Quiz04 Div1 Soln

ME 274 – Spring 2009 Quiz No. 4 – Div 1 Monday, February 9

SOLUTION

The mechanism shown below is made up of links OA and BC. Links OA and BC are pinned to ground at points O and C, respectively. Pin A of link OA is able to slide within a slot that is cut in link BC, as shown. Pins O and C are on the same horizontal line. At the instant shown, • link BC is vertical with L = 400 mm. • link BC is rotating in the CCW sense at a rate of ωBC = 6 rad/sec. y

At the instant shown, find: a) the angular velocity of link OA. Write your answer as a vector.

B

b) the value for L! . A HINT: In relating the velocities of A and C, use an observer attached to link BC. Also, let the xyz axes be attached to link BC. 500 mm

Link OA:

L

v A = vO + ! OA "!r A/O

(

= 0 + (! OA k ) "! 0.3i + 0.4 j

)

ωBC

= #0.4 ! OA i + 0.3! OA j Also,

x

v A = vC + ( v A/C )rel + ! "!r A/C

(

= 0 + L! j + (! BC k ) "! 0.4 j

O

)

= #0.4 ! BC i + L! j Equating and balancing coefficients:

! 0.4 " OA = !0.4 " BC j : 0.3" OA = L!

i:

# #

" OA = ( 6k ) rad / sec L! = ( 0.3) ( 6 ) = 1.8 m / sec

C