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所谓空间弹性梁,即同时考虑受弯曲、拉伸和扭转等力作用而发生空间变形的梁.借助于刚体运动的旋量理论,引入了“变形旋量”这一概念,进而提出了空间弹性梁的旋量理论.在基本的运动学假设和材料力学理论基础上,分析并给出了梁的空间柔度.接着研究了空间弹性梁的动力学,用旋量理论分析了其动能和势能,从而得到了Lagrange算子.通过对边界条件和变形函数的讨论,进一步运用Rayleigh-Ritz方法计算了系统的振动频率.将空间弹性梁与纯弯曲、扭转或者拉伸等简单变形情况下的特征频率做了对比研究.最后,运用所提出的空间弹性梁理论研究了一关节轴线互相垂直的两空间柔性杆机械臂的动力学,通过动力学仿真发现了关节的刚性运动和空间柔性杆的弹性变形运动之间的耦合影响.该文的研究工作阐明了运用旋量系统理论解决具有空间弹性变形杆件的机构动力学问题的有效性.
The so-called space elastic beam, that is, the beam which takes space deformation into account simultaneously by the bending, stretching and torsion etc. With the help of the screw theory of rigid body motion, the concept of “deformation screw ” is introduced, Based on the basic kinematic assumption and the material mechanics theory, the space flexibility of the beam is analyzed and given. Then the dynamics of the space elastic beam is studied, and the kinetic energy of the space elastic beam is analyzed. And the potential energy, we obtain the Lagrange operator.Finally, the Rayleigh-Ritz method is used to calculate the vibration frequency of the system by discussing the boundary conditions and the deformation function.When the space elastic beam is simply deformed with pure bending, twisting or stretching Finally, the dynamics of a two-space flexible rod manipulator with one joint axis perpendicular to each other was studied by using the proposed space elastic beam theory, and the rigid motion of the joint and the space flexible rod were found by dynamic simulation Of the elastic deformation of the coupling between the motion of the paper’s work illustrates the use of spin-system theory to solve the spatial elastic deformation of the bar body power The effectiveness of the problem.