Current issue
Archive
About the Journal
About
Editorial Board
Abstract & Indexing
Contact
Editorial Policies
Authorship & COI
Ethical principles
Principles of Transparent Checklist
Open access
For Authors
Instructions to Authors
Detailing Guidelines for Authors
Review process
Review sheet
How to submit
Open Access license
ORIGINAL PAPER
Condition number analysis of a Three Degrees of Freedom Translational Parallel Cube Manipulator
1
Prosthetics and Orthotics Technologies Department, Polytechnic College Mosul, Northern Technical University
2
Technical Engineering College - Mosul, Northern Technical University
These authors had equal contribution to this work
Submission date: 2025-08-24
Acceptance date: 2026-01-27
Online publication date: 2026-06-01
Publication date: 2026-06-01
Corresponding author
International Journal of Applied Mechanics and Engineering 2026;31(2):110-120
KEYWORDS
TOPICS
ABSTRACT
Robot manipulators are geometrically classified into parallel, serial, and hybrid configurations, with parallel manipulators demonstrating superior characteristics including enhanced payload-to-weight ratios, increased structural stiffness, and improved operational accuracy compared to their serial counterparts. This research investigates a three-degree-of-freedom translational parallel cube manipulator through comprehensive kinematic analysis. The study successfully resolves the inverse kinematics problem and derives the corresponding Jacobian matrix, establishing the mathematical foundation for performance evaluation. The condition number serves as a fundamental performance index for quantifying manipulator dexterity and assessing system sensitivity to geometric parameter variations, including link dimensions and moving platform radius, calculated as the ratio between the highest and lowest singular values of the Jacobian matrix. Condition number values are systematically computed across the entire workspace for various geometric parameter ratios, introducing the concept of "well-conditioned" workspace regions where the condition number remains within acceptable bounds. The percentage of well-conditioned workspace area is calculated to evaluate overall manipulator performance. A specialized Python implementation facilitates comprehensive manipulator analysis and computational processing. Results are presented through graphical visualization, demonstrating the relationship between design parameters and workspace performance characteristics, providing valuable insights for optimal manipulator design and operational planning
REFERENCES (21)
1.
Choi H., Konno A. and Uchiyama M. (2010): Inverse dynamics analysis of a 4-d.o.f. parallel robot H4.– Advanced Robotics, vol.24, No.1, pp.159-177, https://doi.org/10.1163/016918....
2.
Stewart D. (1965): A platform with six degrees of freedom.– Proceedings of the Institution of Mechanical Engineers, vol.180, No.1, pp.371-386, https://doi.org/10.1243/PIME_P....
3.
Beira R., Santos-Carreras L., Rognini G., Bleuler H. and Clavel R. (2011): Dionis: A novel remote-center-of-motion parallel manipulator for minimally invasive surgery.– Applied Bionics and Biomechanics, vol.8, No.2, pp.211-225, https://doi.org/10.3233/ABB-20....
4.
Siciliano B. (1999): The Tricept robot: inverse kinematics, manipulability analysis and closed-loop direct kinematics algorithm.– Robotica, vol.17, No.4, pp.437-445, https://doi.org/10.1017/S02635....
5.
Murray A.P., Pierrot F., Dauchez P. and McCarthy J.M. (1997): A planar quaternion approach to the kinematic synthesis of a parallel manipulator.– Robotica, vol.15, No.4, pp.361-365, https://doi.org/10.1017/S02635....
6.
Chablat D. and Wenger P. (2003): Architecture optimization of a 3-DOF translational parallel mechanism for machining applications, the Orthoglide.– IEEE Transactions on Robotics and Automation, vol.19, No.3, pp.403-410, https://doi.org/10.1109/TRA.20....
7.
Kim J. and Tsai L.W. (2002): A three translational DoFs parallel cube-manipulator.– IEEE Transactions on Robotics and Automation, vol.18, No.4, pp.545-555, https://doi.org/10.1109/TRA.20....
8.
Pennock G.R. and Kassner D.J. (1992): Kinematic analysis of a planar eight-bar linkage: application to a platform-type robot.– Journal of Mechanical Design, vol.114, No.1, pp.87-95, https://doi.org/10.1115/1.2916....
