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👍 | The teaser site and official Twitter of the latest "Lineage" series "Lineage 2M" have been released! January…


The teaser site and official Twitter of the latest "Lineage" series "Lineage 2M" have been released! January…

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It is characterized by growth that combines diversity and freedom, and large-scale battle content by more than 1 players will also appear.

NCSOFT is the latest in the "Lineage" series, the next-generation open world RPG "Lineage 2M" ... → Continue reading


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Degree of freedom

Degree of freedom(Jiyuudo,English: degree of freedom) Is, in general,variableIt is the number of independently selectable ones, that is, the number of all variables minus the number of relational expressions (binding conditions, constraint conditions) that hold between them.Mathematically speakingManifoldIs the dimension of. Expressed as "1 degree of freedom", "1 degree of freedom", etc.

The degree of freedom isMechanics,Mechanics,statisticsThe meaning is based on the above definition, but the specific suggestions for each are different.


MechanicsThen, all the constituents of the systemMass pointThe number of coordinates that can be determined independently.

  • 1 mass: If translation in 3D space is allowed, the degrees of freedom are 3.
  • 2Mass system: If each mass moves independently, the degree of freedom is 6.With the center of mass of both as the representative coordinates of the system,Center of gravityTranslation 3 degrees of freedom, rotation around the center of gravity 2 degrees of freedom, change in relative distance between 2 mass points sandwiching the center of gravity, that isvibrationOften expressed by one degree of freedom.
  • Rigid body : n Mass system (however n In ≥ 3), an algebraic constraint that all mass points are invariant is imposed.Therefore, the total number of degrees of freedom of the system is 3 translational degrees of freedom and 3 rotational degrees of freedom, for a total of 6 degrees of freedom.If the motion is constrained on a plane, there are a total of 2 degrees of freedom, 1 translational degrees of freedom and 3 rotation degree of freedom.

Related item:Statistical mechanics,Energy distribution law


MechanicsRefers to the number of movable variables that determine the structure of the entire mechanism.Make up the mechanismLinks TheRigid bodySince it is regarded as, it follows the definition in mechanics and is the contact point of the link.Even numberSince the constraint condition is expressed algebraically by, it is relatively easy to formulate the degree of freedom calculation.

For example, the total degrees of freedom of a mechanism consisting of one-degree-of-freedom kinematic pair and two-degree-of-freedom kinematic pair on a plane is expressed by the following equation.

However, f Is the degree of freedom,n Is the number of links,n1 Is the total number of kinematic pairs with one degree of freedom,n2 Is the total number of pairs with two degrees of freedom.Further, it is assumed that one of the links forming the mechanism is fixed in the space.

For example, the degree of freedom of a plane 5-node closed link system with 1 links and 5 total kinematic pairs with 5 degree of freedom is


The formula expressing the degree of freedom of the mechanism having a three-dimensional structure is as follows.

However, the degree of freedom i Total number of kinematic pairs ni And

Movement mechanism, that is,Artificial satelliteIn such cases, one base link is not fixed in space, and is virtually 3 degrees of freedom kinematic pair in the case of a plane and 6 degrees of freedom kinematic pair in the case of a solid.Inertial systemConsidered to be bound to.In addition, an inertial frame is added to one of the links.For example, all joints consist of 1 degree of freedom joints, 7 joints with 7 links and 6 joints on one arm and 6 links and 26 joints on one leg.Humanoid robotIn the case of, the total number of links is 28 including the fuselage link and inertial system, so the total degree of freedom is


Further, for example, in the case of a wheel-type moving mechanism, if the wheels do not slip on the road surface, a constraint condition () that cannot be expressed due to an algebraic relationship is imposed.Therefore, the calculation of degrees of freedom is not simple.


thermodynamicsThen,balanceCan be taken freely in the stateState variablesIndicates the number of.

In general,C ingredient P phaseが平衡状態で存在する場合には、自由度 F The

To sayギブズの相律と呼ばれる式で表される。この場合、2 個の状態変数に加え、各成分の割合(から相の数を引いたもの)で状態を記述できる。

例えば、純水が液相のみで存在する場合、1 成分 1 相系であることより、自由度は 2。すなわち 2 個の状態変数(temperatureとpressure, Temperaturevolume, Etc.) can describe the state.


statisticsDefines degrees of freedom for various statistics.

大 き さ n Observation data in the specimen ofx1, x2, ..., xn) Degrees of freedom n And.Specimens obtained from themaverage x The same is true for.

Unbiased dispersion


The relational expression (here x Is the population mean μ The degree of freedom is one less because there is an estimator of n It becomes -1.Therefore, in the denominator n -1 is used.

Japanese Industrial StandardThen,Chi-square distribution,F distributed,t distributedSuch asThe parameter"WhenDefinitiondoing[1].


  1. ^ JIS Z 8101-1: 1999, 2.59 degrees of freedom.


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