Robotics

# Robot Axes and Pathways 280

Robot Axes and Pathways provides an overview of the ways industrial robots move. The axes of the Cartesian coordinate system are used to describe robot movement. Robots may travel along linear axes or around rotational axes by using both revolute and prismatic joints. The number of joints a robot has is equal to the number of axes it can move along. Robots move through three-dimensional (3D) space by following a collection of points known as a path. Trajectories, or time-based paths, allow industrial robots to perform smooth, coordinated operations while avoiding collisions.

After taking this class, users will be able to describe robot motion and the methods used to define, calculate, and plan robot movements. This information is necessary for understanding robot positioning and how it enables robots to perform smooth, efficient tasks.

• Difficulty Intermediate

• Format Online

• Number of Lessons 11

• Language English

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Course Outline
• Robot Movement
• Linear Axes
• Rotational Axes
• Robot Coordinate Systems
• Coordinate System and Axes Review
• Joint Configuration and Axes
• Kinematics
• Jacobians
• Path Planning
• Trajectory Generation
• Final Review
Objectives
• Describe robot movement.
• Describe linear axes.
• Describe rotational axes.
• Distinguish between different robot coordinate systems.
• Describe robot joints and axes.
• Describe the basics of robot kinematics.
• Describe the basics robot Jacobians.
• Describe path planning.
• Describe trajectory generation.
Glossary
Vocabulary Term
Definition

3D

Three-dimensional. Having length, width, and depth. Robots move along paths in 3D space.

acceleration

An increase in the rate of an object's velocity. Acceleration occurs when a force changes an object's momentum.

actuators

A device that activates linear or rotary motion. Robot actuators are often motors located at the joints between links.

articulated robots

A type of robot that closely resembles a human arm. An articulated robot, also known as a manipulator, has a varied number of revolute joints.

auxiliary axis

An additional axis of movement created by adding a joint to a robot. Auxiliary axes, or redundant axes, can be added to provide greater mobility.

axes

An imaginary line or circle that is used to define the position of an object in space. The linear axes are the X, Y, and Z axes of the Cartesian coordinate system.

base coordinate system

A positioning system in which the origin is set at the base of a robot. The base coordinate system is particularly useful for precisely adjusting the position of a floor-mounted unit since the base position is physically fixed.

blended trajectory

A trajectory that moves the robot from the source position to the target position in a smooth, curved path using waypoints. A blended trajectory provides a robot with continuous motion.

Cartesian coordinate system

A positioning system that uses three linear axes perpendicular to each other to locate positions in three-dimensional space. The three linear axes in the Cartesian coordinate system are the X axis, Y axis, and Z axis.

Cartesian coordinates

Numerical values that describe the location of an object along three linear axes. Cartesian coordinates are used for end effector position and orientation.

Cartesian robot

A type of robot that moves along three orthogonal axes. Cartesian robots, or gantry systems, have linear joint movement that gives them a highly rigid structure, allowing them to lift heavy objects.

degree of freedom

DoF. The ability to move in a specific direction in three-dimensional space along or around an axis. Industrial robots typically have a maximum of six degrees of freedom, three for position and three for orientation.

Delta robots

A stationary, high-speed parallel robot. Delta robots are usually suspended above their work area and have three to four parallel arms that are attached to an end effector and driven by motors in the base of the robot.

end effector

A device attached to the end of a robot arm in order to interact with a part, component, or material. An end effector, also known as an end of arm tool, may be a gripper that allows the robot to pick up objects and place them down.

end of arm tool

EOAT. A device attached to the end of a robot arm in order to interact with a part, component, or material. The end of arm tool, also known as an end effector, may be a gripper that allows the robot to pick up objects and place them down.

fixture

A customizable, modular workholding device created by configuring locators, supports, and clamps. Fixtures are useful when holding irregularly shaped workpieces or when holding multiple workpieces for a single operation.

forward kinematics

The calculation and translation of joint angles into Cartesian coordinates. Forward kinematics converts a robot's joint angles into coordinates that describe the end effector's position and orientation.

gantry system

A type of robot that moves along three orthogonal axes. Gantry systems, or Cartesian robots, have linear joint movement that gives them a highly rigid structure, allowing them to lift heavy objects.

industrial robots

A reprogrammable machine sometimes used in place of a person in a manufacturing setting. Industrial robots perform dangerous or repetitive tasks with a high degree of accuracy.

inverse kinematics

The calculation and translation of Cartesian coordinates into joint angles. Inverse kinematics converts coordinates that describe an end effector's position and orientation coordinates into joint angles.