9.
Merlet J.-P. and Daney D. (2008): Appropriate Design of Parallel Manipulators.– In: L. Cheng and A.L. Zelinsky (Eds): Smart Devices and Machines for Advanced Manufacturing, Springer, pp.1-25, https://doi.org/10.1007/978-1-....
10.
Ghasemi H., Ebrahimi I. and Carricato M. (2002): Isotropic design of spatial parallel manipulators.– The International Journal of Robotics Research, vol.21, No.9, pp.842-853, https://doi.org/10.1177/027836....
11.
Mustafa O.A., Abdallah A.S., and Alkhaffaf Z.H.: Experimental Investigation of the Thermal Behavior of Semi-Solid Materials. https://doi.org/10.59441/ijame....
12.
Mohammed S.H., Yousif O.M., and Abedalh A.S. (2026): Use of adsorption pair of activated carbon and methanol in solar ice maker – Appl. Therm. Eng., vol.288, p.129687. https://doi.org/10.1016/j.appl....
13.
Mayoof O.T., Yasin N.J., and Abedalh A.S. (2025): Experimental investigation for utilization of U-shaped heat pipe heat exchanger in the air-conditioning system.– Int. Commun. Heat Mass Transf., vol.163, p.108730. https://doi.org/10.1016/j.iche....
14.
Abedallh A.S., Alomar O.R., and Yasin N.J. (2024): Numerical and experimental investigation on mixed convection heat transfer inside cavity heated from below with reciprocating moving upper surface – Int. Commun. Heat Mass Transf., vol.159, p.108242. https://doi.org/10.1016/j.iche....
15.
Badr A.A., Luhaibi M.T., Almula T.A.D.M.S., Abedalh A.S. (2026): Thermophysical performance enhancement of vapor-compression chiller systems via metal oxide nanofluid integration– Environmental Progress & Sustainable Energy, vol.45, Issue 1. https://doi.org/10.1002/ep.702....
16.
Abedalh A.S., Alyas B.H., Ali F.A., Almula T.A.D.M.S.: Experimental and numerical analysis of hydrothermal behavior for different nanofluids in a shallowly dimpled tube heat exchanger.– https://aiche.onlinelibrary.wi....
17.
Alyas B.H., Ali F.A., Abedalh A.S., Almula T.A.D.M.S.: Entropy generation analysis of nanofluid heat transfer in dimpled heat exchangers.– The Canadian Journal of Chemical Engineering. https://onlinelibrary.wiley.co....
18.
Yassien H.N.S., Abedalh A.S., Yousif O.M., and Hussein A.T. (2025): Impact of CuO+H2O nanofluid on the cooling towers performance with varying packing densities.– Results Eng., vol.26, p.104664. https://doi.org/10.1016/j.rine....
19.
Abedalh A.S., Hussein A.T., and Yousif A.A. (2023): Experimental investigation for vapor compression system performance enhancement through condenser cooling by using shallow fluidized bed.– J. Therm. Anal. Calorim., vol.148, no.21, pp.12301–12310. https://doi.org/10.1007/s10973....
20.
Abedalh A.S. and Mohammed S. (2023): Numerical investigation thermal performance of solar air heater using different angle v-grooved of corrugated absorber plate.– Front. Heat Mass Transf., vol.21, pp.227-243. https://doi.org/10.32604/fhmt.....
21.
Abdallah A.S., Yasin N.J., and Ameen H.A. (2024): A numerical investigation on the effect of nano metal oxide coating fins on the thermal performance of heat pipe heat exchanger.– AIP Conf. Proc., American Institute of Physics. https://doi.org/10.1063/5.0212....
| eISSN: | 2353-9003 |
| ISSN: | 1734-4492 |
Task: edition of a scientific journal, its internationalization and ensuring open access to the journal via the Internet
© 2006-2026 Journal hosting platform by Bentus
We process personal data collected when visiting the website. The function of obtaining information about users and their behavior is carried out by voluntarily entered information in forms and saving cookies in end devices. Data, including cookies, are used to provide services, improve the user experience and to analyze the traffic in accordance with the Privacy policy. Data are also collected and processed by Google Analytics tool (more).
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
