backdrivability and under-actuation
Backdrivability is how easily you can move a robot's joint by pushing on its output end — the part that does the work — instead of by commanding its motor. A backdrivable joint is like a bicycle wheel coasting freely: give it a gentle nudge and it turns, and you can even feel the motor being turned backward through it. A non-backdrivable joint is like a screw jack under a car — you can crank the handle to lift the car, but no amount of pushing down on the car will spin the handle back. Many gear systems trade away backdrivability on purpose: a high gear ratio makes a motor's output strong, but it also makes the joint very hard to move from the outside.
Backdrivability is prized when a robot must work safely and feel responsive around people, because a backdrivable arm can be pushed out of the way by hand and gives way under unexpected contact, rather than stubbornly holding its ground. It also lets a robot sense and respond to outside forces through the joint itself, almost like feeling pressure through your own arm, which can even replace a dedicated force sensor.
Under-actuation is a related idea about counting: it means a mechanism has fewer motors than it has independent ways to move. A robot hand with many finger knuckles but only one or two motors is under-actuated — the fingers curl together in a fixed pattern set by their springs and linkages rather than each being driven on its own. This keeps the design simple, light, and cheap, and a well-designed under-actuated hand can still wrap naturally around objects of different shapes, even though it cannot pose every knuckle independently.
A simple robotic gripper uses one motor to close four jointed fingers; as the fingers meet an oddly shaped cup, the unpowered, backdrivable joints bend to follow its curves and hug it securely.
One motor, many joints: under-actuation plus backdrivability lets a hand mold itself to an object.
The two ideas often appear together: under-actuated hands are usually built to be backdrivable so their unpowered joints can still flex around whatever they grasp.