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<p>As space equipment become larger in size and more flexible, generalized mechanisms are being widely used in space-deployable structures. Dynamic modeling of large-scale generalized space-deployable mechanisms is challenging owing to the coupling between the deformation of flexible links and rigid body motion. This study develops a dynamic modeling method for generalized mechanisms using the local frame of the <i>SE</i>(3) Lie group. The model represents both rigid and flexible links within a unified Lie group setting. The expressions for the velocities of rigid links and deformation of flexible links are derived using the Lie algebra framework. The nonuniqueness of the degrees of freedom of generalized kinematic pairs is considered, and the velocity fields of kinematic pairs in different situations are expressed. The equations of motion are derived using Hamilton’s principle. Because the velocities are expressed in the local frame, the mass matrix in the equation is constant, which yields a compact and unified expression for the dynamic equation. A Lie group generalized-<i>α</i> time integration method is adopted to ensure numerical stability and efficiency in simulating multibody systems with large rotations and deformations. Two numerical examples are studied to demonstrate a formulation that reflects the motion responses under varying configurations and loading conditions. This study broadens the application of the local frame of the Lie group formulation in space mechanisms and provides a new concept for dynamic modeling of generalized mechanisms.</p>

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Dynamics of Generalized Space-Deployable Mechanisms Based on the Local Frame of the SE(3) Group

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月28日

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  • Zijie Zeng,
  • Tuanjie Li,
  • Hangjia Dong

摘要

As space equipment become larger in size and more flexible, generalized mechanisms are being widely used in space-deployable structures. Dynamic modeling of large-scale generalized space-deployable mechanisms is challenging owing to the coupling between the deformation of flexible links and rigid body motion. This study develops a dynamic modeling method for generalized mechanisms using the local frame of the SE(3) Lie group. The model represents both rigid and flexible links within a unified Lie group setting. The expressions for the velocities of rigid links and deformation of flexible links are derived using the Lie algebra framework. The nonuniqueness of the degrees of freedom of generalized kinematic pairs is considered, and the velocity fields of kinematic pairs in different situations are expressed. The equations of motion are derived using Hamilton’s principle. Because the velocities are expressed in the local frame, the mass matrix in the equation is constant, which yields a compact and unified expression for the dynamic equation. A Lie group generalized-α time integration method is adopted to ensure numerical stability and efficiency in simulating multibody systems with large rotations and deformations. Two numerical examples are studied to demonstrate a formulation that reflects the motion responses under varying configurations and loading conditions. This study broadens the application of the local frame of the Lie group formulation in space mechanisms and provides a new concept for dynamic modeling of generalized mechanisms.