Kinematics and Dynamics of Deployable Structures with Scissor-Like-Elements Based on Screw Theory

• Published in: Chinese journal of mechanical engineering Vol. 27; no. 4; pp. 655 - 662
• Main Authors: Sun, Yuantao, Wang, Sanmin, Mills, James K., Zhi, Changjian
• Format: Journal Article
• Language: English
• Published: Beijing Chinese Mechanical Engineering Society 01.07.2014; Springer Nature B.V; School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an, 710072, PR China%Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Rd.,Toronto, Ontario, Canada
• Edition: English ed.
• Subjects: Acceleration; Closed loops; Computer simulation; Deployable structures; Dynamics; Electrical Machines and Networks; Electronics and Microelectronics; Engineering; Engineering Thermodynamics; Equations of motion; Heat and Mass Transfer; Instrumentation; Jacobi matrix method; Kinematics; Machines; Manufacturing; Mathematical analysis; Matrix methods; Mechanical Engineering; Power Electronics; Processes; Screw theory; Screws; Spacecraft; Theoretical and Applied Mechanics; Topology; 元素; 剪刀; 动力学方程; 环结构; 螺旋理论; 运动学; 运动方程; 雅可比矩阵; screw theory; kinematics; dynamics; the principle of virtual work; scissor-like-element
• ISSN: 1000-9345; 2192-8258
• DOI: 10.3901/CJME.2014.0519.098

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.