Q1_NEW

Q1 (a)

Point C is the instantaneous center of rotation (b)~(d) 𝑚𝑚

𝑚𝑚

̅̅̅̅ = 6 ∙ 150 = 900 𝑉𝐷 = ω𝐵𝐷 ∙ 𝐷𝐶 (←) 𝑠𝑒𝑐

𝑉𝐵 = 75 ∙ 16 = 1200 𝑠𝑒𝑐 (↓) 𝑉

1200

𝐵𝐶

200

ω𝐵𝐷 = ̅̅̅𝐵̅ =

=6

𝑟𝑎𝑑 𝑠𝑒𝑐

̅̅̅̅ = 6 ∙ 125 (−𝑠𝑖𝑛 β 𝑖 − cos β𝑗) = 750 (−𝑠𝑖𝑛 β 𝑖 − cos β𝑗) 𝑚𝑚 ⃗⃗⃗⃗ 𝑉𝐺 = ω𝐵𝐷 ∙ 𝐺𝐶 𝑠𝑒𝑐

𝛽 = 𝑐𝑜𝑠 −1

100 = 36.87° = 0.643 𝑟𝑎𝑑 125

(e) 𝑚𝑚

𝑎𝐵 = −75 ∙ ω𝐴𝐵 2 = − 19200 𝑠𝑒𝑐 2 𝑖 ⃗⃗⃗⃗ (f) 𝑎𝐷 = ⃗⃗⃗⃗ ⃗⃗⃗⃗ 𝑎𝐵 + ⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ 𝑎(𝐷⁄ ) 𝐵

= ⃗⃗⃗⃗ 𝑎𝐵 + (𝑎 ⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ ⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ (𝐷⁄ ) )𝑡 + (𝑎 (𝐷⁄ ) )𝑛 𝐵

𝐵

=𝑎 ⃗⃗⃗⃗𝐵 (←) + ̅̅̅̅ 𝐵𝐷 𝛼(−𝑠𝑖𝑛𝛽 𝑖 + 𝑐𝑜𝑠𝛽𝑗) + 𝐵𝐷 ∙ ω𝐵𝐷 2 ∙ (−𝑐𝑜𝑠𝛽 𝑖 − 𝑠𝑖𝑛𝛽𝑗)

𝑎𝐷 = 𝑎𝐷 𝑖 + 0𝑗 = −19200𝑖 + ̅̅̅̅ ⃗⃗⃗⃗ 𝐵𝐷 𝛼(−𝑠𝑖𝑛𝛽 𝑖 + 𝑐𝑜𝑠𝛽𝑗) + 𝐵𝐷 ∙ ω𝐵𝐷 2 ∙ (−𝑐𝑜𝑠𝛽 𝑖 − 𝑠𝑖𝑛𝛽𝑗) ̅̅̅̅ 𝐵𝐷 𝛼𝑐𝑜𝑠𝛽 − ̅̅̅̅ 𝐵𝐷 ω𝐵𝐷 2 𝑠𝑖𝑛𝛽 = 0 → 𝛼 = 26.97

𝑟𝑎𝑑 𝑠𝑒𝑐 2

̅̅̅̅ 𝛼𝑠𝑖𝑛𝛽 − 𝐵𝐷 ̅̅̅̅ ω𝐵𝐷 2 𝑐𝑜𝑠𝛽 = −30445.50 𝑎𝐷 = −19200 − 𝐵𝐷

𝑚𝑚 𝑠𝑒𝑐 2

̅̅̅̅𝛼(−𝑠𝑖𝑛𝛽 𝑖 + 𝑐𝑜𝑠𝛽𝑗) + 𝐵𝐺 ̅̅̅̅⃗⃗⃗⃗⃗⃗⃗⃗⃗ (g) ⃗⃗⃗ 𝑎𝐺 = ⃗⃗⃗ 𝑎𝐵 + (𝑎 ⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ ⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ 𝑎𝐵 + 𝐵𝐺 ω𝐵𝐷 (−𝑐𝑜𝑠𝛽 𝑖 + 𝑠𝑖𝑛𝛽𝑗) (𝐺⁄ ) ) + (𝑎 (𝐺⁄ ) ) = ⃗⃗⃗ 𝐵

𝑡

𝐵

𝑛

𝑚𝑚 ̅̅̅̅ 𝛼 𝑠𝑖𝑛𝛽 − 𝐵𝐺 ̅̅̅̅ ω𝐵𝐷 𝑐𝑜𝑠𝛽 − 𝐵𝐺 𝑠𝑒𝑐 2 𝑚𝑚 = −19200 − 2021.398 − 600.225 = −21821.623 𝑠𝑒𝑐 2

⃗⃗⃗⃗ 𝐶𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡𝑠: (𝑎𝐺 )𝑥 = −19200 +

̅̅̅̅ 𝛼 𝑐𝑜𝑠𝛽 + 𝐵𝐺 ̅̅̅̅ ω𝐵𝐷 𝑠𝑖𝑛𝛽 = 2698.1 + 449.70 = 3147.799 ↑ + 𝐶𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡𝑠: (𝑎𝐺 )𝑦 = 𝐵𝐺 𝑎𝐺 = 22047.491

𝑚𝑚 𝑠𝑒𝑐 2

𝑚𝑚 𝑠𝑒𝑐 2