Primer
Degrees of freedom: why one hand is quoted as 16, 20 and 24
Three counting conventions, one hand. The number on the spec sheet is a decision about what to count, not a measurement.
Actuated DOF counts motors. Total DOF counts joints, including passive ones. Virtual DOF counts the motions a mechanism can achieve, whether or not a motor drives them. Vendors pick whichever number looks best, and the same hand can appear as 16, 20 and 24.
The three numbers
A hand with 16 motors, 16 joints and four fingers is straightforward. A hand with six motors, 12 joints and five fingers is not, and neither is a hand with 20 motors, 24 joints and a wrist. The conventions below explain why the figures in this index rarely match across sources.
| Convention | What is counted | Typical use |
|---|---|---|
| Actuated DOF | Independent motors | Controls, reinforcement learning, action space |
| Total joints | Every articulation, powered or not | Mechanism description, kinematics |
| Virtual DOF | Achievable motions of the mechanism | Grasp analysis, mechanism design |
| Movements | Joints including wrist and coupled linkages | Vendor marketing, humanoid comparisons |
Why 6 over 12 is not 6
Take the Inspire RH56: six motors, 12 joints. Each motor drives a linkage that curls several joints together. The hand can form a power grasp and a pinch grip, and it can do both reliably for years. What it cannot do is hold one finger still while another moves, because the linkage does not permit it.
For a grasping application that is fine. For a research paper that reports a 12-dimensional action space, it is a problem, because only six of those dimensions are independent. The controller will discover this before the author does.
Why 20 and 24 both appear on the Shadow Hand
Shadow describes 24 movements and 20 degrees of freedom. Both are accurate: 24 joints move, 20 are actuated, and four follow the tendon routing. Reports that say 24 DOF are counting joints. The record keeps both numbers with their labels, which is more useful than picking one.
Under-actuation is a design choice, not a defect
The LEAP Hand v2 uses eight motors for 16 joints, with one tendon per finger. When the tendon pulls, the MCP joint bends first, then PIP, then DIP. That produces a natural curl and absorbs contact, and it costs half the motors. It also means the hand cannot independently position a distal joint.
The trade is real in both directions: fewer motors, less mass, more compliance, less control authority. A spec table that lists "16 DOF" for both v1 and v2 hides the entire trade, which is why the price record separates them.
How to read a spec sheet in thirty seconds
- Find the word actuated. If it is absent, assume the number counts joints.
- If the hand has fewer motors than joints, ask which joints are coupled.
- Check whether the wrist is included in the count. It often is, on humanoid hands.
- Compare dollars per actuated joint, not dollars per DOF. The two rankings are different.
- Ignore any force figure without a test condition. It cannot be compared with anything.
| Hand | Actuated | Total joints | Ratio |
|---|---|---|---|
| LEAP Hand v1 | 16 | 16 | 1.0 |
| Allegro V5 | 16 | 16 | 1.0 |
| Inspire RH56DFX | 6 | 12 | 0.5 |
| LinkerBot O6 | 6 | 11 | 0.55 |
| PaXini DexH13 GEN2 | 13 | 16 | 0.81 |
| Unitree Dex5-1 | 16 | 20 | 0.8 |
| Shadow Hand | 20 | 24 | 0.83 |
Questions
Is more degrees of freedom always better?
No. More motors means more mass, more failure points and a larger action space to explore. Match the count to the task.
What does under-actuated mean?
Fewer motors than joints. The remaining joints move as a consequence of the driven ones, usually through tendons or linkages.
Why do vendors quote different numbers for the same hand?
Because they count different things, and the largest defensible number is the one that appears in marketing.