Robot Kinematics and Dynamics
by
Engineering Advice
- January 29, 2018
Introduction to robotics
An industrial robot is a general purpose, programmable machine possessing certain anthropomorphic characteristics. The most obvious anthropomorphic characteristic of an industrial robot is its mechanical arm, that is used to perform various industrial tasks. Other human like characteristics arc the robot's capability to respond to sensory inputs, communicate with other machines, and make decisions. These capabilities permit robots to perform a variety of useful tasks. The development of robotics technology followed the development of numerical control (Historical Note 7.1),and the two technologies are quite similar. They both involve coordinated control of multiple axes (the axes are called joints in robotics), and they both use dedicated digital computers as controllers.
Whereas NC machines arc designed to perform specific processes (e.g., machining, sheet-metal hole punching, and thermal cutting), robots are designed for a wider variety of tasks. Typical production applications of industrial robots include spot welding, material transfer, machine loading, spray painting, and assembly.
Reasons for the commercial and technological importance of industrial robots include the following:
- Robots can be substituted for humans in hazardous or uncomfortable work environments.
- A robot performs its work cycle with a consistency and repeatability that cannot be attained by humans.
- Robots can be reprogrammed. When the production run of the current task is completed, a robot can be reprogrammed and equipped with the necessary tooling to perform an altogether different task.
- Robots are controlled by computers and can therefore be connected to other computer systems 10 achieve computer integrated manufacturing.
- Basic terms used in Robotics:
1.1 Links and Joints: Links are the solid structural members of a robot, and joints are the movable couplings between them.
1.2 Degree of Freedom (dof)- Each joint on the robots introduces a degree of freedom. Each dof can be a slider, rotary, or other type of actuator. Robots typically have 5 or 6 degrees of freedom. Three of the degrees of freedom allow positioning in 3D space, while the other 2or 3 are used for orientation of the end effector. 6 degrees of freedom are enough to allow the robot to reach all positions and orientations in 3D space. 5 dof requires a restriction to 2D space, or else it limits orientations. 5 dof robots are commonly used for handling tools such as arc welders.
1.3 Orientation axes -
Basically, if the tool is held at a fixed position, the orientation determines which direction it can be pointed in. Roll, pitch and yaw are the common orientation axes used. Looking at the figure below it will be obvious that the tool can be positioned at any orientation in space. (imagine sitting in a plane. If the plane rolls you will turn upside down. The pitch changes for takeoff and landing and when flying in a crosswind the plane will yaw.)
1.4 Position axes -
The tool, regardless of orientation, can be moved to a number of positions in space. Various robot geometries are suited to different work geometries. (more later)
1.5 Tool Centre Point (TCP) - The tool centre point is located either on the robot, or the tool. Typically the TCP is used when referring to the robots position, as well as the focal point of the tool. (e.g. the TCP could be at the tip of a welding torch) The TCP can be specified in cartesian, cylindrical, spherical, etc. coordinates depending on the robot. As tools are changed we will often reprogram the robot for the TCP.
Speed - refers either to the maximum velocity that is achievable by the TCP, or by individual joints. This number is not accurate in most robots, and will vary over the workspace as the geometry of the robot changes (and hence the dynamic effects). The number will often reflect the maximum safest speed possible. Some robots allow the maximum rated speed (100%) to be passed, but it should be done with great care.
Payload - The payload indicates the maximum mass the robot can lift before either failure of the robots, or dramatic loss of accuracy. It is possible to exceed the maximum payload, and still have the robot operate, but this is not advised. When the robot is accelerating fast, the payload should be less than the maximum mass. This is affected by the ability to firmly grip the part, as well as the robot structure, and the actuators. The end of arm tooling should be considered part of the payload.
Payload - The payload indicates the maximum mass the robot can lift before either failure of the robots, or dramatic loss of accuracy. It is possible to exceed the maximum payload, and still have the robot operate, but this is not advised. When the robot is accelerating fast, the payload should be less than the maximum mass. This is affected by the ability to firmly grip the part, as well as the robot structure, and the actuators. The end of arm tooling should be considered part of the payload
Repeatability - The robot mechanism will have some natural variance in it. This means that when the robot is repeatedly instructed to return to the same point, it will not always stop at the same position. Repeatability is considered to be +/-3 times the standard deviation of the position, or where 99.5% of all repeatability measurements fall. This figure will vary over the workspace, especially near the boundaries of the workspace, but manufacturers will give a single value in specifications
Accuracy - This is determined by the resolution of the workspace. If the robot is commanded to travel to a point in space, it will often be off by some amount, the maximum distance should be considered the accuracy. This is an effect of a control system that is not necessarily continuous.
Settling Time - During a movement, the robot moves fast, but as the robot approaches the final position is slows down, and slowly approaches. The settling time is the time required for the robot to be within a given distance from the final position.
Control Resolution - This is the smallest change that can be measured by the feedback sensors, or caused by the actuators, whichever is larger. If a rotary joint has an encoder that measures every 0.01 degree of rotation, and a direct drive servo motor is used to drive the joint, with a resolution of 0.5 degrees, then the control resolution is about 0.5 degrees (the worst case can be 0.5+0.01).
Coordinates - The robot can move, therefore it is necessary to define positions. Note that coordinates are a combination of both the position of the origin and orientation of the axes.
1.2 Robot Types:
- Robots come in a wide variety of shapes, and configurations.
- The major classes of robots includes
Arms- fixed in place, but can reach and manipulate parts and tools.
Mobile- These robots are free to move
