OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 6 No. 1 2024 Consider the second Assur group, which is part of the general scheme of the heddle motion mechanism. This is also second-class fi rst-order group (Fig. 9). Fig. 9. The second-class fi rst-type Assur group, which is part of the general scheme of the heddle motion mechanism The following values should be set for this group: the coordinates of points D and O4, the lengths of the links DE, GO4 and the hard angle between EO4 and GO4. From the triangle DEO4, according to the Pythagorean theorem, we determine the hypotenuse DO4 by the formula: ( )2 2 4 1 4 DO O O XD YD = - + . (33) From the triangle DEO4, we fi nd the angle s by the cosine theorem 2 2 2 4 4 4 4 arccos 2 DO EO DE DO EO χ æ ö + - ÷ ç ÷ ç = ÷ ç ÷ ç ⋅ ⋅ ÷ çè ø . (34) The angle ψ is determined by: 4 arcsin YD DO ψ æ ö÷ ç ÷ = ç ÷ ç ÷ çè ø . (35) Then the angle χ1 is found as: 1 χ ψ χ = + . (36) The coordinates of the point E are found as projections on the axes OH and OY: 1 4 4 1 cos( ) XE O O EO χ = - ⋅ , (37) 4 1 sin( ) YE EO χ = ⋅ . (38) The value of motion E is determined by: 2 2 E XE YE = + . (39) The angle of the lever position GO 4 E is found as the angle diff erence: 1 ε χ γ = - . (40) The coordinates and the length of the vector of the point G are defi ned as: 1 4 4 cos( ) XG O O GO ε = - ⋅ , (41) 4 sin( ) YG GO ε = ⋅ . (42)
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