Mechanics

ME 321 Kinematics Exam 1 Retake Name: Student ID: Signature:

Prob. 1 (10 points) Angular velocity of link 2 ω2 = 5 rad/s CCW. Find ω2 and Vp. Use the complex-

algebra method (no credit for other method).

AC = BC = 20 mm, AB = 10 mm, PB = 35 mm.

𝑑(𝑅𝑒𝑗𝜃)

𝑑𝑡 =

𝑑𝑅

𝑑𝑡 𝑒𝑗𝜃 + 𝑗𝑤𝑅𝑒𝑗𝜃 𝑒𝑗𝜃 = 𝑐𝑜𝑠𝜃 + 𝑗𝑠𝑖𝑛𝜃

ret ak

Prob. 2 (14 points) All dimensions are known in mm (not to scale). BD = 11.67 mm, AB = 2 mm, AE = 3

mm, ED = 14 mm. link 2 (Link AE) is rotating CW with an angular velocity of 8 rad/s. (1) (4 points) Find

out the number of links and joints (mark the links and joints on figure), calculate degree of freedom m =

3 * (n-1) – 2*J1 – J2 . (2) (8 points) Find the angular velocity of link 4 (link FCD), (3) (2 points) Draw

point B3 on the velocity polygon (show steps to find B3, by relating to its neighbor). Draw the velocity

polygon to solve this problem. Show the intermediate steps to get full credit. Use a scale of 1 mm on

paper represents 1 mm/s. (or if you are using an inch ruler: 1 inch on paper represents 24 mm/s). The

black dot is the origin point in the velocity polygon. Velocity difference equation: VPQ = ω x RPQ, relative

velocity: VB3 = VB4 + VB3/4

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Prob. 3 (10 points)

All dimensions (not to scale) are known in mm.

Vc = 10 m/s to the left.

Find the instantaneous velocity of

point D and the angular velocity of

links 2 and 3.

Scale: 40 mm represents 10 m/s.

(or 1 inch on paper represents

5 m/s) Show all steps.

ret ak