1. The planetary gear train shown below is made up of two planetary stages. The input, shaft 1, drives the arms of both stages at 300 RPM CCW. Gear D is the output of the first stage and the input of the second stage.

a. Determine the speed and direction of the output (shaft 2).

b. If the required output torque is 400 ft-lb_f, determine the input power requirement (assume 96% efficiency of the gear train).

2. A cam with a base circle diameter of 4 inches requires the timing diagram shown below and utilizes a cycloidal displacement function. The cam is operating at a constant speed of 2600 RPM and has maximum displacement of the follower of 0.5 inches.

a. If the follower has a mass of 0.3 lb_m, determine the upward maximum upward force on the follower during the rise.

b. What is the value of s at the location of the maximum force?

c. Would you expect the magnitude of the maximum downward force during the fall to be the same, greater than, or less than the maximum upward force during the rise?  Explain your answer.

3. The uniform slender rod with spherical ends is initially balanced vertically as shown. The rod has a mass of 6 kg and a length of 4.0 meters.  The kinetic coefficient of friction between the rod and inclined surface is 0.20. The angle of the incline θ is 20°. The rod is released and begins to slide down the ramp (translate and rotate).

a. Develop the appropriate simultaneous equations and write the MATLAB code that uses the symbolic solver to determine the linear acceleration of the center of mass of the rod and the angular acceleration of the rod.

4. Given the fourbar offset crank slider shown below, θ₂ = 70° and ω₂ = 20.0 rad/s constant CCW. The length of link 2 is 40 cm and the length of link 3 is 70 cm.  Note: drawing is not to scale.

a. If the mass of the slider is 10 kg, determine the motor torque applied to link 2 required to accelerate the slider at this instant (assume frictionless and ignore the mass of the other links).