Kinematic Calibration And Elasto-dynamic Analysis Of A Parallel Tracking Mechanism

Tracking mechanism is an important component of the inter-satellite link antenna of relay satellite,which drives the antenna to realize real-time tracking of spacecrafts on medium and low orbit.The commonly used inter-satellite link antenna tracking mechanisms are all in serial topology.The traditional large load serial tracking mechanisms have many drawbacks,such as large moment of inertia,large joint friction,small orientation workspace,blindness zone and structure singularity.Compared with the serial mechanism,the parallel tracking mechanism has become an effective solution for the continuous tracking and control system of the medium and low orbit spacecrafts due to its advantages of large orientation workspace,high stiffness / mass ratio and good dynamic performance.Meanwhile,the precision assurance technology is the key technology of parallel tracking mechanism.In order to meet the major requirements of national aerospace engineering,the 4-RSR&SS parallel tracking mechanism developed by Tianjin University is taken as the research object,and the accuracy assurance technology of the inter satellite link antenna tracking mechanism is systematically studied.With the help of screw theory and flexible multi-body dynamics and other mathematical tools,the research work of kinematics and rigid body dynamics analysis,geometric error modeling,kinematic calibration,elasto-dynamic analysis and related experimental research work of parallel tracking mechanism are carried out.The main research contents are listed as follows:(1)Kinematics and rigid body dynamics.The forward and inverse kinematics models of the mechanism are established by means of the closed-loop position vector equation.Secondly,the screw theory is used to obtain the velocity and acceleration model of the tracking mechanism.After that,gravity wrenches and inertia force wrenches are established.Then the dynamic model of rigid body is constructed by using the principle of virtual work.Finally,the effectiveness of the rigid body dynamics model is verified by simulations with MATLAB and ADAMS software.(2)Geometric error modeling.The geometric error models of each limb of tracking mechanism are established by using the screw theory.Then,the error models of each limb are integrated into the overall error model.The explicit expression of the error model of the over-constrained mechanism is obtained by means of the generalized inverse of the direct Jacobian matrix.After that,the sensitivity of geometric error is analyzed using the error sensitivity coefficient.Extracted error items which are sensitive to pose errors of the moving platform are strictly controlled in part tolerance design process.Finally,the effectiveness of the error model is verified by simulations using Solid Works software.(3)Kinematic calibration.The actual inverse kinematic model of the tracking mechanism is established.The objective functions are constructed based on the deviation between the actual input angles and the calculated input angles by the singlelimb actual inverse kinematic model.Then,the hybrid genetic algorithm is used to optimize the objective functions so as to identify the geometric errors.Finally,the calibration process is simulated using Solid Works software to verify the effectiveness of the novel calibration method.(4)Flexible multi-body dynamics modeling.Shape functions of three-dimensional isoparametric beam elements considering curvature are utilized,then the kinetic energy,elastic potential energy and gravity potential energy of beam element are derived with floating coordinate method,and then the Lagrange dynamic equation of spatial beam element is deduced.Secondly,the dynamic equations of flexible bodies are obtained by assembling the dynamic equations of beam elements,and then the dynamic equations of tracking mechanism without constraints are acquired.Finally,the joint constraint equations are introduced by the augmented Lagrangian multiplier method to obtain a complete flexible multi-body dynamics model of the parallel tracking mechanism.(5)Dynamic characteristics analysis and natural frequency sensitivity analysis.The natural frequencies of the tracking mechanism are studied by using the rigidflexible coupling dynamic model,which is verified by finite element software.Secondly,by taking the stiff characteristics of elasto-dynamic equations into consideration,an efficient numerical algorithm is adopted to solve the problem.After that,the effectiveness of the model is further verified by comparing the numerical calculated results with the simulation results using ADAMS software.Then,the flexible parts of the mechanism and the effect of vibration on the accuracy are studied.Finally,the natural frequency sensitivity of the tracking mechanism is analyzed by direct differential method.A new sensitivity coefficient based on the root mean square of the first three-order natural frequency sensitivity coefficients is proposed to guide the physical prototype design.(6)Experiments on kinematic calibration and dynamic characteristics test of tracking mechanism.Based on the physical prototype of tracking mechanism designed by our research group,with the help of laser tracker and LMS dynamic analyzer,kinematics calibration experiments and vibratory mode experiments of the physical prototype of the tracking mechanism are carried out.Finally,the effectiveness of the theoretical models is verified by comparing them with the simulations,and the corresponding performance of the physical prototype is tested and improved.The aforementioned research achievements might enrich the basic theoretical study of parallel mechanism and contribute to the development and application of the tracking mechanism of the inter-satellite link antenna with excellent performance.Therefore,it has important scientific significance and application value.