Question

Given : Figure 2 , 1024 = 4 . 0 rml , [ 40 = 8 . 0 cm , e = 225° , O2 = 15 rad / s CW , M2 = 1rad / s2 CCW .2 ܂ Find: 63, 14,

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Answer #1

02A = 4cosizi + 4sind27

AD = 8cosizi +8sin 3.7

02D = -101 + y2

Vector Loop: Position analysis.

02D = 02 A+ AD

Substitute individual vectors and separate i and j components.

4cost2 + 8cost3 = -10; 4sint2 + 8sin 3 = y;

given02 = 2250

→ 4cos 225 + 8cos3 = -10 * cos(3 = -0.89645 + 03 = 153.6950

74= y = 4sin 225 + 8sin 153.6950 = 0.717 cm

Velocity analysis:

Consider this:

4cost2 + 8cost3 = -10; 4sint2 + 8sin 3 = y;

Take the derivative of the equations.

- 4sin 2 * W2 – 8sind3 * W3 = 0; 4cos02 * W2 + 8cost3 * W3 = y;

given w2 = 15rad/sCW = -15rad/s(CCW is + ve)

Substituting all known values:

→-4sin 225 * (-15) – 8sin 153.695 * W3 = 0 = W3 = -11.97rad/s

dr 4 = y = 4cos 225 * (-15) + 8cos153.695 *(-11.97) = –128.27cm/s dt

Acceleration analysis:

Consider this:

- 4sin 2 * W2 – 8sind3 * W3 = 0; 4cos02 * W2 + 8cost3 * W3 = y;

Take the derivative of the equations.

-4cos02 * w - 4sin02 * a2 - Scost3 * wz - 8sintz * a3 = 0; 4cos02 * a2 - 4sin 2 * W3 + 8cos(3 * a3 - 8sin03 * wa = ;

given a 2 = lrad/s2CCW

Substituting all known values:

→-4cos 225*152-4sin 225*1-8cos153.695*11.972-8sin153.695*03 = 0;

→ a3 = 470.15rad/s2

y = 4cos 225*1-4sin 225*152 +8cos 153.695*470.15-8sin 153.695*11.972

Pra = j =-3246.11cm/s?

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