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Research on the maximum range of motion of Stewart platform

the size of the range of motion is an important index to measure the Stewart six degree of freedom platform. In recent years, many articles have carried out in-depth discussion on its range of motion, but most of them are limited to the calculation method of the range of motion, while the literature discussing the relationship between structural size and range of motion has not been seen. The structural size of the mechanism is closely related to the size of the range of motion. A reasonable structural size, on the one hand, should enable the mechanism to have a large range of motion, on the other hand, should not cause the mechanism to have mechanical interference. From the viewpoint of kinematics, this paper makes a dimensionless analysis of the maximum motion range of Stewart six degree of freedom platform on the premise that there is no mechanical interference between the connecting rods of the mechanism. 1 dimensionless representation of Stewart platform a typical Stewart motion platform is shown in Figure 1. It is composed of a hexagonal motion plane with the vertex Si (I = 1, 2,..., 6), a hexagonal fixed plane with the vertex Bi (I = 1, 2,..., 6), and six connecting rods whose length can vary in spite of the complexity, which are connected by a spherical hinge at one end and a cross hinge at the other end. In practical application, hydraulic cylinders are often used for connecting rods. By controlling the stroke of the piston rod of the hydraulic cylinder, the motion plane can realize the movement of six degrees of freedom in space. Figure 1 is also the schematic diagram of a Stewart motion platform produced by our experimental machine manufacturer in batch 1. The permanent deformation and temporary deformation of the leaf spring after strong pressure treatment should not be greater than 0.5mm. Due to the diversity and uncertainty of the tasks faced by this kind of motion mechanism in actual work, its design generally adopts a symmetrical structural form, that is, the motion plane and the fixed plane are a hexagon with a certain symmetrical form. Let the six vertices Si (I = 1, 2,..., 6) of the motion plane be distributed on a circle with radius R1, and the adjacent center angle be α 1、 β 1； The six vertices Bi (I = 1, 2,..., 6) of the fixed plane are distributed on the circle with radius R2, and the adjacent center angle is α 2、 β 2。 The reference coordinate system oxyz is fixedly connected with the fixed plane; The motion coordinate system orxryrzr is fixed on the motion plane. Take X-axis parallel to side b3b4 and XR axis parallel to side s3s4. Use (I = 1, 2,..., 6) to represent the three-dimensional vector of the vector Orsi on the motion plane in the reference coordinate system oxyz, and use to represent the three-dimensional vector of the corresponding vector in the motion coordinate system orxryrzr. There are the following relations between and: (1) here R is the transformation matrix of the motion coordinate system orxryrzr to the reference coordinate system oxyz. The position of the origin or of the motion coordinate system orxryrzr in the reference coordinate system oxyz is represented by a vector, so the cylinder length Li (I = 1, 2,..., 6) of the six hydraulic cylinders is: (2) in order to make the following analysis universal, the structural parameters of the Stewart motion platform are dimensionless relative to the fixed plane radius R2. The dimensionless radius of the plane of motion is the ratio of R1 to R2 λ express; The dimensionless minimum length of the hydraulic cylinder is expressed by the ratio lmin of its minimum length to R2; The dimensionless hydraulic cylinder brings new development opportunities. The large length is expressed by the ratio of its maximum value to R2, Lmax. It is known from literature [1], α 1、 α 2 the smaller the value, the more helpful it is to reduce the value of the condition number of the Jacobian matrix of the mechanism and improve its motion control accuracy. Therefore, in combination with the structural characteristics of the actual Stewart platform, we take α 1＝ α 2＝5°。 2. The interference of the mechanism the motion range of Stewart platform is determined by the structural parameters of the mechanism, the minimum length and maximum length of the hydraulic cylinder, the rotation angle of the hinge and other factors. When the structural parameters of the mechanism and the form of the hinge are determined, the motion range of the platform is determined by the length of the six hydraulic cylinders. For a reasonable motion platform, there should be no mechanical dryness when the six hydraulic cylinders are in any length

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