Rotation Transformation Matrix of the Joint Coordinate System with the Application to the Knee Joint
Апстракт
The human musculoskeletal system is comprised of various joints which are characterized by
their unique morphology and kinematics. The joint coordinate system is tailored to comply with
the observed mechanical properties of joints, making their research more intuitive and in
accordance with standard clinical terminology. This coordinate system allows for spatial orientation to be described by three sequence independent Euler angles (the so-called “jaw-pitch-roll” angles), which mirrors the sequence independency of the final position of human limbs. The knee joint is the most complex, both anatomically and mechanically. It can be modeled as a four link open kinematic chain to which the joint coordinate system is applied. This coordinate system is usually described in Denavit-Hartenberg parameters, and the rotation transformation matrix is obtained using standard methods of vector algebra. In this paper another approach is used to derive the rotation transformation matrix, namely, the... Rodrigues’ rotation formula. The utility of this algorithm is evident: the Rodrigues’ method provides an elegant solution which is obtained in a concise and efficient manner.
Кључне речи:
biomechanics / knee joint / joint coordinate system / rotation transformation matrix / Rodrigues’ rotation formulaИзвор:
Proceedings of the 8th International Congress of Serbian Society of Mechanics, Kragujevac, Serbia, June 28-30, 2021., 2021Издавач:
- Beograd: Srpsko društvo za mehaniku
Финансирање / пројекти:
- Динамика хибридних система сложених структура. Механика материјала (RS-MESTD-Basic Research (BR or ON)-174001)
Колекције
Институција/група
Mašinski fakultetTY - CONF AU - Rosić, Nevena PY - 2021 UR - https://machinery.mas.bg.ac.rs/handle/123456789/4641 AB - The human musculoskeletal system is comprised of various joints which are characterized by their unique morphology and kinematics. The joint coordinate system is tailored to comply with the observed mechanical properties of joints, making their research more intuitive and in accordance with standard clinical terminology. This coordinate system allows for spatial orientation to be described by three sequence independent Euler angles (the so-called “jaw-pitch-roll” angles), which mirrors the sequence independency of the final position of human limbs. The knee joint is the most complex, both anatomically and mechanically. It can be modeled as a four link open kinematic chain to which the joint coordinate system is applied. This coordinate system is usually described in Denavit-Hartenberg parameters, and the rotation transformation matrix is obtained using standard methods of vector algebra. In this paper another approach is used to derive the rotation transformation matrix, namely, the Rodrigues’ rotation formula. The utility of this algorithm is evident: the Rodrigues’ method provides an elegant solution which is obtained in a concise and efficient manner. PB - Beograd: Srpsko društvo za mehaniku C3 - Proceedings of the 8th International Congress of Serbian Society of Mechanics, Kragujevac, Serbia, June 28-30, 2021. T1 - Rotation Transformation Matrix of the Joint Coordinate System with the Application to the Knee Joint UR - https://hdl.handle.net/21.15107/rcub_machinery_4641 ER -
@conference{ author = "Rosić, Nevena", year = "2021", abstract = "The human musculoskeletal system is comprised of various joints which are characterized by their unique morphology and kinematics. The joint coordinate system is tailored to comply with the observed mechanical properties of joints, making their research more intuitive and in accordance with standard clinical terminology. This coordinate system allows for spatial orientation to be described by three sequence independent Euler angles (the so-called “jaw-pitch-roll” angles), which mirrors the sequence independency of the final position of human limbs. The knee joint is the most complex, both anatomically and mechanically. It can be modeled as a four link open kinematic chain to which the joint coordinate system is applied. This coordinate system is usually described in Denavit-Hartenberg parameters, and the rotation transformation matrix is obtained using standard methods of vector algebra. In this paper another approach is used to derive the rotation transformation matrix, namely, the Rodrigues’ rotation formula. The utility of this algorithm is evident: the Rodrigues’ method provides an elegant solution which is obtained in a concise and efficient manner.", publisher = "Beograd: Srpsko društvo za mehaniku", journal = "Proceedings of the 8th International Congress of Serbian Society of Mechanics, Kragujevac, Serbia, June 28-30, 2021.", title = "Rotation Transformation Matrix of the Joint Coordinate System with the Application to the Knee Joint", url = "https://hdl.handle.net/21.15107/rcub_machinery_4641" }
Rosić, N.. (2021). Rotation Transformation Matrix of the Joint Coordinate System with the Application to the Knee Joint. in Proceedings of the 8th International Congress of Serbian Society of Mechanics, Kragujevac, Serbia, June 28-30, 2021. Beograd: Srpsko društvo za mehaniku.. https://hdl.handle.net/21.15107/rcub_machinery_4641
Rosić N. Rotation Transformation Matrix of the Joint Coordinate System with the Application to the Knee Joint. in Proceedings of the 8th International Congress of Serbian Society of Mechanics, Kragujevac, Serbia, June 28-30, 2021.. 2021;. https://hdl.handle.net/21.15107/rcub_machinery_4641 .
Rosić, Nevena, "Rotation Transformation Matrix of the Joint Coordinate System with the Application to the Knee Joint" in Proceedings of the 8th International Congress of Serbian Society of Mechanics, Kragujevac, Serbia, June 28-30, 2021. (2021), https://hdl.handle.net/21.15107/rcub_machinery_4641 .