Notes_03_04 - Notes_03_04 page 1 of 9 POLYCENTRIC HINGE -...

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Notes_03_04 page 1 of 9 POLYCENTRIC HINGE - SKELETAL DIAGRAM POLYCENTRIC HINGE - VECTORS Vector Position of Length (mm) Angle (deg) 1 H wrt A 21.67 constant 0.00 constant 2 B wrt A 26.69 constant 181.61 var 3 C wrt B 26.00 constant 36.95 var 4 D wrt E 14.00 constant 99.38 driver 5 E wrt F 17.83 constant -15.87 var 6 F wrt H 22.47 constant 146.31 θ 9 - 5.33 ° 7 G wrt H 22.03 var 171.56 var 8 G wrt A 3.23 constant 92.21 θ 2 - 89.40 ° 9 C wrt H 31.33 constant 151.64 var 10 D wrt C 24.62 constant 15.36 θ 3 - 21.59 ° 0 R R R R 1 9 3 2 = - - + 0 R R R R R R R 1 6 5 4 10 3 2 = - - - - + + 0 R R R 1 7 8 = - - A B C D E H F G A B C D E H F G 2 6 3 4 5 8 7 1 1 R 2 R 7 R 6 R 5 R 4 R 3 R 10 R 9 R 8 R 1
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Notes_03_04 page 2 of 9 Sewing Machine Determine angles θ , φ and ψ as well as distance s for this sewing machine linkage at the position shown below. 45 ° 2 4 3 O 2 5 6 O 4 A B C E D O 2 A = 1.60 cm AB = 3.57 cm O 4 B = 2.24 cm BC = 1.60 cm O 4 C = 2.74 cm CD = 3.81 cm O 2 E = 1.42 cm O 4 E = 3.81 cm O 4 BC = 90 ° BO 4 C = 35.73 ° ϖ 2 θ φ ψ s O 2 O 4 E (O 2 O 4 ) 2 = (O 2 E) 2 + (O 4 E) 2 O 2 O 4 = 4.066 cm tan(EO 4 O 2 ) = (O 2 E) / (O 4 E) EO 4 O 2 = 20.44 ° 20.44 ° O 2 O 4 A 24.56 ° α e O 4 B A β γ e E 20.44 ° ψ γ e 2 = (O 2 A) 2 + (O 2 O 4 ) 2 - 2 (O 2 A) (O 2 O 4 ) cos 24.56 ° e = 2.694 cm sin α / (O 2 A) = sin 24.56 ° / e α = 14.29 ° e 2 = (O 4 B) 2 + (AB) 2 - 2 (O 4 B) (AB) cos γ γ = 48.94 ° sin β / (AB) = sin γ / e β = 87.77 ° or 92.23 ° ??? check (AB) 2 = e 2 + (O 4 B) 2 + - 2 e (O 4 B) cos β β = 92.23 ° EO 4 O 2 - α + β = θ + BO 4 C θ = 62.65 ° θ + BO 4 C + γ + ψ = 180 ° ψ = 32.68 ° (O 4 C) sin θ = (O 2 E) + (CD) sin φ φ = 15.43 ° s + (O 4 E) = (O 4 C) cos θ + (CD) cos φ s = 1.12 cm O 2 O 4 E s θ φ C D
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Notes_03_04 page 3 of 9
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Notes_03_04 page 4 of 9 Determine the angular velocity of links 2, 3, 4 and 5 as well as the velocity of needle 6 for the sewing machine linkage as shown below when sewing at 4 stitches per second constant speed. 15.4 ° 45 ° 32.7 ° 62.7 ° 2 4 3 O 2 5 6 O 4 A B C E D O 2 A AB = 3.57 cm O 4 B = 2.24 cm BC = 1.60 cm O 4 C = 2.74 cm CD = 3.81 cm O 2 E = 1.42 cm O 4 E = 3.81 cm O 4 BC = 90 ° BO 4 C = 35.7 ° constant ϖ 2 ϖ 2 = 4 stitches/sec = +8 π rad/sec V A = (O 2 A) ϖ 2 = 40.21 cps A / B A B V V V + = ?
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Notes_03_04 - Notes_03_04 page 1 of 9 POLYCENTRIC HINGE -...

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