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Kinematics and dynamics of deployable structures with scissor-like-elements based on screw theory

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Abstract

Because the deployable structures are complex multi-loop structures and methods of derivation which lead to simpler kinematic and dynamic equations of motion are the subject of research effort, the kinematics and dynamics of deployable structures with scissor-like-elements are presented based on screw theory and the principle of virtual work respectively. According to the geometric characteristic of the deployable structure examined, the basic structural unit is the common scissor-like-element(SLE). First, a spatial deployable structure, comprised of three SLEs, is defined, and the constraint topology graph is obtained. The equations of motion are then derived based on screw theory and the geometric nature of scissor elements. Second, to develop the dynamics of the whole deployable structure, the local coordinates of the SLEs and the Jacobian matrices of the center of mass of the deployable structure are derived. Then, the equivalent forces are assembled and added in the equations of motion based on the principle of virtual work. Finally, dynamic behavior and unfolded process of the deployable structure are simulated. Its figures of velocity, acceleration and input torque are obtained based on the simulate results. Screw theory not only provides an efficient solution formulation and theory guidance for complex multi-closed loop deployable structures, but also extends the method to solve dynamics of deployable structures. As an efficient mathematical tool, the simper equations of motion are derived based on screw theory.

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Authors and Affiliations

  1. School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an, 710072, PR China

    Yuantao Sun, Sanmin Wang & Changjian Zhi

  2. Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Rd., Toronto, Ontario, Canada

    James K. Mills

Authors
  1. Yuantao Sun
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  2. Sanmin Wang
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  3. James K. Mills
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  4. Changjian Zhi
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Corresponding author

Correspondence to Yuantao Sun.

Additional information

Supported by National Natural Science Foundation of China(Grant No. 51175422)

SUN Yuantao, born in 1985, is currently a PhD candidate at School of Mechanical Engineering, Northwestern Polytechnical University, China. His main research internets include space deployable structure and multi-bodies systems dynamics.

WANG Sanmin, born in 1961, is a professor at School of Mechanical Engineering, Northwestern Polytechnical University, China. His research interests include mechanism, mechanical vibration and control and mechanical dynamics.

MILLS James K, is a professor at Mechanical & Industrial Engineering, University of Toronto. His research interests include robot control, control of multi-robots, design of actuators, localization, development of fixtureless assembly technology, design and control of high speed machines.

ZHI Changjian, born in 1984, is a PhD candidate at School of Mechanical Engineering, Northwestern Polytechnical University, China.

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Sun, Y., Wang, S., Mills, J.K. et al. Kinematics and dynamics of deployable structures with scissor-like-elements based on screw theory. Chin. J. Mech. Eng. 27, 655–662 (2014). https://doi.org/10.3901/CJME.2014.0519.098

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  • DOI: https://doi.org/10.3901/CJME.2014.0519.098

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