Research On Motion And Dynamic Modeling Of Manipulator Based On Screw Theory

The research on robotics is a multidisciplinary and multi-scenario field with broad development prospects.As an important branch of robotics,the mechanical arm has the characteristics of flexibility and directness,which are more conducive to improving the work range,work accuracy,and reducing the error rate.Accurate and concise modeling methods are the basis for improving the accuracy and efficiency of the mechanical arm,which can make control methods more targeted.Therefore,researching precise and efficient modeling methods has theoretical value and significance.The mechanical arm is a nonlinear system with multiple inputs and outputs,and traditional modeling methods for analyzing motion,velocity,and force are relatively isolated and lack universality.Therefore,this study is based on the spinor theory,taking the six-degreeof-freedom mechanical arm as the research object,and proposes a method of using spinor theory for modeling the motion and dynamics of the mechanical arm.The results show that this method achieves clear,accurate,and universal physical meanings,laying a foundation for efficient control methods.Firstly,the kinematic model is analyzed.Based on the spinor theory,mathematical models of the mechanical arm’s kinematics are derived,combined with mathematical tools such as Lie groups and Lie algebras,and the advantages of spinor methods are analyzed.For the kinematic inverse solution algorithm,the idea and method of decomposing the motion mechanism are used to improve the computational efficiency of the inverse solution algorithm.The correctness of the kinematic model and inverse solution algorithm is verified through simulation experiments,laying the foundation for subsequent studies on dynamics.Secondly,the singular and workspace of the mechanical arm are analyzed.The role and significance of the Jacobian matrix in the study of mechanical arms are described,and the relationship between the space velocity Jacobian and the object velocity Jacobian based on spinor theory is derived.The reasons for the occurrence of singular positions of the mechanical arm and the solution of singular points are explained,and three singular configurations are obtained.The reachable workspace of the mechanical arm is analyzed using the Monte Carlo method to obtain a simulation model.Finally,the dynamic model is analyzed.By comparing the time complexity of different algorithms for dynamic modeling,the advantages of Kane’s equations in establishing the dynamics model were validated.Based on the concepts of spinors and Kane’s equations,the dynamic model parameters,including the active force spinor,for the robotic arm were defined.On this basis,the dynamic model of the robotic arm was constructed.Subsequently,simulations were performed by integrating the constructed dynamic model with the three-dimensional model of the robotic arm,confirming the correctness of the dynamic mathematical model.