### Do you really understand the knowledge of these industrial robot motion axes?

“With the progress of society and the development of science and technology, the application of industrial robots is becoming more and more common. Because of its many types, motion axes and coordinate systems, it is easy to make mistakes, especially for beginners. This paper mainly introduces the nomenclature of the motion axes of industrial robots, the principle of determining the coordinate system and its common types, in order to serve as a reference for the application of industrial robots.

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With the progress of society and the development of science and technology, the application of industrial robots is becoming more and more common. Because of its many types, motion axes and coordinate systems, it is easy to make mistakes, especially for beginners. This paper mainly introduces the nomenclature of the motion axes of industrial robots, the principle of determining the coordinate system and its common types, in order to serve as a reference for the application of industrial robots.

1. Robot motion axis

In production, industrial robots generally need to be equipped with peripheral equipment in addition to their own performance characteristics, such as a turntable for rotating the workpiece, a mobile table for moving the workpiece, etc. The motion and position control of these peripheral devices all need to cooperate with industrial robots and require corresponding precision. Generally, the robot motion axis can be divided into robot axis, base axis and tool axis according to its function, and the base axis and tool axis are collectively referred to as external axis.

The robot axis refers to the axis that operates the body, which belongs to the robot itself. At present, most of the commercial industrial robots mainly use 8 axes. The base axis is a general term for the axis that makes the robot move, mainly referring to the travel axis (moving the slide table or guide rail). The tooling axis is a general term for axes other than the robot axis and the base axis, which refers to the axis that flips and rotates the workpiece and the fixture, such as the rotary table and the turning table. Commonly used in actual production is a 6-joint industrial robot, which has 6 movable joints (axes). The attached table and Figure 1 are the definitions of the motion axes of common industrial robots. It is worth noting that the definitions of motion axes of different industrial robots are also different. The axis used to ensure that the end effector reaches any position in the workspace is called the basic axis or the main axis; the axis used to realize the arbitrary spatial attitude of the end effector is called the wrist axis or secondary axis; Figure 2 shows the motion axes of the YASKAWA industrial robot Relationship.

Figure 1. Each motion axis of a typical robot

Figure 2 The relationship between the motion axes of the YASKAWA industrial robot

2. Robot coordinate system determination

The positions of all points in the robot program are associated with a coordinate system, and this coordinate system may also be associated with another coordinate system.

The various coordinate systems of the robot are determined by the orthogonal right-hand rule, as shown in Figure 3. Defined as A , B , and C when rotating about axes parallel to the X , Y , and Z axes, respectively. The positive directions of A , B , and C are the forward directions of the right-hand spiral in the positive directions of X , Y , and Z respectively (see Figure 4).

Figure 3 Right-handed coordinate system

Figure 4 Rotating the coordinate system

Commonly used coordinate systems are absolute coordinate system, machine base coordinate system, mechanical interface coordinate system and tool coordinate system.

(1) The absolute coordinate system has nothing to do with the motion of the robot. It is a fixed coordinate system with the earth as the reference system (see Figure 5), and the symbols are O 0, X 0, Y 0, and Z 0. The origin O 0 and the +X 0 axis are determined by the user according to their needs; the +Z 0 axis is collinear with the vector of the gravitational acceleration, but in the opposite direction.

(2) The coordinate system of the base is the coordinate system with the installation plane of the robot base as the reference system, and the symbols are O 1, X 1, Y 1, and Z 1. The origin O 1 is specified by the robot manufacturer; the +Z 1 axis is perpendicular to the mounting surface of the robot base and points to the robot body; the X1 axis direction points from the origin to the center point Cw of the robot workspace (see GB/T12644-2001) on the mounting surface of the base projection on. When this convention cannot be fulfilled due to the construction of the robot, the direction of the X1 axis can be specified by the manufacturer.

(3) The coordinate system of the mechanical interface takes the mechanical interface as the reference system, and the symbols are O m, X m, Y m, and Z m. The origin O m is the center of the mechanical interface; the direction of the +Z m axis is perpendicular to the mechanical interface center, and thus points to the end effector; the +X m axis is defined by the mechanical interface plane and the X 1, Z 1 planes (or parallel to the X 1 , Z 1 Figure 2 The relationship between the motion axes of the YASKAWA industrial robot Figure 3 Right-handed coordinate system Figure 4 Rotational coordinate system Figure 5 Coordinate system example Figure 6 Tool coordinate system (plane) is defined by the intersection line, while the main and auxiliary joint axes of the robot in the middle of the range of motion. When the robot construction cannot fulfill this convention, the main joint axis position shall be specified by the manufacturer. The +X m axis points away from the Z 1 axis.

