بخشی از مقاله (انگلیسی)
Nonlinear dynamic of a flexible slender truss-structure mounted manipulator for on-orbit assembly, which can be simplified as a beam–rotating link interaction system, is theoretically investigated. The governing partial differential equations (PDEs) of beam with time-varying coefficients is established by using the D’Alembert principle incorporated with the moment balance method where the beam is of a Euler–Bernoulli type and the influence of slope is considered. Such system is a typical parametrically excited system. The multiple scales method is used to determine the approximate solution and the conditions of the primary resonance ( ω1≈ωref ) and sub-harmonic resonance ( ω1≈ 2ωref , ω1≈ 3ωref and ω1≈ 4ωref ) are obtained. In addition, the nonlinear response, stability and bifurcations for primary and sub-harmonic resonance conditions have also been investigated by varying system parameters. Moreover, the results of some specific conditions by the perturbation analysis are compared with the numerical solution and are found to be in good agreement. This work has certain guiding significance for autonomous on-orbit assembly task and the method can be extended to the more general three-dimensional case.
Future space exploration puts forward some new requirements of space structure, such as establishment of large space solar power plants to cope with energy depletion which is huge volume (from thousands of meters or even dozens of kilometers). To meet the requirements of such space missions, the space structures will be constructed too large to be launched and deployed as a whole –. It is identified as one of the most appealing solutions in which the manipulator is mounted on the long truss-structures to assemble or maintain the several adjacent blocks . One problem of great concern is that of low-frequency structure may be easily excited by high-frequency robotic and hardly damped out in space environment due to the low-damping characteristics of the flexible structures , . The vibration may cause inaccuracy of manipulator positioning, and more seriously, the premature fatigue failure of flexible structure  and it could be reduced by improving the dynamic model of the system. Therefore, it is significant to conduct studies to apprehend dynamic characteristics of such system and find some structural parameter design criterion to minimize the vibration amplitude.
In this paper, a typical flexible slender truss-structure mounted manipulator (FSTMM) for on-orbit assembly, as shown in Fig. 1(a), is studied. During the robot is assembling the truss structure, the robot is mounted on the long truss to assemble the next module of the truss. To focus on the fundamental issues of the dynamic problem, the long truss structure can be simplified as a flexible beam ,  and only the first link of manipulator is considered. Such system is a typical beam–rotating link interaction system. A very limited work of such system has been reported. For example, the speed exclusion zone of a wind turbine, which was regarded as a typical cantilever beam structure attached with a rotating unbalanced mass, was investigated to prevent tower resonance . The nonlinear dynamic behavior of a non-ideal unbalanced motor in a simple cantilever beam system was investigated and the results indicate there appears the jump phenomenon, namely the Sommerfeld effect , . A model using RLC circuits with variable capacitance based on the saturation phenomenon is used to control the vibration of a hinged-hinged beam supporting unbalanced machine . A nonlinear dynamical model of a robot manipulator consisting of a flexible cantilever beam and rigid second link is derived using a Lagrange equation and a Lyapunov-based feedback control law is then introduced to suppressing bending vibrations in the flexible link .
Nonlinear dynamic of a flexible slender truss-structure mounted manipulator for on-orbit assembly, which can be simplified as a beam–rotating link interaction system, is theoretically investigated for primary and sub-harmonic resonance. The PDEs of system is established by using the D’Alembert principle incorporated with the moment balance method in which the slope of beam is considered. Such system is a typical parametrically excited system. The multiple scales method is used to solve the second-order ODEs which is reduced by the Galerkin’s method with a single mode approach from obtained PDEs. Then, the non-linear response, stability and bifurcations for primary and all sub-harmonic resonance conditions have been investigated by varying system parameters. By inspecting the results of this analysis, the following conclusions could be made:
When the excitation frequency of manipulator ω1 near equal to the linear natural frequency of flexible truss-structure ωref , there will exist simple resonance condition and only have nontrivial steady state solution. The system resonance could be classified into monostable and bistable region by saddle-node (SN) bifurcation point. The steady state responses of the system in bistable region are determined by the initial condition and a slight change of initial conditions may cause a significant change. On the other hand, increasing the level of damping, as well as decreasing the mass of rigid manipulator and installation position of manipulator close to fixed end will reduce steady state responses of beam.