Kinematic modeling of parallel mechanisms is the foundation for performance analysis, scale optimization design, and precise control. Researchers have done a lot of related work, mainly focusing on kinematic forward and inverse solutions, workspace, singularity analysis, and other aspects.

The forward kinematics solution involves determining the position and posture of the end effector of a robot under a given joint variable. Researchers have established mathematical models to accurately describe the motion process of robots. The inverse solution is an inverse problem, which is a mathematical problem of determining joint variables given the position and attitude of the end effector. These two aspects of research provide important foundations for robot trajectory planning, dynamic analysis, and more.

Workplace analysis focuses on the spatial range that robots can reach, which is crucial for determining what work scenarios robots are suitable for and how to optimize design scales.

Singular analysis focuses on the special positions that may appear in the robot kinematic model, namely singular points, which may cause the robot to lose its motion ability or produce abnormal kinematic solutions.

The following are the basic steps for general kinematic analysis of parallel robots:

Definition of 01 coordinate system: The coordinate system that determines the workspace of a robot, usually including the base coordinate system and the end effector coordinate system. The selection of these coordinate systems is usually determined by the structure and task requirements of the robot.

Definition of 02 degrees of freedom of motion: Determine the degree of freedom of motion of a robot, which is the parameter that the robot can freely change in space. The degree of freedom of motion of each joint is crucial for the kinematics of parallel robots.

03 Modeling of Link and Joint Parameters: Mathematical modeling of the robot's structure, including the length of each link, the position of the joint's rotational axis, and the motion pairs connecting each part. This usually involves modeling using algebraic or geometric methods.

Derivation of motion equation 04: Using the geometry and motion relationship of robots, derive mathematical equations that describe robot motion. These equations are usually expressed in matrix or vector form to describe the position and direction of the robot's end effector in the workspace.

Calculation of Jacobian Matrix 05: The Jacobian matrix describes the relationship between the position and direction of the robot's end effector relative to the joint position. By using the Jacobian matrix, the motion relationship between the robot in joint space and workspace can be calculated.

06 Singularity analysis: Singularity refers to the situation where the Jacobian matrix may lose full rank during robot motion. The analysis of singularities is crucial for robot motion planning and avoiding possible abnormal movements.

By completing the above steps, the kinematic model of the parallel robot in the workspace can be obtained, providing a foundation for control algorithms, path planning, and simulation work.

Kinematic modeling is a crucial part of parallel robot research, providing a foundation for subsequent related research work, and its importance is self-evident. Therefore, many experts and scholars are committed to conducting in-depth research on the kinematic modeling and analysis of parallel robots.

In the next article, we will use multiple case studies to understand that the researchers' work on kinematic modeling of parallel mechanisms provides a crucial theoretical basis for promoting the continuous advancement of robotics technology.