OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 6 1 4 Fig. 8. The second-class fi rst-type Assur group The coordinates of point B are found as projections on the X and Y axes: 1 2 2 cos( ) XB O O BO δ = - ⋅ , (20) 2 sin( ) YB BO δ = ⋅ . (21) By determining the coordinates of point B, you can fi nd the resulting value according to the expression: 2 2. B XB YB = + (22) For the second-class fi rst-type Assur group (Fig. 8), the following values are set: coordinates of point B and O3, lengths of links BC, CO3, and CD (Table 1), as well as the angle determining the position of vector B. To determine the coordinates of point D, it is necessary to determine the angle f of the lever DC and the value of the segment BO3 from the triangle BO2O3 according to the cosine theorem. 1 1 3 arctan y f O O x æ ö÷ ç ÷ = ç ÷ ç ÷ ç è - ø , (23) 2 2 3 2 2 3 2 2 3 1 2 cos( ) BO BO O O BO O O f = + - ⋅ ⋅ ⋅ , (24) 2 2 2 3 3 2 3 3 arccos 2 BO CO BC f BO CO æ ö + - ÷ ç ÷ ç = ÷ ç ÷ ç ⋅ ÷ çè ø , (25) 1 2 ( ) f f f π = - + . (26) The coordinates of points C and D are found as projections on the OX and OY axes: 1 3 3 cos( ) XC O O CO f = + ⋅ , (27) 3 sin( ) YC CO f = ⋅ , (28) 1 3 3 cos( ) XD O O DO f = - ⋅ , (29) 3 sin( ) YD DO f = ⋅ . (30) Further, according to the Pythagorean theorem, their resulting values were found: 2 2 C XC YC = + , (31) 2 2 D XD YD = + . (32)
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