Dynamic Calculation Model Of Delta Parallel Robots For Real-time Control

The parallel robot is an important robot in modern industry. The Delta parallel robot is the most typical parallel robot of three translational degrees of freedom. Its whole structure is simple and compact and the driving part is evenly distributed on the static platform. These characteristics make it have good kinematic and dynamic characteristics. However, the computation of the dynamic model of the Delta parallel robot is relatively complex. In practical applications, the computational burden and long computing time strongly affect the efficiency of the whole motion control and influence the real-time performance of the Delta parallel robot. Therefore, it is necessary to decrease the computing time of dynamic model. The main goal of this dissertation is to establish a numerically simplified dynamic model of the Delta parallel robot, decreasing the computing time of this model. The new model must ensure that the computing time is less than one servo period and even it also meets the demand of the controller, whose servo period is shorter. From that, this dissertation has important implications for real-time motion control of the Delta parallel robot.This dissertation analyzes the mechanical model of the Delta parallel robot. The mechanical model is simplified according to its structural features. Based on the simplified mechanical model, the inverse solution of the position, the forward solution of the position, the model of the velocity and the model of the acceleration are analyzed. And they are verified by simulation software. Besides, the Jacobian matrix is deduced. The points of the Delta parallel robot’s boundary are obtained based on the method of bisection and the workspace of the Delta parallel robot is drawn by Matlab.On the basis of kinematics analysis, this paper studies the dynamic model of the Delta parallel robot deeply. This dissertation studies the mass matrix of the fully parallel robot and the mass matrix of the rigid bar. The dynamic equation is established by the virtual work principle. Through the analyses of the fully parallel robot and the rigid bar, the dynamic model and the mass matrix for the Delta parallel robot are established. And the mass matrix is simplified.This dissertation studies the mass matrix in depth and analyzes the changes of every elements of the mass matrix with the changes of the robot’s position. It gives out the method to simplify the computation of the mass matrix according to the symmetrical characteristic of the mass matrix. Besides, this dissertation analyzes the old dynamic model and come up with the influence parameters of the inertia item, the speed item and the gravity item. It draws the figures of the behaviors of the influence parameters and finds out the transition surfaces in every figures. In addition, the dissertation introduces the method of getting the equations of the transition surfaces. The transition surfaces distinguish the regions, where the computation of items should be ignored or simplified, from the regions, where the items should not be omitted. It simplifies the computation of the inertia item, the speed item and the gravity item in different conditions to get the simplified dynamic model. And it compares the simplified model with the dynamic model through simulations. It calculates the error and the saving time of the simplified model in the workspace. The simplified model is verified and its accuracy and rapidity are tested.