Jacobians

A matrix quantity that maps velocities in joint space to velocities in Cartesian space. Jacobians relate velocities of the end effector to the robot's joint velocities.

jerk

A sudden jolt created by a change in an object's velocity and direction. Jerk creates unstable robot motion.

joint angles

The angular measurement of a revolute joint from its initial position to its final position. Joint angles describe the angle between two connected robot links.

joint space

A set of joint positions defined by a robot's joint angles or displacements rather than Cartesian coordinates. Joint space describes the configuration of a manipulator by specifying the position of each joint.

joint space trajectory

A trajectory created using joint positions of the robot. A joint space trajectory allows for smooth actuator functioning.

joints

A connecting component of a robot that enables relative motion between connecting links. Joints on a robot mimic the movement of human joints, such as wrists or elbows.

kinematic chain

An assembly of rigid bodies connected by joints that provide constrained motion. A robot's kinematic chain extends from the base to the end effector.

kinematics

The science of motion without regard to the forces that cause motion. Kinematics describes the relationship between the positions, velocities, and accelerations of a robot's joints and links.

linear axes

An axis that describes linear movement. Linear axes describe side-to-side, front-to-back, or up-and-down movement.

A rigid body between two joints. A robot's link movement is actuated by motors in the joints.

manipulators

A type of robot that closely resembles a human arm. A manipulator, also known as an articulated robot, has a varied number of revolute joints.

map

A function that matches elements from one data set to a unique element in another data set. In robotics, Jacobians map data from joint space to Cartesian space.

matrix quantity

A set of values expressed as a series of vectors. A matrix quantity displays the number of velocities equal to the number of joints.

mobile platform

An automated machine that can move around a space and provide movement to a stationary robot. Mobile platforms can allow a robot to perform tasks in a workspace larger than its typical work envelope.

motion control

Controlling the movement of machine elements. Motion control uses a mechanical source of power like an actuator.

offset

A displacement caused by the addition of a robotic end effector. The end effect's offset is compensated by TCP.

orientation

Rotational position in three-dimensional space. Orientation is determined by rotation around the X, Y, and Z axes.

origin

A fixed, central point in the Cartesian coordinate system where the X, Y, and Z axes intersect. The origin has a numerical value of zero.

path

A route taken by a robot to travel from one location to another. A robot's path is made up of different points.

path planning

The process of mapping a robot's route for a task. Path planning determines the positions and orientations of a robot and its end effector during a task.

perpendicular

Forming a 90° angle with another plane or object. X, Y, and Z axes are perpendicular to each other.

pitch

Rotational movement around the Y axis. Pitch is movement on the RY axis.

point-to-point trajectory

A trajectory that moves the robot from the source position to the target position without using waypoints. A point-to-point trajectory provides fast, time-optimized movement.

prismatic joints

A joint that moves in a straight line along a single axis. Prismatic joints generate translational motion.

reach

The length of a fully extended robot from its base to the tip of the end effector. A robot's reach determines the size of its work envelope.

redundant axis

An additional axis of movement created by adding a joint to a robot. Redundant axes, or auxiliary axes, can be added to provide greater mobility.

revolute joints

A joint that moves in a circular path along a single axis. Revolute joints generate rotational motion.

robotic arms

Robots that closely resemble human arms. A robotic arm has at least three revolute joints.

roll

Rotational movement around the X axis. Roll is movement on the RX axis.

rotational axes

An axis that describes rotation around a linear axis. The rotational axes are designated as the RX, RY, and RZ axes.

rotational motion

Movement in a circular path. Rotational motion can occur in both directions around an axis.

