Kinematic Comparisons of Hybrid Mechanisms for Bone Surgery: 3-PRP-3-RPS and 3-RPS-3-PRP
1
Department of Mechanical Engineering, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia
2
Faculty of Mechanical Engineering, The University of Danang-University of Technology and Education, Danang 550000, Vietnam
3
Department of Mechanical Engineering, National Central University, Taoyuan City 32001, Taiwan
*
Author to whom correspondence should be addressed.
Academic Editor: Antonio J. Marques Cardoso
Machines 2022, 10(11), 979; https://doi.org/10.3390/machines10110979
Received: 19 July 2022
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Revised: 10 September 2022
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Accepted: 18 October 2022
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Published: 26 October 2022
(This article belongs to the Section Automation and Control Systems)
This paper proposes an approach to derive the Jacobian matrix of a hybrid mechanism by applying a velocity operator to the transformation matrix. This Jacobian matrix is capable of deducing hybrid singularities, which cannot be identified by using the screw-based Jacobian or velocity-based Jacobian. The transformation matrix was obtained based on the algebraic geometry approach, and it becomes the key point since it was used to not only formulate the Jacobian matrix, but also to define the motion type of hybrid mechanisms. In this paper, two hybrid mechanisms were investigated, which were composed of two distinct parallel mechanisms mounted in series. Hybrid Mechanisms 1 and 2 were composed of 3-PRP-3-RPS and 3-RPS-3-PRP (the underlined P is an actuated joint), respectively. The motion types of Hybrid Mechanisms 1 and 2 were determined from the product of the transformation matrices of the 3-PRP and 3-RPS parallel mechanisms, and vice versa. The developed method was employed to establish the Jacobian matrix to which the conditioning index was applied. Therefore, the kinematic performances of the two hybrid mechanisms can be compared for a given bone surgery trajectory within the workspace. It turns out that Hybrid Mechanism 1 has superior performance than that of Mechanism 2, which indicates that Mechanism 1 is better at transmitting power to the moving platform.
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Keywords:
hybrid mechanisms; transformation matrix; Jacobian; singularities; workspace; performance indices
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MDPI and ACS Style
Reinaldo, C.; Phu, S.N.; Essomba, T.; Nurahmi, L. Kinematic Comparisons of Hybrid Mechanisms for Bone Surgery: 3-PRP-3-RPS and 3-RPS-3-PRP. Machines 2022, 10, 979. https://doi.org/10.3390/machines10110979
AMA Style
Reinaldo C, Phu SN, Essomba T, Nurahmi L. Kinematic Comparisons of Hybrid Mechanisms for Bone Surgery: 3-PRP-3-RPS and 3-RPS-3-PRP. Machines. 2022; 10(11):979. https://doi.org/10.3390/machines10110979
Chicago/Turabian StyleReinaldo, Christopher, Sinh Nguyen Phu, Terence Essomba, and Latifah Nurahmi. 2022. "Kinematic Comparisons of Hybrid Mechanisms for Bone Surgery: 3-PRP-3-RPS and 3-RPS-3-PRP" Machines 10, no. 11: 979. https://doi.org/10.3390/machines10110979
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