An improved dynamic modeling of a multibody system with spherical joints |
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Authors: | Ali Rahmani Hanzaki Subir Kumar Saha P V M Rao |
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Affiliation: | (1) Mechanical Engineering Dept., Shahid Rajaee University, Lavizan, Tehran, Iran;(2) Mechanical Engineering Dept., IIT Delhi, Hauz Khas, New Delhi, 110016, Delhi, India |
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Abstract: | A dynamic modeling of multibody systems having spherical joints is reported in this work. In general, three intersecting orthogonal
revolute joints are substituted for a spherical joint with vanishing lengths of intermediate links between the revolute joints.
This procedure increases sizes of associated matrices in the equations of motion, thus increasing computational burden of
an algorithm used for dynamic simulation and control. In the proposed methodology, Euler parameters, which are typically used
for representation of a rigid-body orientation in three-dimensional Cartesian space, are employed to represent the orientation
of a spherical joint that connects a link to its previous one providing three-degree-of-freedom motion capability. For the
dynamic modeling, the concept of the Decoupled Natural Orthogonal Complement (DeNOC) matrices is utilized. It is shown in
this work that the representation of spherical joints motion using Euler parameters avoids the unnecessary introduction of
the intermediate links, thereby no increase in the sizes of the associated matrices with the dynamic equations of motion.
To confirm the efficiency of the proposed representation, it is illustrated with the dynamic modeling of a spatial four-bar
Revolute-Spherical–Spherical-Revolute (RSSR) mechanism, where the CPU time of the dynamic modeling based on proposed methodology
is compared with that based on the revolute joints substitution. Finally, it is explained how a complex suspension and steering
linkage can be modeled using the proposed concept of Euler parameters to represent a spherical joint. |
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Keywords: | Spherical joint Dynamic modeling Euler parameters Closed loop |
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