Abstract:

For the robot with flexible manipulators,a rigid-flexible coupling dynamics model was established based on the Jourdain variation principle. Assumed model method was used to transform physical coordinate to modal coordinate, and to decouple the dynamics equations. According to adult arm size, ADAMS was adopted to built virtual prototype for simulation. The element interpolation function was designed. An algorithm was programmed using MATLAB to solve dynamics equations. And angle curves of manipulator obtained by ADAMS and MATLAB were compared. In view of four kinds of material: carbon fiber, aluminum, polyethylene and polypropylene, swing simulation of manipulators were done under the gravity. Figures and tables quantitatively described displacement of end deformation, spectrum and first-order and second-order vibration modal. And deformation and modal parameters were contrastively analyzed. The results show that the natural frequency of the manipulator increases and the transverse displacement of the manipulator end decreases as the ratio of the elastic modulus and density increases. Carbon fiber can be approximately modeled as a rigid body; carbon fiber and aluminum material are suitable for humanoid robot body parts; polypropylene has better integrated performance of the stiffness and flexible. The dynamics and solving method are proper.

Key words: flexible manipulator, assumed modal method, dynamics, rigid-flexible coupling, simulation

摘要：

以机器人柔性手臂为对象,基于Jourdain变分建立了刚柔耦合动力学模型;通过假设模态法将物理坐标变换成模态坐标,对动力学方程进行解耦。参考人体参数,利用ADAMS建立了虚拟样机模型,设计了形函数矩阵。在MATLAB中编写了方程求解算法。对比了ADAMS和MATLAB对柔性手臂转角的仿真。针对碳纤维、铝合金、聚乙烯和聚丙烯4种材质手臂仿真重力作用下的摆动运动,绘出了末端横向变形位移和频谱图;量化分析了变形量和模态。结果表明随着弹性模量与密度的比值增大,手臂固有频率增大,横向变形位移减小;碳纤维材质可近似建模为刚体;碳纤维和铝合金适合做手臂机构;聚丙烯材质刚度和柔顺性较好。
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关键词: 柔性手臂, 假设模态法, 动力学, 刚柔耦合, 仿真