The Study Of The Certainty Motion For Under-actuated Mechanism With Flexible Joints

The kinematic and dynamic constraints of under-actuated mechanism are incomplete and its movement is uncertain.The elastic reaction of flexible joints involved in an under-actuated mechanism can make up for the incompleteness of dynamic constraints in a way,but the kinematics and dynamics equations are still unsolvable,and the certainty of the motion still related to the initial state of the mechanism and the stiffness of the flexible joint.Aimed at these issues,a numerical iterative algorithm is proposed to solve the kinematics and dynamics,and we strive to research the deterministic motion of the mechanism by solving the definite solution of kinematics and dynamics equations.Firstly,the development status of under-actuated mechanism and compliant mechanism are summarized briefly,and then the relevant concept and research status about the under-actuated mechanism with flexible joints are introduced.Secondly,we take a planar 2-DOF under-actuated mechanism with a flexible joint as an example to analyze,the kinematics model and dynamics model are set up using the closed vector method and Lagrange equation method,and then how to solve the kinematics and dynamics equations are briefly analyzed.Thirdly,given the initial conditions of all the components and the motion law of the active joint,a numerical iterative algorithm is proposed based on the theory that velocity and acceleration is the same in an extremely brief period,then using MATLAB programming,the kinematics and dynamics equation is solved,so the correctness of the proposed method is verified.The algorithm makes up for the fact that acceleration can not be integral in an under-actuated system because of the second order nonholonomic constraints.Finally,based on the deterministic solution of kinematics and dynamics equations,the optimal stiffness range under different initial state are obtained,and the fitted curve between optimal driving torque and spring stiffness are also obtained by analyzing multiple sets of data.All these pieces of work have provides a new train of thought in the field of control areas.