Kinematic Reliability Modeling Technology Of Modified Delta Parallel Mechanism Based On Dynamic Analysis

Delta parallel mechanism was presented by R. Clavel in 1988, it is 3-DOF, the high-speed parallel mechanism, and is currently one of the most successful parallel mechanisms in the commercial applications. But its biggest drawback is that there are several spherical joints, which is difficult to process and guarantee accuracy. L. W. Tsai invented a modified 3-DOF Delta parallel mechanism. It’s most important feature is that all of the kinematic joints are the revolute joints, there are large workspace, high positioning accuracy, high stiffness, and accumulated error is small. So there are good prospects in the industrial field.Kinematic reliability is an ability to finish accurately, timely, harmoniously the given mechanical motions within the given time, under the given working conditions. Nowadays, the improving of kinematic reliability of the product has become the key to improving product quality. Parallel industrial mechanism is not widely applied in high precision industrial field because its kinematic reliability is still not up to the higher requirements. The output movement of the mechanism will deviate from the ideal trajectory when the parallel industrial mechanism is moving, because dimension and geometric tolerances, kinematic pair clearance, elastic deformation of components under the force, active joint stiffness, and other factors lead to the unsatisfactory transfer motion of mechanism. Therefore, it is necessary to expose the kinematic error mechanism of the mechanism based on dynamics analysis and elastic deformation of parallel mechanism, considering the randomness of every input error components, math model of kinematic reliability of the mechanism is deduced; and the evaluation and calculation methods of kinematic reliability of the mechanism are put forward. Kinematic reliability is the key factor of evaluate kinematic accuracy of robot; and kinematic reliability analysis provides the foundations for optimum design and error compensation of the robot. Therefore, the study based on the dynamics for the reliability of body movement is of great significance.The paper focuses on the modified Delta parallel mechanism. The primary contents of this thesis are:(1) This thesis carried out research on the kinematics problems of the modified Delta parallel mechanism. With the Applying of the vector method, inverse solution of the mechanism was calculated; by using of coordinate transformation elimination method, the mechanism’s kinematic forward solution is derived. The question of choices for many results is solved by the kinematic simulation. The Jacobian matrix of the mechanism can efficiently be obtained by using Taylor’s expansion of pose equation, then, mapping relationship between the velocity of the centroids of moving platform, the velocity and angular velocity of all bars, the velocity of all the joints and the synthetic angular velocity of driving arm can be found by using the vector method and its operation rules. Acceleration and angular acceleration expression of the moving platform, all joints and all bars’centroids can be showed.(2) By means of principle of virtual displacement, a method about static analysis of the modified Delta parallel mechanism is presented. Using the method, the balance relationship between the driving torque and external forces is obtained. Gravities of all parts are added to the static balance relationship by using the vector method and the conservation law of energy. By means of combining separating bar method and principle of virtual displacement, the constraint force of all joints are calculated. At the same time, the influence of the balance driving torque is found too.The principle of virtual work is applied to solving the dynamics equation of the modified Delta parallel mechanism. The balance relationship expression between the driving torque and external forces, gravity of all parts, inertial forces/inertial moments is obtained. At the same time the constraint force of all joints are calculated.(3) Based on the stiffness matrix of the modified Delta parallel mechanism that is defined as the Hessian matrix of a potential, a new continuous stiffness mapping model of the modified Delta mechanism is established, it not only reckons the influence of stiffness of active and passive joints and gravities factor on the mechanism stiffness, but also takes the influence of the change of the mechanism’s configuration and all parts’ elastic deformation under the constraint force on the mechanism stiffness into account. And, the stiffness characteristics of the mechanism are analysed and discussed according to distribution of stiffness index. A novel idea is proposed to evaluate the stiffness performance by the elastic deformation of the mechanism. The elastic deformation under the constrained force and gravity is calculated by superposition principle. Then, the comprehensive elastic deformation of the mechanism is obtained by a coordinate transformation method. The stiffness characteristic of the mechanism is further analyzed.(4) The errors of end-effector can be divided into the position and orientation errors by using error vector analysis. The errormapping function between the position and orientation errors of end-effector and size errors, position, orientation errors of the component, rotating pair errors is established. In addition, the mapping model between the position error of mechanism and active joint stiffness, rod’s elastic deformation is established too.In addition, based on the above dynamic analysis, combined with research and analysis about active joint stiffness of parallel mechanism, Dynamic factors of gravity, inertia force and inertia moment of all the units are added to the active joint stiffness model, so the active joint stiffness error model based on dynamic analysis is obtained. Then, the components’elastic deformation error model is established based on dynamic analysis.(5) By using of Monte Carlo method, the error sources which are obtained by random sampling test are substituted into the comprehensive error model which consisted of the size of form and position errors, and active joint stiffness and the units’elastic deformation errors based on dynamics analysis, so the huge amounts of statistical characteristics of the mechanism’s position error are obtained, and, kinematic reliability probability of the modified Delta parallel mechanism can be analysed by these data. The modified Delta parallel mechanism kinematic reliability sensitivity analysis method is given. According to the characteristics of error transfer mechanism of all kinds of error sources, the mechanism’s kinematic reliability sensitivity can be calculated by constructing the response surface function method. And sensitivity analysis is adopted to describe the contribution of the mean and variance of each error resource to reliability.In addition, with the application of redevelop function of ADAMS, a Monte Carlo simulation model for kinematic reliability analysis of parallel mechanism is established. To solve the simulation problem of elastic deformation of components, the rigid flexible hybrid model is established by replace the original rigid body as flexible body, and flexible body can be generated by the ADAMS/flex module of ADAMS software. When establishing Monte Carlo simulation model. First, a parametric virtual prototype of parallel mechanism was set up in ADAMS. The normally distributed error random variables can be obtained by programming. So, the simulation model with randomly error source is generated. Then some rigid component will be replaced by flexible component with same size. Reliability at any time is finally calcuated by analyseing motion trajectories of the end effector in ADAMS.