Mechanical principle link mechanism

The mechanism which consists of a number of rigid members connected by a low pair (rotating pair, moving pair), and the plane of motion of each point on each member is not parallel to each other, is also known as space low pair mechanism. In the space linkage mechanism, the members connected with the frame often rotate and move relative to a fixed axis, or make movements of turning and moving, or make complex rotations around a fixed point; the rest of the links not connected with the frame generally make complex space movements. Using the space linkage mechanism, the rotation of one axis can be changed into the rotation of any axis or the movement in any direction, and the movement in a certain direction can be changed into the rotation of any axis, and some kind of spatial displacement of the rigid body can be realized, or the trajectory of a certain point on the linkage can be approximated to a certain spatial curve. Compared with the plane linkage mechanism, space linkage mechanism often has a compact structure, diversified movement, flexible and reliable, but the design is difficult, the manufacture is more complex. Space linkage mechanism is often used in agricultural machinery, light machinery, textile machinery, transportation machinery, machine tools, industrial robots, prosthetics and aircraft landing gear.

Types of space linkage mechanism often refers to a single degree of freedom space closed chain (see kinematic chain) mechanism, but with the development of industrial robotics and prosthetics technology, multi-degree-of-freedom space open chain mechanism also has a lot of uses. A single-degree-of-freedom single-ring planar link mechanism contains only four rotating pairs, while a single-degree-of-freedom single-ring spatial link mechanism contains seven rotating pairs, i.e., a spatial seven-bar mechanism. When multiple degrees of freedom are used in a space link mechanism, such as spherical or cylindrical, the number of members can be reduced to form a simple and stable space four-bar or three-bar mechanism. In order to show the composition type of space linkage mechanism, commonly used R, P, C, S, H, respectively, said that the rotation vice, mobile vice, cylindrical vice, spherical vice, spiral vice. General space linkage mechanism from the frame connected to the beginning of the movement of the vice, in turn, with some of the symbols to indicate. Commonly used four-bar spatial mechanisms include RSSR, RRSS, RSSP and RSCS mechanisms (Figure 1). These mechanisms are relatively simple in structure because they contain two spherical pairs, but the local degrees of freedom of free rotation around the two spherical centers affect the high-speed performance. A spherical four-bar mechanism in which the axes of all the rotating pairs meet at one point (Fig. 2 Spherical four-bar mechanism) is also a kind of widely used space linkage mechanism, such as the universal coupling mechanism. In addition, there are some special space linkage mechanisms, such as the Bennett mechanism, where the angle between the axes of the moving pairs and the scale of the members are required to satisfy some special relationships.

Motion analysis and synthesis The analysis and synthesis of space linkage mechanism are more complex and difficult than that of planar linkage mechanism, which largely affects the popularization and application of space linkage mechanism. The study of space rod mechanism is based on the graphical method and the analytical method using the mathematical tools such as vectors, logarithms, matrices and tensors. The graphical method has some limitations, and the analytical method, which is more convenient for computers, is used more often. An important but difficult problem in the analysis of space link mechanism is displacement analysis. For a space link mechanism with more than 4 rods, it is usually necessary to solve multiple nonlinear equations or high order algebraic equations by numerical iteration method because the intermediate kinematic variables are not easy to be avoided or eliminated when the input is used to find the output displacements. For the 7R mechanism, which is the most difficult to analyze displacement, the algebraic equations for solving the output displacement from the inputs can be as high as 32 times. The basic problems of motion synthesis for space linkage mechanism are: when the motion law of the active member is certain, the linkage follower is required to move according to certain corresponding positions or approximately according to a certain functional relationship; the linkage is required to move according to certain spatial positions to realize the guidance of the rigid body in the space; and the linkage is required to move approximately along the given spatial curves at a certain point. Since these problems are similar to the synthesis problems of planar connecting rod mechanisms, the planar Barmerstahl theory can be analytically generalized to the guidance problems of spatial rigid bodies and other motion synthesis problems. In addition, there is the use of mechanism closure equivalent conditions to establish the design equation and the use of optimization techniques and other integrated methods.