OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 6 1 4 To prevent jamming and ensure the strength of the cam pair of the mechanism, it is necessary to know the numerical values of the pressure angles, which in our case should not exceed 45 °. The program developed for this purpose calculated the pressure angle values. Because the determination procedure is cumbersome, it is not presented in the paper. They did not exceed acceptable values in the entire range of studies conducted. To confi rm the accuracy of the selected roller dimension, its value was compared with the actual radius of curvature, determined by the formula: ( ) ( ) 3 2 2 2 2 2 2 i i i i i y y y y y y ρ é ù ê + ú ë û = + ⋅ - ⋅ , (16) where , , , i i i i y y y ρ are the radius vectors of the center profi le of the cam and the derivatives at the i-th point. A program for the mathematical software package was developed for this purpose. The calculation results are shown in Fig. 5. The conditions agree well with the expression: min 0 0, 7 ; 0, 4 r r r ρ £ ⋅ £ ⋅ , (17) where min ρ is the minimum radius of curvature of the cam’s center profi le. The data analysis results suggest that the roller radius choice for the cam mechanism is accurate. Next, the cam profi le (radius vectors of the cam r(i)) was determined using equation (15). The calculation was carried out in a mathematical sotware package; the matrix of values of radius vectors and the shape of the cam profi le are shown in Fig. 6. To confi rm the accuracy of the selected link dimensions, it is necessary to conduct a kinematic analysis for individual Assur groups. If their graphs have smooth and continuous characteristics, we assume that the synthesis was accurate. For kinematic analysis, the dimensions of the links obtained as a result of the lever system synthesis were used (see Table 1). Kinematic analysis began with a fi rst-class fi rst-order mechanism, which was used as a variable radius vector shown in the table (Fig. 6) [10–12, 19, 24–28, 35– a b c Fig. 4. Graphs of kinematic characteristics’ analogs for the center of the roller: (a) acceleration; (b) speed; (c) motion Fig. 5. Pressure angles for the cam mechanism
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