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ABSTRACT
The basic characteristics of mechanism kinematics are investigated to explain the background for the dynamic simulation procedure developed herein, which is especially suitable for pantographic deployable masts (PDM). Natural Cartesian coordinates are used due to their simplicity. The kinetic energy of the uniform rod can thus be expressed in terms of the Cartesian coordinates of the joints. First, dynamic differential equations are formulated with respect to a series of dependent coordinates. The constraint equations of the rigid body, scissor-like-element (SLE), and slider, etc., are formulated in succession. Then, based on the first and second differentials of the constraint equations and the null-space base of the constraint Jacobian matrix, we introduce the constraints into the differential dynamic equations, which are so reduced with respect to the independent generalized coordinates. Furthermore, a Runge–Kutta 4th-order (RK-4) algorithm, together with numerical stabilization techniques, is used to get the time history solutions of the dynamic equations. Finally, three numerical tests are presented, and dynamic deployment simulations are carried out for four particular PDM. The results show that the algorithm is efficient for dynamic simulations of a foldable truss.
*Communicated by E. Zahariev.
Acknowledgments
Notes
*Communicated by E. Zahariev.
