**1st Method**

In the conventional method, the degrees of freedom bound by each motion pair is subtracted from the sum of the degrees of freedom of all rigid bodies.

The advantage of this method is that it is easy to design analysis and calculation by analysts.

Especially in the analysis of the degree of freedom of the planar mechanism, the calculation of the virtual constraint and the local degree of freedom by the calculator can almost complete the calculation of the degree of freedom of most institutions.

However, for the space organization, since the virtual constraint and the local degree of freedom are difficult to identify, and the size of the mechanism itself and the position of the constraint are different, the actual freedom of motion of the mechanism may vary greatly.

This formula has been difficult to perform the task of calculating the degree of freedom of the organization.

However, it is hard to deny that this formula has made outstanding contributions in the history of mechanical design.

Many classic mechanisms and mechanical devices are designed based on this formula.

**2nd Method**

The degree of freedom is calculated by constructing the kinematics equation of the mechanism and analyzing its rank.

Or separate each closed chain of the mechanism, and analyze the degree of freedom of the mechanism through the virtual displacement matrix method.

The advantage of this method is that the degree of freedom of the mechanism can be calculated perfectly in theory.

The calculation method is simpler in understanding.

However, although this method is simple to understand, the calculation process itself is cumbersome, and the method is suitable for the analysis of the designed mechanism, and it is not convenient to use the formula for the mechanism design.

However, this method is also relatively mature and best understood, and many books have been introduced.

**3rd Method**

The agency’s Jacobian matrix calculates its null space to analyze the degree of freedom of the organization.

Although this method can theoretically solve the degree of freedom calculation, the application is relatively rare.

One is that the calculation of zero space is very difficult, and even using software is difficult to solve.

The second is that this method is also applicable to the analysis and calculation of existing institutions, and it is difficult to use this method to achieve innovation.

**4th Method**

The problem of degree of freedom calculation is solved based on the knowledge of group theory, Lie algebra and differential geometry.

Group theory, Lie algebra, and differential geometry are the magic weapons for solving complex institutional problems.

If mastered, the design and analysis of the organization, the design and calculation of the parallel mechanism, and even the conceptual design of the organization have very positive significance.

Many modern theories of mechanics and robotics are based on this.

However, this method requires a high level of knowledge for the designer and is not practical for ordinary designers and undergraduates.

**5th Method**

A method of calculating the degree of freedom based on spiral theory.

The spin is also a tool for solving institutional problems.

Although this method does not solve all the degrees of freedom problem perfectly.

But in terms of understanding, it is closer to the first one.

It is greater than the second in understanding difficulty, and the calculation difficulty is smaller than the second.

It can have a subtle influence on the conceptual design of the organization.

However, for ordinary designers and undergraduates, understanding is still difficult.

Overall, there was no perfect solution for institutional freedom calculations until 2015.