RX

The rotational axis that describes motion around, or about, the X axis. Movement on the RX is called roll.

RY

The rotational axis that describes motion around, or about, the Y axis. Movement on the RY is called pitch.

RZ

The rotational axis that describes motion around, or about, the Z axis. Movement on the RZ is called yaw.

SCARA robots

Selective Compliance Assembly Robot Arm robots. A type of cylindrical robot that has four axes of movement: X, Y, Z, and Theta Z. SCARA robots are often used for material handling applications.

Selective Compliance Assembly Robot Arm robots

SCARA robots. A type of cylindrical robot that has four axes of movement: X, Y, Z, and Theta Z. Selective Compliance Assembly Robot Arm robots are often used for material handling applications.

source position

The starting position of a robot. The source position of a robot is the first position of its path.

straight line trajectory

A trajectory that moves the robot from the source position to the target position in a straight path without using waypoints. A straight line trajectory provides a robot with the shortest path.

target position

The end position of a robot. The target position of a robot is the end position of its path.

A trajectory created using the Cartesian coordinates of the end effector. A task space trajectory allows a robot to navigate obstacles better than a joint space trajectory.

TCP

tool center point. A coordinate system that defines the tip of the end effector and adjusts for its offset. The TCP must be configured for each end effector used.

three-dimensional

3D. Having length, width, and depth. Robots move along paths in three-dimensional space.

tool center point

TCP. A coordinate system that defines the tip of the end effector and adjusts for its offset. The tool center point must be configured for each end effector used.

tool coordinate system

A positioning system in which the origin is set at the robot's wrist. The tool coordinate system moves as the tool attached to the robot moves.

trajectory

The timed path a robot moves along beginning at an initial starting point and ending at a desired destination point. Trajectories determine how a robot will move and perform a programmed task.

trajectory generation

The process of creating a timed schedule for a robot as it follows a path. Trajectory generation accounts for any variables such as position, velocity, and acceleration.

translational motion

Movement along a straight line. Translational motion allows a Cartesian robot to move along three linear axes.

user coordinate system

A positioning system in which the origin is set by the user. In the user coordinate system, the origin is usually set to the worktable or a workholding device.

velocity

The rate of change in an object's position with respect to a frame of reference. The velocity of a robot&apos;s actuators controls its motion.

via points

An intermediate point in a path between a robot's source and target positions. Via points, also known as waypoints, determine the shape and route of a robot's path.

waypoint trajectory

A trajectory that moves the robot from the source position to the target position using waypoints. A waypoint trajectory provides a robot with good motion control.

waypoints

An intermediate point in a path between a robot's source and target positions. Waypoints, also known as via points, determine the shape and route of a robot's path.

work cell

The area in which a robot, a controller, and its auxiliary equipment are arranged. A robot work cell is its entire workspace.

work envelope

The defined area of space through which a robot can move. The work envelope is dangerous for operators to enter unless the robot is powered down.

work-object coordinate system

A positioning system in which the origin is set to a point on the workpiece. The work-object coordinate system is most useful when workpieces may be moved during a manufacturing operation, such as flipping a part so it can be welded on both sides.

worktable

The component that supports a workpiece during a manufacturing operation. Worktables use workholding devices to rigidly hold workpieces.

world coordinate system

A positioning system in which the origin is set to a fixed point in the manufacturing area. The world coordinate system facilitates programming of two or more robots that must work together.

X axis

The linear axis that describes side-to-side movement. The X axis is one of the two horizontal axes in the Cartesian coordinate system.

Y axis

The linear axis that describes front-to-back movement. The Y axis is one of the two horizontal axes in the Cartesian coordinate system.

yaw

Rotational movement around the Z axis. Yaw is movement on the RZ axis.

Z axis

The linear axis that describes up-and-down movement. The Z axis is the single vertical axis in the Cartesian coordinate system.