Florida International University, Department of Mechanical and Materials Engineering

EML 4806 and EML 5808

Homework assignment 3

Use analytical analysis to solve the following problems

In the above mechanism, if a =1 cm, b = 4cm, θ = 60°, dθ/dt˙ =10 rad/sec (constant),

determine:

e) The angle ϕ of link b, and position c of the slider.

f) The angular velocity dϕ/dt of link b, and velocity of the slider.

g) The angular acceleration d²ϕ/dt² of link b, and acceleration of the slider.

Problem 2.6

In the mechanism shown below, link 2 is rotating CW at the rate of 100 rad/s (constant). In the position shown, link 2 is horizontal. Use loop equation approach to determine:

a) The position of the slider and angle θ₃ of the link 3.

b) The velocity V_c4 of the slider and angular velocity ω₃ of link 3.

c) The acceleration a_c4 of the slider and angular acceleration α₃ of link 3.

In the mechanism in Problem 5.3 assume that dϕ/dt is 10 rad/s CCW. Use the loop equation approach to determine the velocity and acceleration of slider 4 for the position defined by ϕ = 60°.

In the mechanism in Problem 5.5, determine the angular acceleration of link 3, the velocity and acceleration of slider 4.

Problem 2.2

In the mechanism shown below, link 2 is rotating CCW at the rate of 500 rad/s (constant). In the position shown, link 2 is vertical. Use loop equation approach analytic methods to determine:

a) The angle θ₃ of the link 3 and θ₄ of the link 4.

b) The angular velocity ω₃ of the link 3 and ω₄ of the link 4.

c) The angular acceleration α₃ of link 3 and α₄ of link 4.

Link lingths: AB = 1.2 in, BC = 2.42 in, CD = 2 in.

Problem 3.13

In the mechanism shown below, the angular velocity of link 2 is 2 rad/s CCW and angular acceleration is 5 rad/s² CW. Use loop equation approach to determine:

a) The position of the slider r_B4 and angle θ₄ of the link 4.

b) The velocity v_B4 of the slider and angular velocity ω₄ of link 4.

c) The acceleration a_B4 of the slider and angular acceleration α₄ of link 4.

d) The velocity v_D4 and acceleration a_D4 at the point D of link 4.