A Workspace Visualization Method for a Multijoint Industrial Robot Based on the 3D-Printing Layering Concept

The workspace of a robot provides the necessary constraint information for path planning and reliable control of the robot. In this paper, a workspace visualization method for a multijoint industrial robot is proposed to obtain a detailed workspace by introducing the 3D-printing layering concept. Firstly, all possible joint-angle groups of one pose in the joints’ ranges are calculated in detail according to the POE (product of exponential) theory-based forward-kinematics expressions of the multijoint industrial robot. Secondly, a multisolution selection method based on the key degree of the joint is proposed to select the appropriate joint-angle groups. The key degrees of all joints and their key order are obtained according to the sensitivity expressions of all joint angles, calculated from the Jacobian matrix of the robot. One principle based on the smallest differences of the nominal angle is established to select the possible solutions for one joint from the possible solutions for the joint with the smaller key order. The possible solutions for the joint with the highest key order are the appropriate joint-angle group. Thirdly, a workspace visualization method based on the layering concept of 3D printing is presented to obtain a detailed workspace for a multijoint industrial robot. The boundary formula of each layer is derived by forward kinematics, which is expressed as a circle or a ring. The maximum and minimum values of the radius are obtained according to the travel range of the joint angles. The height limitations of all layers are obtained with forward kinematics. A workspace boundary-extraction method is presented to obtain the array of path points of the boundary at each layer. The proposed postprocessing method is used to generate the joint-angle code of each layer for direct 3D printing. Finally, the effectiveness of the multisolution selection method and the workspace visualization method were verified by simulation and experiment.