degrees of freedom
In plain wordsThe number of independent ways something can move. A robot arm with six motorized joints has six; a free-floating object can slide three ways and turn three ways.
- 1
Mechanics and robotics
A count of the independent ways a mechanical system can move — formally, how many independent quantities, such as joint angles or positions, are needed to pin down its configuration. A free rigid body in space has six: three translations (surge, sway, heave) and three rotations (roll, pitch, yaw). For a robot the count usually equals its independently actuated joints: a typical industrial arm has six, enough to place its end effectorend effector, n.: The tool at the end of a robot arm that actually touches the world, such as a gripper, suction cup, welding torch, paint sprayer or robotic hand. at any position and orientation within reach, while arms with seven, like the human arm (three at the shoulder, one at the elbow, three at the wrist), are kinematically redundant and can use the spare freedom to avoid obstacles or joint limits. Humanoid robots commonly have from about 20 to over 40. Engineers distinguish the degrees of freedom of a mechanism from those that can be directly controlled: a car has three positional degrees of freedom on the ground but only two controls, which makes it non-holonomic and complicates motion planningmotion planning, n.: Working out how a robot should move from where it is to where it needs to be, without hitting anything and within the limits of what its body can do.. The dimension of a robot's configuration spaceconfiguration space, n.: An imaginary space in which a robot's whole body position is a single point, which turns 'move this many-jointed robot without hitting things' into 'find a path for a dot'. equals its degrees of freedom.
The new wrist adds a seventh degree of freedom, so the arm can reach around the fixture.
- 2
Statistics
The number of values in a calculation that are free to vary once its constraints are imposed, such as n − 1 for a sample variance computed around the sample mean; it fixes the shape of reference distributions such as Student's t and chi-squared.
Origin
The mechanical concept comes from nineteenth-century analytical mechanics; its counting rule for linkages is the Chebyshev–Grübler–Kutzbach mobility criterion (late nineteenth to early twentieth century). The statistical term was popularized by Ronald Fisher, beginning with his 1922 work on chi-squared tests, although William Gosset and, earlier, Carl Friedrich Gauss had used the underlying idea.
Usage note
Vendor figures are not always comparable: some count every finger joint, others only actuated joints, so a '40-DoF humanoid' may have far fewer motors.
Related
- configuration spaceconfiguration space, n.: An imaginary space in which a robot's whole body position is a single point, which turns 'move this many-jointed robot without hitting things' into 'find a path for a dot'.
- forward kinematicsforward kinematics, n.: The math that works out where a robot's hand or tool ends up, given the angles of all its joints, by chaining together the movement each joint adds.
- inverse kinematicsinverse kinematics, n.: Working backward from where you want a robot's hand to be to the joint angles that will put it there, like working out how to bend your arm to touch your nose.
- end effectorend effector, n.: The tool at the end of a robot arm that actually touches the world, such as a gripper, suction cup, welding torch, paint sprayer or robotic hand.
- actuatoractuator, n.: The 'muscle' of a machine: a motor or similar device that turns electrical, hydraulic or air power into movement, such as turning a robot's joint or closing its gripper.
- humanoid robothumanoid robot, n.: A robot built roughly in human shape, with a head, torso, two arms and usually two legs, so that it can work in spaces and with tools designed for people.
Mentioned in
actuatoractuator, n.: The 'muscle' of a machine: a motor or similar device that turns electrical, hydraulic or air power into movement, such as turning a robot's joint or closing its gripper., end effectorend effector, n.: The tool at the end of a robot arm that actually touches the world, such as a gripper, suction cup, welding torch, paint sprayer or robotic hand., industrial robotindustrial robot, n.: A programmable robot arm used in factories for jobs such as welding, painting, assembling and moving parts, traditionally working inside a safety cage., inverse kinematicsinverse kinematics, n.: Working backward from where you want a robot's hand to be to the joint angles that will put it there, like working out how to bend your arm to touch your nose., motion planningmotion planning, n.: Working out how a robot should move from where it is to where it needs to be, without hitting anything and within the limits of what its body can do., pose estimationpose estimation, n.: Working out the position and orientation of something from images: where a person's joints are and how their body is posed, or exactly how an object or camera is placed and turned in space., configuration spaceconfiguration space, n.: An imaginary space in which a robot's whole body position is a single point, which turns 'move this many-jointed robot without hitting things' into 'find a path for a dot'., cross-embodiment learningcross-embodiment learning, n.: Training one robot AI on data from many differently shaped robots, such as arms, robot dogs, drones and humanoids, so that skills learned on one body help another., dexterous manipulationdexterous manipulation, n.: Skilled handling of objects with robot fingers, such as spinning a pen, turning a key or rotating a cube in one hand: the fine finger work people do without thinking., forward kinematicsforward kinematics, n.: The math that works out where a robot's hand or tool ends up, given the angles of all its joints, by chaining together the movement each joint adds.