空间弹性变形梁动力学的旋量系统理论方法

Screw Theoretic View on Dynamics of Spatially Compliant Beam

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.

Beam with spatial compliance can be deformed as bending in the plane,twisting and extending.In terms of the screw theory on rigid body motion,the concept of＇deflection screw＇was introduced,spatial compliant beam theory via the deflection screw was then proposed,and the spatial compliance of such a beam system was presented and analysed based on material theory and fundamental kinematic assumptions.To study the dynamics of spatially compliant beam,the potential energy and the kinetic energy of the beam were discussed using screw theory,and then,the lagrangian was obtained.The Rayleigh-Ritz method was further used to compute the vibrational frequencies after a discussion of boundary conditions and shape functions.The eigenfrequencies of the beam with spatial compliance were compared with that of individual deformation cases,pure bending,extension or torsion.Finally,dynamics of a robot with two spatial compliant links and perpendicular joints was studied using the spatial compliant beam theory,and the coupling effects between the joint rigid body motions and the deformations of spatial compliant links can be easily found by our dynamic simulation.The study convinces that the effectiveness of using screw theory to deal with the problems of dynamic modeling and analysis of mechanisms with spatially compliant links.