Delta parallel robot is widely used in the manufacturing process of food, medicine, electronics and military industries, which is a highly nonlinear system with strongly uncertain dynamics. Therefore, there are many difficulties in the controller design of delta robot. Based on the simplified dynamic model, a nonlinear PD+ controller with nonlinear disturbance observer is proposed for Delta parallel robot in this article, which can realize high-precision trajectory tracking in high-speed and high-acceleration motion. Then, the asymptotic stability of the closed-loop system’s equilibrium point is proven by utilizing Lyapunov techniques and LaSalle’s invariance theorem. It is obvious that the proposed controller is significantly less dependent on the accuracy of the dynamic model. Besides, a disturbance observer based on the generalized momentum is constructed, which can effectively observe and compensate the disturbances. What’s more, the constructed disturbance observer avoids the calculation of the inverse of inertia matrix, which will greatly improve the response speed of the controller. The simulation results show that the proposed controller can assure better trajectory tracking accuracy in high-speed and high-acceleration motion. And the disturbance observer can effectively estimate the disturbance. The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article:This work was supported by the National Natural Science Foundation of China (grant number51474320).

To monitor fatigue crack initiation and propagation, and to judge the fatigue damage status of ferromagnetic material, fatigue bending tests of four-point single edge notch bend (SENB4) specimens were carried out. Metal magnetic memory signals were measured during the whole fatigue process. The results showed that the fatigue process could be divided into four stages by observing the morphology of the fracture surface. With the increase of fatigue loading cycles, the tangential component of the magnetic field (Hx) and the normal component of the magnetic field (Hy) increased. At the notch Hx presented a “trough” shape and had a maximum value at the midpoint, while Hy at the notch rotated clockwise around the midpoint. Compared with the tangential characteristic parameters, the variation of normal characteristic parameters (i.e., maximum gradient value of Hy (Ky-max) and the variation range of Hy at the notch (∆Hyn), with the fatigue loading cycles are more similar to the variation of fatigue crack length with loading cycles), both Ky-max and ∆Hyn had a good linear relationship with fatigue crack length. Plastic deformation accumulated on both sides of the fatigue crack, and metal magnetic memory (MMM) signals measured from the specimens were able to indicate the location of the fatigue crack and the variation of the fatigue crack length. Furthermore, the distribution of magnetic signals was analyzed according to the theories of stress magnetization and magnetic flux leakage.

By considering both motion smoothness and dynamic stress, a trajectory planning method for Delta robots, with the goal of determining the two optimal normalized time factors that dominate the motion path in operation space, is presented in this article. First, based on the semianalytical elastodynamics model of parallel robots, which considers the compliance of the limbs and joints, a dynamic stress model of the kinematic chain was built. Two indices were proposed to reflect the motion smoothness and dynamic stress. A sensitivity analysis and an optimization of the normalized time factors for a modified fifth-order B-spline approach were conducted in Isight and MATLAB. The results show that the two normalized time factors have an important impact on the motion smoothness and dynamic stress. A comparison showed that the trajectory planning approach based on the modified fifth-order B-spline reduced the dynamic stress while improving the motion smoothness. The approach proposed in this work can also be applied in trajectory planning for other parallel or hybrid robots.

Considering the real-time control of a high-speed parallel robot, a concise and precise dynamics model is essential for the design of the dynamics controller. However, the complete rigid-body dynamics model of parallel robots is too complex for online calculation. Therefore, a hierarchical approach for dynamics model simplification, which considers the kinematics performance, is proposed in this paper. Firstly, considering the motion smoothness of the end-effector, trajectory planning based on the workspace discretization is carried out. Then, the effects of the trajectory parameters and acceleration types on the trajectory planning are discussed. But for the fifth-order and seventh-order B-spline acceleration types, the trajectory will generate excessive deformation after trajectory planning. Therefore, a comprehensive index that considers both the motion smoothness and trajectory deformation is proposed. Finally, the dynamics model simplification method based on the combined mass distribution coefficients is studied. Results show that the hierarchical approach can guarantee both the excellent kinematics performance of the parallel robot and the accuracy of the simplified dynamics model under different trajectory parameters and acceleration types. Meanwhile, the method proposed in the paper can be applied to the design of the dynamics controller to enhance the robot's performance.