational method of determination of internal efforts in links of mechanisms and robot manipulators with statically definable structures considering the distributed dynamically loadings" , (paper presented at the European Congress on Computational Methods in Applied Sciences and Engineering Biometrics, Crete, Greece, June 5-10, 2016).
