Solution to the Inverse Problem of the Angular Manipulator Kinematics with Six Degrees of Freedom

Andrieiev, Yurii; Breslavsky, Dmytro; Shabanov, Hennadii; Naumenko, Konstantin; Altenbach, Holm

doi:10.3390/app15052840

Open AccessArticle

Solution to the Inverse Problem of the Angular Manipulator Kinematics with Six Degrees of Freedom

by

Yurii Andrieiev

^1,†

,

Dmytro Breslavsky

^1,†

,

Hennadii Shabanov

^1,†

,

Konstantin Naumenko

^2,*,†

and

Holm Altenbach

^2,†

¹

Department of Computer Modelling of Processes and Systems, National Technical University “Kharkiv Polytechnic Institute”, 2, Kyrpychova Str., 61002 Kharkiv, Ukraine

²

Institute of Materials, Technologies and Mechanics, Otto von Guericke University Magdeburg, D-39106 Magdeburg, Germany

^*

Author to whom correspondence should be addressed.

^†

These authors contributed equally to this work.

Appl. Sci. 2025, 15(5), 2840; https://doi.org/10.3390/app15052840

Submission received: 28 January 2025 / Revised: 26 February 2025 / Accepted: 1 March 2025 / Published: 6 March 2025

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Abstract

New analytical solutions for the inverse kinematics problem of a 6R manipulator are proposed. Based on the assumption that the rotation axes of the last three links intersect at a common point, the problem is divided into orientation and transition problems. The position of the common point and the rotation angles of the first three links are determined using the equations of motion of the output link. A matrix equation for the rotation angles of the last three links is formulated. Solutions to the inverse kinematics problem are obtained for three models. In the first two, the rotation axis of the fourth link may not intersect the vertical rotation axis of the first. In the third model, the rotation axis of the fourth link intersects neither the vertical rotation axis of the first link nor the intersection point of the axes of the last two links. For all models, an analytical solution in closed form is obtained from the geometry of the mechanism. The solution for the third requires a preliminary search for the root of the transcendental equation for the rotation angle of the fourth link. Illustrative examples of calculations for a specific manipulator are given.

Keywords: angular manipulator; kinematics; robotics; manipulator orientation; inverse kinematic problem; algorithm; orientation of the gripper; computer modeling

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MDPI and ACS Style

Andrieiev, Y.; Breslavsky, D.; Shabanov, H.; Naumenko, K.; Altenbach, H. Solution to the Inverse Problem of the Angular Manipulator Kinematics with Six Degrees of Freedom. Appl. Sci. 2025, 15, 2840. https://doi.org/10.3390/app15052840

AMA Style

Andrieiev Y, Breslavsky D, Shabanov H, Naumenko K, Altenbach H. Solution to the Inverse Problem of the Angular Manipulator Kinematics with Six Degrees of Freedom. Applied Sciences. 2025; 15(5):2840. https://doi.org/10.3390/app15052840

Chicago/Turabian Style

Andrieiev, Yurii, Dmytro Breslavsky, Hennadii Shabanov, Konstantin Naumenko, and Holm Altenbach. 2025. "Solution to the Inverse Problem of the Angular Manipulator Kinematics with Six Degrees of Freedom" Applied Sciences 15, no. 5: 2840. https://doi.org/10.3390/app15052840

APA Style

Andrieiev, Y., Breslavsky, D., Shabanov, H., Naumenko, K., & Altenbach, H. (2025). Solution to the Inverse Problem of the Angular Manipulator Kinematics with Six Degrees of Freedom. Applied Sciences, 15(5), 2840. https://doi.org/10.3390/app15052840

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Solution to the Inverse Problem of the Angular Manipulator Kinematics with Six Degrees of Freedom

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