Research On The Dynamic Solution Method Of Four-dof Manipulator Based On Quantized State System

In the field of engineering dynamics of modern machinery,numerical solution is the core of its analysis.When solving ordinary differential equations of general dynamics,the traditional integral solution method based on time discretization is usually adopted,but it shows some limitations when solving complex dynamic models such as stiff,strong coupling and non-linearity.Quantized state system(QSS)is a new numerical integration method,which is different from the traditional time discretization integration methods.The QSS method discretizes state variables and calculates the time required for each transition of variables.Compared with traditional methods,QSS method has certain advantages in solving,but QSS method is not suitable for solving strongly stiff dynamic equations.To solving these problems,in order to effectively improve the solving accuracy of the stiff ODE systems,a step correction optimization algorithm(SCOA)based on QSS is proposed.This algorithm combines the ideas of the QSS method and the implicit trapezoidal integral method.The feasibility of this algorithm is proved by the simulation of three typical stiff ODE cases.The performance of this algorithm is compared with that of the traditional integration methods and QSS methods in terms of simulation time and simulation accuracy.The results show that the SCOA algorithm can effectively improve the simulation efficiency,and at the same time,the simulation accuracy can be significantly improved by appropriately reducing the quantum size.To further verify the effectiveness and engineering applicability of the proposed algorithm,the dynamic model of the four degree of freedom manipulator,which is highly nonlinear,strongly stiff and strongly coupled,is simulated and analyzed.Firstly,the dynamic mathematical model of the four degree of freedom manipulator is established by using Lagrange method,and then the mixed differential and algebraic dynamics equation is transformed into the first order ordinary differential which can be solved directly by the algorithm in this paper,finally,the traditional numerical method and QSS and other methods are used for simulation and comparison.The results show that the dynamic equation of the four degree of freedom manipulator based on the algorithm presented in this paper has some advantages in solving the simulatin efficiency and accuracy.Therefore,the algorithm in this paper provides an idea and reference for solving complex dynamic systems in the engineering field.