Abstract:

Teaching and learning the kinematics of robot manipulators in Robotics subjects of undergraduate studies becomes easier when educators and students make use of computer tools for simulation and visualization, as multi-body kinematics is a discipline that requires a good knowledge of mathematics that can be overwhelming for many students. This is especially true when the studied robots have a non-spherical wrist, which complicates the inverse kinematic analysis of robot manipulators, in contrast to the typical robot manipulators used in industry, which have a spherical wrist where three axes of rotation are concurrent. Computer tools help students to understand the kinematic concepts of robot manipulators before having to analyze or solve their equations, which can be too difficult to handle manually without the help of a computer.

There exist many computer tools for simulating and visualizing the kinematics of robot manipulators, but they typically include robots with spherical wrists. Although such robots are the most typical in industry, during the last years there has been an increase of robots with non-spherical wrists, which typically are collaborative robots (or cobots) designed to intimately operate in contact with humans, without safety barriers separating them. Examples of such cobots are the Sawyer robot by Rethink, or the UR5 robot by Universal Robots. Considering the growing tendency to incorporate such cobots in industry, it is essential to provide students with tools that help them to understand the kinematics of these robots.

Taking this into account, this paper contributes a simulation package to analyze the kinematics of a typical cobot with non-spherical wrist, namely, a UR5 robot. This package consists of a series of functions and scripts for Matlab, which is a computer software widely used in engineering studies. The proposed simulation package consists of a graphical user interface (GUI) that shows a realistic 3D virtual representation of the robot, which can be moved by the student under two modes: forward kinematic mode and inverse kinematic mode. The first mode allows the student to introduce the angles rotated by all joints, obtaining the unique corresponding position and orientation of the gripper of the robot. The second mode allows the student to introduce the desired position and orientation of the gripper, obtaining and comparing all the solutions of the inverse kinematic problem. The developed GUI also represents the singularities, as well as the reachable and constant-orientation workspaces of the robot, and the student can move the gripper in the workspace to discover how the solutions of the inverse kinematic problem change as a consequence. The UR5 robot can also be studied in the developed GUI as a kinematically-redundant robot when the roll rotation of the gripper is unimportant for the task of the robot, which allows the student to visualize the transformation of self-motion manifolds when varying the position of the gripper.

The functionalities of the developed software make it useful for understanding how the solutions of the inverse kinematic problem change when varying the position and orientation of the gripper, and for doing simulation exercises where the students are requested to plan and program trajectories of the gripper of the robot between different target positions, considering singularities and the plurality of solutions.

Keywords:

Simulator, Robot, Kinematics, Workspace, Redundant.