Nonlinear engineering and robotics

Singularity Analysis and Research on the Mechanism Workspace with Three Degrees of Freedom

S. Yu. Misyurin^a, N. Yu. Nosova^a, G. V. Kreinin^a, L. A. Rybak<sup>b

a</sup> Blagonravov Mechanical Engineering Research Institute of the Russian Academy of Sciences, 4 Mal. Kharitonyevskiy per., Moscow, 101990 Russia
^b Belgorod State Technological University named after V. G. Shukhov, ul. Kostyukova 46, Belgorod, 308012 Russia

Abstract: This article discusses the mechanism of parallel structure, which includes hinged parallel- ograms. These mechanisms have a certain peculiarity when composing kinematics equations, consisting in the fact that some of the equations have a linear form. This simplifies the system of coupling equations as a whole. By solving direct and inverse kinematics, we will determine the size and shape of the working area. A method was chosen by solving the inverse kinematics to determine the workspace. The size and shape of the working area of the mechanism under consideration with three degrees of freedom are experimentally determined under given initial conditions. The presence of a large working area allows us to recommend this mechanism for use in various branches of robotics, medicine, simulators, etc. The Jacobian matrix of the coupling equations of the mechanism is written out to determine the singularities.

Keywords: parallel mechanism, singularity, hinged parallelogram, coupling equations, Jacobian matrix

MSC: 68T40, 70Q05, 70B15, 93C85

Received: 29.07.2024
Accepted: 29.11.2024

Language: English

DOI: 10.20537/nd250102