1) For the system below, link 2 is rotating with w2 = 20 rad/s and a2 = -5 rad/s2 at the given position

1) For the system below, link 2 is rotating with w₂ = 20 rad/s and a₂ = -5 rad/s² at the given position. The coordinate system Is set as in the picture. The coordinates of point D is indicated in the picture. DE 1s an extension of link 4. DE is perpendicular to CD. Dimensions are inches.

4 D(2.2".1.1")

¥ ° E

B .

2 4 .

3 AB = DE= 1.0m

55° - BC = 2.0 n

A Y CD=1.5m

C

Paper portion (40 points): write down all equations (or equation numbers) on paper

a) (10 pts) Use analytical method (vector loop), compute position vector Re

b) (15 pts) Use analytical method (vector loop), compute velocity vector Ve

c) (15 pts) Use analytical method (vector loop), compute acceleration vector Ar

d) (Extra 10 pts) Compute Ve using instant center method.

2) For the system below, block 2 1s sliding down with v_A = 8 in/s and a_A = 2 in/s* (both downward direction). Link 5 is connected to link 3 via a revolute (pin) joint at

B. The coordinate system is set as in the picture. Dimensions are inches.

Jay

1 AC = 2.4" )

JQ {A BD = 3.7" ‘

1 \\ BC = 1.2" D

: ()

: 3 ‘

B L

2.05" \R y

Va — 8 in/s ²

aa = 2 in/s² 45

‘ ay

C ‘

—<+___—_—_) 4", ————_>

Paper portion (60 points): Use the analytical method to solve for

a) (10 pts) position vector of point B (Rp)

b) (15 pts) angular velocity of link 3 (@ 3) and velocity vector of point B (Vg)

c) (15 pts) angular acceleration of link 3 (a3) and acceleration vector of point B (Ag)

d) (10 pts) position vector of point D (Rp)

e) (10 pts) angular velocity of link 5 (ws)

f) (Extra 10 pts) velocity vector of point D (Vp)

g) (Extra 10 pts) How many instant centers does the system have? Find all of them.