Motion accuracy is an important indicator to evaluate the performance of robots. The driven arm of the Delta robot is composed of a pair of parallelogram mechanisms. Because of the errors in components processing and installation, the parallelogram-driven mechanism will tilt. In addition, the load will have greater inertia impact on the end-effector in high-speed working condition. Therefore, the parallelogram-driven mechanism and loading effect will cause the parallelism error of the moving platform and affect motion accuracy of the robot. Aiming at the error analysis and motion accuracy of the Delta robot, currently, most studies mainly consider the influence of dimension error, clearance error, and driving error. There are few research conducted on the kinematics and error analysis considering parallelism error of the mechanism. The purpose of this article is to study the influence of parallelism error on motion accuracy of the robot. Firstly, the space vector method in mathematics is used to calculate the forward solution of the robot, and the kinematic equations of each kinematic chain are established. Secondly, the article analyzes the influence of the non-parallelism of the driven mechanism on motion error of the robot. Taking the D3PM-1000 robot as an example, it is obtained from the simulation results that with the increase in the tilt angle of the moving platform, the motion error caused by parallelism error also increases and the variation value is obvious, especially in the z direction, meaning that the parallelism error has a great influence on the motion error of the mechanism. The article effectively complements the research field of error analysis and provides a theoretical reference for the error compensation of the robot.

The Delta robots are widely used in packaging, sorting, precision positioning, and other fields. Motion accuracy is an important indicator for evaluating robot performance. However, due to the existence of mechanism errors, the motion accuracy of the robot will be reduced. Therefore, how to reduce motion errors and improve accuracy are important issues for robots. The purpose of the present study is to analyze the motion error and propose an error compensation scheme to improve the motion accuracy of the robot. Firstly, the kinematic model of the robot is established by the D-H matrix transformation method. An error model considering dimension error, the error of revolute joint clearance, driving error, and the error of spherical joint clearance is established. Additionally, the influence of different errors on the motion accuracy is analyzed. Secondly, an error compensation strategy of controlling the driving angle is proposed. The analysis of error compensation is carried out by a numerical example. Comparing the results before and after compensation, it is known that the robot can move along the desired position, so the notion error of the robot is compensated, which proves that this method is effective for improving the motion accuracy of the robot.

Delta parallel robots are widely used in assembly detection, packaging sorting, precision positioning, and other fields. With the widespread use of robots, people have increasing requirements for motion accuracy and reliability. This paper considers the influence of various mechanism errors on the motion accuracy and analyzes the motion reliability of the mechanism. Firstly, we establish a kinematic model of the robot and obtain the relationship between the position of the end effector and the structural parameters based on the improved D–H transform rule. Secondly, an error model considering the dimension error, the error of revolute joint clearance, driving error, and the error of spherical joint clearance is established. Finally, taking an actual robot as an example, the comprehensive influence of mechanism errors on motion accuracy and reliability in different directions is quantitatively analyzed. It is shown that the driving error is a key factor determining the motion accuracy and reliability. The influence of mechanism errors on motion reliability is different in different directions. The influence of mechanism errors on reliability is small in the vertical direction, while it is great in the horizontal direction. Therefore, we should strictly control the mechanism errors, especially the driving angle, to ensure the motion accuracy and reliability. This research has significance for error compensation, motion reliability analysis, and reliability prediction in robots, and the conclusions can be extended to similar mechanisms.

The kinematics and redundant space analysis of redundant robots constitutes important research content. Currently, methods such as geometric method and iterative optimization method are relatively complicated and inconvenient for programming and practical control applications. Moreover, little research has been conducted on redundant space analysis. This paper takes the 4-DOF PowerCube redundant robot as the research object. The forward and inverse kinematics equation of the robot are established based on the D-H matrix method, projection and cosine theorem method, and vector coordinate method. Then, the redundant space of the robot is obtained and the redundant space range of the robot is analyzed. Finally, the simulation of kinematic and redundant space research is conducted. It is shown that the change of each joint angle of the robot is smooth without mutation, so it can ensure the stable motion of the robot. Additionally, the different position and redundant variable have a big influence on robotic configuration. The calculation amount is relatively small and convenient for programming application, and the path calculation data of the joints are obtained, which are conducive to the motion control of modular robots. The method used in this paper can be extended to the multi-DOF redundant robot. Finally, the motion optimization, control, and obstacle-avoidance of redundant robots are briefly studied. The results of this paper provide an important basis for these aspects of research.

Redundant robots can complete other tasks while performing main task and have excellent motion performance. Although redundant robots have redundancy characteristics, they may still fall into singular configuration or cannot overcome joint limits due to the limitation of their own structure and motion law. Besides, currently, most of the research mainly focus on obstacle avoidance at the end of the robot. So comprehensive study is conducted on avoidance of obstacle, singularity, and joint limit of redundant robot. Firstly, the kinematics model of robot is obtained by D-H matrix method. Space vector distance method is proposed to calculate the position relationship between robot and obstacle, and potential function is constructed. Based on gradient projection method, using the damped generalized inverse and the weighted norm method, the mathematical models of obstacle avoidance, singularity avoidance, and joint limit avoidance are constructed. The simulation results show that the robot can avoid the obstacle in three-dimensional redundant space. At the same time, manipulability and minimum singular value of the robot are always positive. After adding the function of avoiding joint limit, during the whole control process, the motion range of joint angle is reduced and the angular velocity is relatively small, which ensure the motion stability of robot. Namely, the singular configuration and joint limit of robot are avoided. The research is of great significance for practical application of redundant robot.