OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 5 No. 1 2023 The kinematic characteristics of the center of the roller of the cam mechanism can be found by differentiating the obtained displacement function (Fig. 2). Fig. 2. Program listing determining the kinematic characteristics of the cam mechanism: v(i) – roller center velocity analogue; h(i) – current value of roller center displacement; a(i) – differential of v(i); a1(i) – acceleration analogue; i = φ – cam rotation angle : d v i h i di ; velocity and acceleration: ( ) 0 ( ) : ( ) 2 0 v i if i v i v i if i otherwise ; ( ) : ( ) d a i v i di ; ( ) 0 1( ) : ( ) 2 0 a i if i a i a i if i otherwise . This synthesis algorithm is also used for further calculations, but with a change in some input parameters that do not affect the program, but lead to a change in the kinematic characteristics of Assur groups. The values and nature of the change in velocity analogs are shown in Figure 3. The size of the rocker is set based on the design parameters of the roller, its axis, as well as the dimensions of the hub. The maximum pressure angle is chosen taking into account the effi ciency of the entire mechanism. To determine the missing dimensions of the cam mechanism, let’s mark the position of point A of the rocker arm 3. Further, on the rays connecting point O1 and point A, segments equal to the values of velocity analogues in certain intervals of rotation angles are intercept (Fig. 4). Markings are made both for the growing phase and for the lowering phase. In our case, 8 values are given, which determined the hodograph of analogues of the velocity of point A of the mechanism. Drawing tangents to points A at an angle of 90° – δmax, we got a family of tangents that form a shaded area in Figure 4, which determine the position of the cam axis point. Figure 4 shows the point of intersection of the tangents only for the case of maximum analogues of velocities. Then the distance from the point O to the beginning of the trajectory of the roller center will be equal to the least radius of the cam min = R = = 90 mm. After the basic parameters for the cammechanism are received, let’s proceed to the synthesis of the rocker group. The parametric synthesis of the Assur group of the second class of the third type is proposed to begin with the defi nition of input parameters and conditions that should be set in this case. The kinematic characteristics of this group depend on the dimensions of the rocker arm L, the angle of its location with respect to the shoulder of the rocker arm of the cam group θ, which should be determined from the condition that at the moment the collet enters the groove of the rocker, the angle O1BO2 is equal to 90° (Fig. 1). Taking the size of the arm, on which the collet is located, equal to L = 60 mm, let’s determined the angle between the arms θ, for which it is necessary to consider the scheme of the mechanism shown in Fig. 1. Then 2 2 2 arccos 2 a L LA . (2) Fig. 3. Cam roller center velocity analogs
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