Research On The Kinematics And Dynamics Of Tetrahedral Deployable Unit Mechanism Of Truss Antenna

Spatial deployable mechanism is widely used in the modular assembly of large-scale spatial deployable antenna due to its foldability and high stability.There are many common basic modules,among which tetrahedral deployable unit mechanism has been used in large-scale truss antenna due to its high storage ratio and high precision,and has been in orbit.However,due to the multi closed-loop and multi redundant structure of tetrahedral deployable unit mechanism,its configuration design,kinematics and dynamics analysis are difficult.In this paper,the theoretical calculation and software simulation analysis are used to study the degrees of freedom and dynamic characteristics of tetrahedral deployable unit mechanism.At the same time,because the joint clearance is inevitable in the actual mechanism,this paper also studies the clearance dynamic characteristics and the influence of clearance parameters on the dynamic mechanical characteristics of the mechanism.First of all,the method of module decomposition and combination of mechanism is put forward,the topological graph of geometric constraint of mechanism is drawn step by step by using the knowledge of graph theory,the screw constraint equations of each link are listed in combination with the screw theory,which are expressed in the form of matrix,the formula of freedom degree of mechanism is deduced,and then the freedom degree of mechanism is obtained;the screw speed of mass center of mechanism component is deduced by using the speed transfer relation of mechanism,and the screw speed of mechanism component is built Kinematic equation of the mechanism.Secondly,the Jacobian matrix of the component’s center of mass is derived from the component’s local coordinate system,and the screw acceleration of the component’s center of mass is derived from the mechanism’s dynamic transmission process;the absolute acceleration of the component’s center of mass is solved by the rigid body acceleration synthesis principle,and the mechanism’s dynamic theoretical model is established by combining the virtual work principle.Then,the multi closed-loop mechanism is divided into tree system module and cutting hinge module by using the cutting hinge method.The modular Jacobian matrix of each module of the mechanism is established by combining the body hinge vector and path vector of graph theory,and the clearance dynamic model of the mechanism is established by using the Lagrangian multiplier method of the first kind,and the kinematic and dynamic characteristics of the mechanism are analyzed by the clearance parameters Influence.Finally,based on the results of theoretical analysis,Adams is used for simulation analysis,and Matlab is used to solve the kinematics and dynamic equations,and the correctness of the theoretical model is verified by comparing the theoretical calculation results with the simulation analysis results.