Linking link setting with preset time-scale gear rocker sliding block system

The size constraint of the gear rocker slider mechanism and its basic size are respectively the length of the connecting rod AB, the connecting rod BC and the slider track and the horizontal direction. The gear is hinged to the frame by a hinge A, the gear is fixed to the connecting rod BC, the idler is mounted on the rocker BC, and the gear and the gear are exactly the same size. Therefore, when the gear rotates at a uniform speed for a full circumference, the gear can be driven to rotate at a constant speed by the idler, which is proved as follows.
Let 1, 2, 3, and H be the gears, respectively, and the absolute angular velocity of the frame rod AB relative to the frame. z1, z2, and z3 are the gears, and the number of teeth, then the gear ratio between the gears and the gears i, H=1. -H2-H= z3z2z1z3= z2z1 Gear rocker slider mechanism diagram The above formula is arranged to 1z1=2z2 (z1-z2)H When taking z1=z2, there is 1=2.
Since the gear is fixed to the connecting rod BC, the connecting rod BC also rotates at a constant speed.
In order to realize that the connecting rod BC can rotate all the way, the mechanism must satisfy the geometric relationship l2 l3l1 Since the mechanism of the proportional relationship of the length of the corresponding rod in the planar four-bar mechanism has the same motion output characteristics, it can be uniformly processed [4] This processed size is called the basic size of the mechanism. Since the basic size is dimensionless, the basic size of the gear rocker slider mechanism can be expressed as l1, l2, l3, and l1 l2 l3 = 300 for the basic size of the gear rocker slider mechanism. Said that the size constraint of the connecting rod can rotate all the way is l2 l3l1 and 0 2 gear rocker slider mechanism linkage trajectory mathematical model point P on the link BC plane polar coordinate position; is the initial position angle of the link BC; for the entire mechanism around the coordinate origin rotation angle (ie slider guide and The angle between the positive axes of the x-axis; the hinge point A in the coordinate system because the gear acts as the driving wheel to drive the gear through the idler gear to rotate at a constant speed, so the connecting rod BC also rotates at a constant speed. When the connecting rod BC rotates one turn, the trajectory of the reference point P forms a closed curve, and the connecting rod AB also swings for one cycle, so if taken as the corner of the connecting rod BC, the swing angle of the connecting rod AB is The periodic function of the independent variable. According to the motion output characteristics of the planar four-bar mechanism, when the basic size of the gear rocker mechanism is determined, the swing angle function of the connecting rod will be determined, and the yoke angle operator ej will be determined accordingly.
(1) Since the connecting rod BC rotates at a constant speed, the harmonic component of the connecting rod angle operator ej after the two-dimensional fast Fourier transform (FFT) has only one positive term, so the series expansion of the connecting rod angle operator can be written. For ej.
If the mechanism is in the standard installation position (ie, the middle point A coincides with the coordinate origin R=0, the slider track is parallel to the x-axis ie =0 (the starting position of the link BC is 0, then the reference point P on the link at this time) (3) Comparing equation (2) with equation (1), it is known that, except for the positive term, the harmonic components of all corresponding terms are equal when formula (2) is divided by l1; and equations (3) and (1) It is known that when the equation (3) is divided by the constant l1ej, except for the 0th term and the positive term, the amplitudes of the harmonic components of the other corresponding terms are equal, and the phases are different by n degrees. This reveals the linkage of the mechanism. The intrinsic relationship between the trajectory and its oscillating angle operator lays a theoretical foundation for the integration of the scale of the organization.
3. Establishment of the numerical map library of the linkage angle operator of the mechanism and the fuzzy recognition process. Since the basic size of a gear rocker slider mechanism corresponds to a swing angle operator, a swing angle operator can be used to represent The basic size of the group organization. The harmonic components of the different frame swing angle operators are calculated by two-dimensional FFT, and in order to eliminate the influence of the rod length and position size, the harmonic components are also normalized to obtain the linkage rod. Harmonic characteristic parameters of the swing angle operator. Then the basic size of different organizations and several harmonic characteristic parameters are stored in the computer in the form of a database. This database is called the numerical map library of the mechanism linkage angle operator. The numerical map library established in this paper contains a total of 17205 sets of basic size types.
In the synthesis of the mechanism scale, the given link trajectory is firstly subjected to two-dimensional FFT and normalization to obtain the harmonic characteristic parameters, and then the harmonic characteristic parameters and values ​​of the given trajectory are obtained by the computer through the fuzzy recognition method. The corresponding items of each set of harmonic characteristic parameters in the library are compared, and a plurality of basic size types with the smallest weighted Hamming distance are respectively calculated and selected for use in the actual size of the following computing mechanism.
4 The actual size and installation position parameter calculation of the mechanism. After the basic size type of the mechanism is identified by the fuzzy recognition technology, the harmonic component amplitude (8) of the basic size type of the swing angle operator is calculated by using the two-dimensional FFT. The two coordinate values ​​(9) of the hinge point A of the frame rod have been fuzzyly recognized due to the basic size of the mechanism, and the link rod l1 has been calculated by the above formula, then the link length l2 and the offset length l3 of the mechanism can be It is determined according to the actual size of the mechanism and the length of the basic size.
A given linkage trajectory 5 mechanism synthesis example is a given linkage trajectory, representing 64 sample point locations on the trajectory. The actual size and installation position parameters of the mechanism are determined using the scale synthesis method and the theoretical calculation formula described above. The actual size and mounting position dimensions of the 10 mechanisms vary. The fitting of the link trajectory generated by each actual mechanism with the given trajectory, the link trajectory, and the dotted line are the trajectories generated by the actual mechanism. It can be seen that the mechanism integrated by this method can better achieve the expected trajectory.
6 Conclusion The gear rocker slider mechanism is obtained by combining the rocker slider mechanism and the gear mechanism. Compared with the common flat four-bar mechanism, the combined mechanism does not have a dead center position during the whole movement, and the transmission performance of the mechanism is also good. Since the idler is added to the gear transmission, and the gear I and the gear are required to have the same size, it is convenient to realize the constant rotation of the link when the driving wheel rotates at a constant speed. The mathematical model of the connecting rod trajectory of the gear rocker slider mechanism is established by using Fourier series theory and complex vector theory, and the mathematical formulas of the actual size and installation position of the calculation mechanism are derived. The numerical scale method is used to realize the scale synthesis of the link trajectory of the gear rocker mechanism. The comprehensive examples given show the effectiveness and feasibility of the proposed method.

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