# Principles of construction and structural classification...

## Principles of construction and structural classification of mechanisms

The method of classification of flat mechanisms and the principles of their construction were developed at the beginning of the 20th century. United States scientist LV Assur. The method proposed by him makes it possible to classify plane mechanisms that satisfy Chebyshev's formula (1.3). Academician II Artobolevsky extended the classification of LV Assur to spatial mechanisms. The practical significance of the classification was that it made it possible to establish the correspondence between the degree of complexity of the mechanism (its class) and the methods of its investigation and construction.

The construction of the mechanism by Assur consists in the successive attachment to the leading links and the rack of special kinematic chains, called structural groups or Assurian groups, without changing the degree of mobility of the mechanism as a whole. Assur group - kinematic chain with zero degree of mobility relative to those links to which it is attached by its end elements and which does not break down into simpler kinematic chains with zero degree of mobility .

Consider the principle of constructing mechanisms by the method of stratifying the Assurian groups by the example of a plane mechanism with one degree of freedom, in which the position of all links is determined by specifying one generalized coordinate (φ or s). The construction of the mechanism begins with the unification of the leading link and the rack. According to the Assur-Artobolevsky classification, the mechanism obtained in this way is called the initial mechanism of the 1st class (Figure 1.8, a, b). The initial mechanism has one degree of mobility. More complex mechanisms are formed by joining (stratification) to the initial mechanism of Assurian groups. Assurian groups have only kinematic pairs of the 5th class, therefore, using the formula (1.3), with W = 0 we find Hence

Thus, the number of links in the group n should be even, and the number of kinematic pairs - a number that is a multiple of three. Possible combinations of the number of links and kinematic pairs make it possible to obtain structural groups of varying complexity. The simplest of them has and is called a two-lead group (by the number of links-leashes) (Figure 1.9). If one extreme element of such a group (the element B in Figure 1.9, a) is attached to the leading link 1, and the other, the extreme element D to the rack 2, then a mechanism is created called the flat hinged four-section (see Figure 1.1).

Fig. 1.8

Fig. 1.9

Assur groups have internal and external kinematic pairs. The internal pairs connect the links of the group with each other, and the group joins the external group in the costal kinematic chain. The number of external kinematic pairs determines the order of the Assur group. For example, the two-lead group mentioned above is called the second-order Assur group.

Structural groups that have , depending on the number of rotational and translational kinematic pairs and their sequence of arrangement, can be of five different types (Figure 1.9, a-d ). Four-tiered structural groups that have can be of the third-order three-way type (Figure 1.10, o) and second-order four-links with a movable quadrilateral contour (Figure 1.10, b). A distinctive feature of the three-drive group is the presence of an internal basic link entering into three kinematic pair. The different types of the last two Assyrian groups can also be obtained by replacing rotational kinematic pairs by translational ones. Structural groups with more than four links are very rare in mechanisms.

And. I. Artobolevsky expanded and modified the classification of LV Assur. According to I. Artobolevsky's classification, the two-lead structural group is conditionally related to the groups of the second class and has a second order. The group class above the second is determined by the number of kinematic pairs entering the closed loop, which is formed by internal kinematic pairs. Therefore, a three-drive group, which has three internal kinematic pairs and a ba-

Fig. 1.10

The pivot link (see Figure 1.10, a), refers to the third class and has a third order (by the number of external kinematic pairs). A four-link group with four internal kinematic pairs (see Figure 1.10, b), refers to the 4th class and is second-order.

Structural analysis of mechanisms (study of the structure of mechanisms) suggests:

• determination of the number of links of the mechanism, the number and class of its kinematic bunks;

• Determine the degree of mobility of the mechanism;

• separation of the mechanism into initial mechanisms and structural groups;

• Definition of the class and order of structural groups.

The result of the structural analysis is the definition of the class of the entire mechanism, which corresponds to the highest class of the Assur group that is part of the mechanism. The definition of the class of the mechanism, according to Assur - Artobolevsky classification, is possible if as a result of preliminary structural analysis the following conditions are established:

• the degree of mobility of the mechanism corresponds to the number of leading links;

• in the mechanism there are only kinematic pairs of the 5th class.

If there are kinematic heads of the 4th class in the flat mechanism, the structural analysis is performed on the replacement mechanism [1] •

The following sequence of separation of structural groups from the kinematic chain of the mechanism is recommended. The separation of groups begins with links most distant from the leading link. First of all, Assur groups of the lowest class are separated. It should be borne in mind that after the separation of each group, the degree of mobility of the mechanism must remain unchanged, and each link and the kinematic pair can enter only one structural group. The separation of the kinematic chain of the mechanism into Assur groups is carried out until only the initial mechanisms (the leading links and the rack) remain.

Let us explain the structural analysis and classification of mechanisms by Assur-Artobolevsky using the example of the mechanism shown in Fig. 1.11. The mechanism has five movable

Fig. 1.11

links (n = 5) and seven kinematic pairs of the 5th class . By the formula (1.3) we determine the degree of mobility of the mechanism

The leading link 1 with the pillar 6 form the mechanism of the 1st class. The driven kinematic chain can be divided into two Assyrian groups of the 2nd class (marked in Figure 1.11 by contour lines), beginning with the group consisting of the units 4, 5.

Since the mechanism has only Assyrian groups of the 2nd class in its composition, it should be attributed to the mechanisms of the second class.

The principles of constructing mechanisms on Assur - Artobolevsky are convenient to use both in structural analysis and in the structural synthesis of mechanisms. Already at the design stage of machines their pawned performance and reliability largely depend on how correctly and rationally the scheme of the mechanism construction and its structure are chosen.

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