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Reduced transfer equations of ball-and-socket joint elements incorporated with Euler parameters.

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Title: Reduced transfer equations of ball-and-socket joint elements incorporated with Euler parameters.
Authors: Zhang, Xizhe1,2 (AUTHOR), Rui, Xiaoting1,2 (AUTHOR), Zhang, Jianshu1,2 (AUTHOR) jszhang@njust.edu.cn, Chen, Feifei1,2 (AUTHOR), Wang, Guoping1,2 (AUTHOR)
Source: Archive of Applied Mechanics. Dec2024, Vol. 94 Issue 12, p3731-3751. 21p.
Subjects: Euler angles, Degrees of freedom, Transfer matrix, Relative motion, Acceleration (Mechanics)
Abstract: The reduced multibody system transfer matrix method is a completely recursive method utilizing joint coordinates and applicable for evaluating the generalized accelerations of a multibody system at any given moment, provided that the generalized coordinates and velocities are known. For an open-loop multi-rigid-body system, the generalized coordinates of the system are composed of the generalized relative coordinates of the joint elements. Typically, for each joint element, the dimension of the generalized relative coordinates is equal to its relative motion degrees of freedom, leading to minimum dimension of the generalized coordinates of the system, which is equal to the degrees of freedom of the system. However, this may result in singularity for a ball-and-socket joint element when evaluating its generalized accelerations if any triad of Euler angles is utilized as its generalized relative coordinates. The tetrad Euler parameters are an alternative to Euler angles to resolve such a singular problem, which is a common practice in the dynamics approaches using body coordinates as generalized coordinates; nevertheless, it has not been observed in the completely recursive methods with joint coordinates. In this paper, the self-constraint equations of Euler parameters are taken into account to establish the corresponding reduced transfer equations characterized by a symmetric generalized inertial matrix, which are in completely recursive form. Fundamental numerical stability analyses are conducted via condition numbers of corresponding matrices, demonstrating that employing Euler parameters to describe the relative kinematics of a ball-and-socket joint element enhances numerical stability compared to Euler angles. [ABSTRACT FROM AUTHOR]
Copyright of Archive of Applied Mechanics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: The reduced multibody system transfer matrix method is a completely recursive method utilizing joint coordinates and applicable for evaluating the generalized accelerations of a multibody system at any given moment, provided that the generalized coordinates and velocities are known. For an open-loop multi-rigid-body system, the generalized coordinates of the system are composed of the generalized relative coordinates of the joint elements. Typically, for each joint element, the dimension of the generalized relative coordinates is equal to its relative motion degrees of freedom, leading to minimum dimension of the generalized coordinates of the system, which is equal to the degrees of freedom of the system. However, this may result in singularity for a ball-and-socket joint element when evaluating its generalized accelerations if any triad of Euler angles is utilized as its generalized relative coordinates. The tetrad Euler parameters are an alternative to Euler angles to resolve such a singular problem, which is a common practice in the dynamics approaches using body coordinates as generalized coordinates; nevertheless, it has not been observed in the completely recursive methods with joint coordinates. In this paper, the self-constraint equations of Euler parameters are taken into account to establish the corresponding reduced transfer equations characterized by a symmetric generalized inertial matrix, which are in completely recursive form. Fundamental numerical stability analyses are conducted via condition numbers of corresponding matrices, demonstrating that employing Euler parameters to describe the relative kinematics of a ball-and-socket joint element enhances numerical stability compared to Euler angles. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Archive of Applied Mechanics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s00419-024-02692-5
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        Text: English
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        Type: general
      – SubjectFull: Degrees of freedom
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      – SubjectFull: Transfer matrix
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      – SubjectFull: Relative motion
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              M: 12
              Text: Dec2024
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