(4) The tool coordinate system takes the end effector installed on the mechanical interface as the reference system (see Figure 6), and the symbols are O t, X t, Y t, and Z t. The origin O t is the tool center point (TCP); the +Zt axis is related to the tool and is usually the tool pointing; in the case of a flat jaw type gripper, +Y t is the direction of the finger movement plane.

Figure 5 Example of a coordinate system

Figure 6 Tool coordinate system

3. Common coordinate systems for industrial robots

(1) The base coordinate system (B as eCoordinate System), also known as the base coordinate system, is located at the base of the robot. As shown in Figure 5, it is the most convenient coordinate system for the robot to move from one location to another. The base coordinate system has a corresponding zero point in the robot base, which makes the movement of the fixed-mounted robot predictable. In a normally configured robotic system, a worker can move this coordinate system through a joystick.

(2) World Coordinate System, also known as geodetic coordinate system or absolute coordinate system. If the robot is installed on the ground, it is easy to teach and program in the base coordinate system, but when the robot is hoisted, the movement of the end of the robot is not intuitive, so it is difficult to teach and program.

In addition, if two or more robots work together, for example, one is installed on the ground and the other is upside down, the base coordinate system of the inverted robot will also be upside down (see Figure 7). When the motion control is performed in the base coordinate systems A and B of the two robots, it is difficult to predict the cooperative motion.

Figure 7 World coordinate system

At this point, a common world coordinate system C can be defined instead. Unless otherwise specified, the world coordinate system and base coordinate system of a single robot are coincident.

(3) User Coordinate System, the robot can work with different workbenches or fixtures, and a user coordinate system is established on each workbench. Most of the robots use the teaching and programming method, and the steps are cumbersome. For the same workpiece, if it is placed on a different workbench for operation, there is no need to reprogram, and it only needs to be transformed to the current user coordinate system accordingly. The user coordinate system is established in the base coordinate system or the world coordinate system.

(4) The Object Coordinate System is related to the workpiece, and is usually the most suitable for programming the robot. The workpiece coordinate system corresponds to the workpiece, which defines the position of the workpiece relative to the geodetic coordinate system (or other coordinate system).

The workpiece coordinate system has certain additional properties that are mainly used to simplify programming. It has two frames: the user frame (related to the earth base) and the artifact frame (related to the user frame). The robot can have several workpiece coordinate systems, representing different workpieces, or representing several states of the same workpiece at different positions. Programming a robot is all about creating targets and paths in the workpiece coordinate system. When repositioning a workpiece in the workstation, simply change the position of the workpiece coordinate system and all paths will be updated accordingly. Workpieces moved by external axes or conveyor rails are allowed to be manipulated, as the entire workpiece can be moved along with its path.

(5) Displacement Coordinate System is also known as displacement coordinate system. Sometimes it is necessary to process the same workpiece and the same track in different stations. In order to avoid reprogramming every time, a displacement coordinate system can be defined. The displacement coordinate system is defined based on the workpiece coordinate system. As shown in Figure 8, when the displacement coordinate system is activated, all points in the program will be displaced.

Figure 8 Replacement coordinate system

(6) Both the WristCoordinate System and the tool coordinate system are used to define the tool direction. In simple applications, the wrist coordinate system can be defined as the tool coordinate system, and the two coincide. The Z axis of the wrist coordinate system coincides with the sixth axis of the robot. As shown in Figure 9, the origin of the coordinate system is located at the center of the end flange, and the direction of the X axis is the same as that of Figure 8 Replacement coordinate system Figure 9 Mark on the flange of the wrist coordinate system The holes are oriented in the same or opposite directions, the Z axis is straight out, and the Y axis follows the right-hand rule.

Figure 9 Wrist coordinate system

(7) Tool Coordinate System The tool installed on the end flange needs to define a tool coordinate system at its center point (TCP). Through the transformation of the coordinate system, the robot can be operated to move in the tool coordinate system to Easy to operate. If the tool is worn or replaced, simply redefine the tool coordinate system without changing the program. The tool coordinate system is established under the wrist coordinate system, that is, the relative position and attitude between the two are determined.

(8) The Joint Coordinate System (Join tCoordinate System) is used to describe the motion of each independent joint of the robot, and the joint types may be different (such as moving joints, rotating joints, etc.). If the robot end is moved to the desired position and operated in the joint coordinate system, each joint can be driven to move in sequence, so as to guide the robot end to reach the specified position.

4. Conclusion

Due to the large variety of industrial robots, there are also many coordinate systems for each industrial robot. Although there are standards for their naming and determination methods, some manufacturers do not follow the standards, and each has its own name. It is very confusing and troublesome in actual production applications. This paper introduces the naming of industrial robot coordinate axes and the determination of common coordinate systems in detail, in order to help users.

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