1st Method
The conventional method involves subtracting the degrees of freedom bound by each motion pair from the total degrees of freedom of all rigid bodies.
One advantage of this method is that it simplifies the design, analysis, and calculation process for analysts. Particularly, in analyzing the degree of freedom of planar mechanisms, the calculation of virtual constraints and local degrees of freedom can almost completely determine the degree of freedom of most mechanisms.
However, for spatial mechanisms, identifying virtual constraints and local degrees of freedom can be challenging, and the size and position of the mechanism and its constraints can greatly affect its actual freedom of motion. Therefore, this formula may not be suitable for calculating the degree of freedom of spatial mechanisms.
Despite its limitations, it is undeniable that this formula has made significant contributions to the history of mechanical design. Many classic mechanisms and devices have been designed based on this formula.
2nd Method
The degree of freedom can be calculated by either constructing the kinematics equation of the mechanism and analyzing its rank or by separating each closed chain of the mechanism and analyzing the degree of freedom through the virtual displacement matrix method.
The advantage of using this method is that the degree of freedom of the mechanism can be calculated perfectly in theory. Additionally, the calculation method is easy to understand.
However, although the method is simple to comprehend, the actual calculation process can be cumbersome. Therefore, this method is best suited for analyzing a pre-designed mechanism and is not convenient to use for mechanism design.
Nevertheless, this method is relatively mature and well-understood, and there are many books that introduce it.
3rd Method
The Jacobian matrix of the agency is used to calculate its null space and analyze the degree of freedom of the organization. However, this method is rarely used in practice.
One reason is that calculating the null space is a challenging task, and even with the assistance of software, it can be difficult to solve.
Secondly, this method is primarily suited for analyzing and calculating existing institutions, and it may not be effective for promoting innovation.
4th Method
The calculation of degrees of freedom is a problem that can be solved through the application of group theory, Lie algebra, and differential geometry.
These disciplines serve as powerful tools in addressing complex institutional problems. Proficiency in these fields is crucial for the design and analysis of organizations, the calculation and design of parallel mechanisms, and even for the conceptual design of institutions. Many contemporary theories in mechanics and robotics rely on these principles.
Nevertheless, this approach demands a high level of expertise from designers, making it impractical for ordinary designers and undergraduates.
5th Method
A method for calculating degrees of freedom based on spiral theory is available. Spin is also a tool for addressing institutional problems. Although this method does not perfectly solve all problems related to degrees of freedom, it is closer to the first method in terms of understanding. Additionally, it is easier to calculate than the second method.
It can subtly influence the conceptual design of an organization. However, ordinary designers and undergraduates may still find it difficult to understand. Overall, until 2015, there was no perfect solution for calculating institutional freedom.
