The Stewart parallel robot platform used in this article is shown in Figure 1, which mainly includes an upper platform, a lower platform and six supports. The two ends of six of the struts use upper and lower horizontal Hooke hinges to connect the upper and lower platforms together. Each strut uses an electric cylinder, and the length of the strut is controlled by controlling the servo motor of the electric cylinder, thereby adjusting the end position of the Stewart parallel robot.

It can be seen from the above that the Stewart parallel robot consists of an upper platform, a lower platform and 6 supports. For the convenience of description, the robot is abstracted into a simplified structural diagram as shown in Figure 2. In this figure, the horizontal Hooke hinge of the upper platform is The center of rotation is defined as Ai (i=1,2,…,6), which is distributed on a circle with a radius Ra. The lines connecting the center points of six upper-platform horizontal Hooke hinges form a hexagon. By analogy, the rotation center of the lower platform horizontal Hooker hinge is defined as Bi (i=1, 2,...,6), distributed on a circle with a radius of Rb, and the rotation center of the six lower platform horizontal Hooker hinges The lines connecting the center points also form a hexagon. Connect the rotation centers corresponding to the serial numbers, which respectively represent the length Li of the electric cylinder (i=1, 2,...,6). This length includes the body length of the electric cylinder.

In order to describe the structure of the Stewart parallel robot, there are currently two main description parameters.

The first type of structure description parameters are as follows:

(1) Radius Ra of the distribution circle of the upper platform horizontal Hooke hinge rotation center point;

(2) The radius of the distribution circle of the horizontal Hooke hinge rotation center point of the lower platform Rb;

(3) The length of the short side of the hexagon at the center point of the horizontal Hooke hinge of the upper platform is Da;

(4) The length of the short side of the hexagon Db at the center point of the horizontal Hooke hinge of the lower platform;

(5) When the upper platform is working at the zero position, the distance between the horizontal Hooke hinge rotation center points of the upper and lower platforms is L.

The second type of structure description parameters are as follows:

(1) Radius Ra of the distribution circle of the upper platform horizontal Hooke hinge rotation center point;

(2) The radius of the distribution circle of the horizontal Hooke hinge rotation center point of the lower platform Rb;

(3) The center angle φa of the short side of the hexagon at the center point of rotation of the horizontal Hooke hinge on the upper platform;

(4) The center angle of the short side of the hexagon φb at the center point of the horizontal Hooke hinge of the lower platform;

(5) The shortest distance Lmin between the upper and lower platform horizontal Hooke hinge rotation center points.

The above two structural description parameters both use five parameters. The first four parameters describe the same physical meaning. The difference lies in the definition of the fifth parameter. One is defined based on the actual working state, and the other is defined based on the physical structure of the robot. . This article uses the second type of structural description parameters. The structural description parameters of the Stewart parallel robot in Figure 1 are shown in Table 2.1. According to the above definition, the rotation center point Ai (i=1, 2,...,6) of the upper platform horizontal Hooker hinge can be calculated, and the rotation center point Bi (i=1, 2,..., of the lower platform horizontal Hooker hinge) can be calculated. , 6) The coordinates are shown in the following formula.