抓握结构中弹性棒变形的P-稳定性  

P-Stability for the Deformations of Elastic Rod in Gripper Structure

作　　者：殷先军[1] 

机构地区：[1]北京理工大学理学院,北京100081

出　　处：《北京理工大学学报》2004年第6期559-562,共4页Transactions of Beijing Institute of Technology

基　　金：北京市自然科学基金资助项目(1042007)

摘　　要：研究抓握结构中弹性棒变形的P-稳定性.将存在于机械手的抓握结构和机器人行走系统中的一类弹性单元抽象为变形直弹性棒,通过建立相应的物理和数学模型——常微分方程的边值问题,利用流型法画出数学模型的分支图,得到系统的多解性,借助Liapunov-Schmidt方法,通过建立分支方程,得到相应弹性变形的P-稳定性.The P-stability for deformations of a straight elastic rod in gripper structure is studied. The elastic parts in the gripper structure of a manipulator and knee joint in a robot are simplified into a deformed straight elastic rod. A boundary value problem for a pendulum equation is abstracted as the mathematical model to represent the deformation of the elastic rod. The bifurcation diagram of the mathematical model is obtained by manifold method. With the aid of Liapunov-Schmidt method and the bifurcation equation, the multiplicity and P-stability of solutions of the deformed elastic rod are achieved.

关 键 词：抓握结构 弹性变形 P-稳定性 分支图 Liapunov-Schmidt方法 

分 类 号：O175.13[理学—数学]