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

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.