Modeling And Analysis Of The Stiffness Of The Cable Tight Coupling Multi Robot Crane System

With the rapid development of robot application technology,the demand for robot function is increasing.The applicable workplace of the robot and the use of methods are constantly expanding,but for the more complex work,the use of a single robot to complete the work is not the best practical plan,it uses multiple robots to work together to form a multi robot system.Firstly,the mechanics and kinematics of the cable tight coupling multi robot suspension system are analyzed.For the static analysis,the space force balance equation is derived,and then the tension on each cable is obtained.By analyzing the force and deformation on the robot,the static stiffness of the robot is obtained.Secondly,the dynamic analysis of the cable tight coupling multi robot crane system is carried out.According to the Darren Bell principle,the dynamic equation of the cable system is derived.Then,the kinematics of the cable tight coupling multi robot crane system is analyzed.In the analysis of the positive motion,the kinematics of the robot is analyzed firstly,and then the motion relationship between the robot end and the crane is established by the end position of the robot and the length of the cable.The inverse kinematics is analyzed and its inverse kinematics is relatively complicated.Firstly,the inverse kinematics of the lifting objects and the end of the robot is analyzed.Then analysis of inverse kinematics of robot and the inverse kinematics analysis of the cable tight coupling multi robot suspension system is carried out.Study of the properties of the static stiffness and dynamic stiffness of the cable tight coupling multi robot crane system are analyzed and validated.First of all,considering that the analysis of the system model,the static stiffness model of the crane system is established,and combined with the actual situation that the cable stiffness is less than the stiffness of the robot,it is concluded that the influence of the cable stiffness on the crane system is greater than the stiffness of the robot.Based on the space force balance equation,a model of the deformation and the cable deformation of the robot with the end position of the variable robot is established.The model considers not only the unidirectional tension of the cable and the characteristic of the freedom of the cable,but also the stiffness model of the crane system.Based on the geometric position relationship of the space,the location model of the crane is established.Secondly,the dynamic stiffness model of the cable system is obtained,the relationship between the crane system and its natural frequency is analyzed.The feasible region of the cable tight coupling multi robot lifting system is analyzed.Firstly,the feasible region of robot end-effector is analyzed.The feasible region model of the robot is obtained.Secondly,this paper analyzes the geometric position of the cable tight coupling multi robot crane system.The constraint conditions are analyzed and the coordinate equation of lifting objects is established.The feasible region of the cable tight coupling multi robot crane system based on stiffness is obtained.The feasible region of the lifting system is obtained by simulation,and the comparison experiment is carried out.The influence of stiffness on the feasible region is analyzed under different stiffness conditions,and the feasible region model based on stiffness is obtained.It can provide the theoretical basis for further feasible region planning.The model considers the influence of the static stiffness of the robot on the feasible region of the crane system.Based on the simulation results,the feasible region of the cable tight coupling multi robot crane system considering the static stiffness is obtained.The results of the analysis show that the feasible region is deformed after deformation,and the deformation is the largest in the vertical direction.Finally,the simulation trajectory of the lifting object is obtained based on analysis of the influence of the stiffness.The stiffness model of the cable tight coupled multi robot crane system is verified by experiments.First of all,the feasibility and operability of the experimental scheme are considered,and the basic scheme of the experiment is established according the theoretical requirements and the actual situation.Secondly,the experimental platform is built,and the requirements of the experimental equipment is introduced,it consists of the upper computer,the motion control card,the stepper motor driver,the guide rail,the motor,the load and the position and attitude measurement device.Finally,the data acquisition of the experiment is planned,and the comparison between the experimental data and the theoretical results is achieved.It includes the contrast experiment in static state and the contrast experiment in the dynamic state.The static stiffness test verifies the relationship between the weight and the displacement of the coordinate position.The experimental results show that the dynamic stiffness model is consistent with the actual trajectory.Considering the vibration of the motor itself and objective reasons such as flexibility of robot and cable.By comparing the simulation trajectory obtained from the theoretical model with the actual trajectory,it is found that there is a high consistency between them.The correctness of the theoretical model is proved.