IntermediateTopic 54 of 102Manufacturing, Robotics & Systems
Degrees of freedom and workspace
Joints define motion capability and reachable volume.
In depth
DOF is the number of independent joint variables: 6 DOF suffice to place and orient an end effector in 3D (3 position + 3 orientation). More DOF give redundancy and obstacle avoidance. Workspace is the set of reachable positions (reachable vs dexterous). Gruebler/Kutzbach formula counts DOF.
Key points
- Task space vs joint space
- Redundant manipulators
- Singular configurations
ExampleA 7-DOF arm can reach around obstacles by using its extra joint.
Degrees of freedom determine how a robot can move, and the workspace shows where it can reach, which must match the task.
What is Degrees of freedom and workspace?
Joints define motion capability and reachable volume.
Why is it important to understand degrees of freedom and workspace?
Degrees of freedom determine how a robot can move, and the workspace shows where it can reach, which must match the task.
What is a degree of freedom?
An independent joint motion that the robot can make, such as a rotation or a translation.
Why do we need six degrees of freedom in general?
Three for position and three for orientation give a robot full freedom to place and orient a tool in space.
How is Degrees of freedom and workspace used in practice?
Typical applications include checking that a six-axis arm can reach all points on a workpiece, choosing the number of axes needed for a pick and place task and identifying reach limits for a robot placed in a cell.
What should I learn before Degrees of freedom and workspace?
Study "Robot configurations" first (topic 53 of 102 in Manufacturing, Robotics & Systems). It covers the groundwork this topic builds on.
What are the key points of Degrees of freedom and workspace?
Task space vs joint space. Redundant manipulators. Singular configurations.
Can you give an example of Degrees of freedom and workspace?
A 7-DOF arm can reach around obstacles by using its extra joint.
What comes after Degrees of freedom and workspace?
The next topic is "Homogeneous transformations", which builds directly on this one.
How difficult is Degrees of freedom and workspace?
It is classed as Intermediate in Manufacturing, Robotics & Systems (topic 54 of 102). It is an intermediate topic. Work through the beginner topics in Manufacturing, Robotics & Systems first.