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Research Article Volume 9 Issue 1
Compilation of a system equations dynamics of a six-link mechanism with branching using complex functions
A Borisov, А Korotkikh
Received: March 03, 2026 | Published: March 26, 2026
Citation: Borisov A, Korotkikh A. Compilation of a system equations dynamics of a six-link mechanism with branching using complex functions. Open Access J Sci. 2026;9(1):120-123. DOI: 10.15406/oajs.2026.09.00295
Abstract
The article proposes a new method for constructing a mathematical model of a six-link mechanism with branching in the form of a system of differential equations of motion in the form of Lagrange equations of the second kind based on complex variable functions. The use of complex variable functions simplifies and speeds up the process of determining the coordinates of the links, which are defined by a single complex function in exponential form, when constructing the system of differential equations of motion. This simplifies the calculation of the squares of the velocities of the links’ centers of mass and speeds up the process of calculating the kinetic energy of the system, which is necessary when using Lagrange equations of the second kind. The method is illustrated by a mechanism model with six movable links, two of which branch off from the branching point. In this case, the free end of one of the links is assumed to be fixed on a stationary cylindrical hinge that is rigidly connected to the support surface. The angles are measured from the horizontal coordinate axis of the fixed reference system, in accordance with the definition and method of measuring the argument of a complex number. The model of a mechanism with six movable links connected by hinges has drives in the hinges that create control moments and uniquely determine the positions of the links. In practice, the proposed model can be used to create robotic manipulators for industrial production, medical robots, and anthropomorphic mechanisms such as robots, exoskeletons, spacesuits, prosthetics, and simulators. It can be used to model and study the biomechanics of the human musculoskeletal system, solve direct and inverse problems of anthropoid structure control, select drives and materials, and optimize the design.
Keywords: complex variable function, mechanism with six movable links, lagrange differential equations of the second kind, cylindrical hinge, control torques, rotation angles, angular velocities, angular accelerations, robot, exoskeleton
©2026 Borisov, et al. This is an open access article distributed under the terms of the, which permits unrestricted use, distribution, and build upon your work non-commercially.