Angular Momentum, Kinetic Energy/3D Equations of Motion/Precession

A robot arm manipulates an axisymmetric part during manufacture of a vehicle. The part has a total mass M and radius of gyration k about its centre of mass G and spin axis z. During manufacturing the robot arm simultaneously slews about its base at Ω rad/s and spins the part about its axisymmetric spin axis z at p rad/s.

At this instance, the cylindrical arm OG has length L and is oriented at an angle Ø between the vertical Z and spin axis z. The transverse mass moment of inertia of the part about G is 60% of

the spin axis mass moment of inertia. Assume the motion is steady at this instance.

a)Calculate the angular momentum components of the manipulated part with respect to point O and point G. Explain any differences with respect to point O and point G. (8 marks)

b)Calculate the kinetic energy of the manipulated part.

c)Determine the reaction torque on the robot arm at point O accounting for the weight of the part. Neglect the weight of the robot arm. (8 marks)

d)Determine the free precession rate of the part about O and the reaction torque on the robot arm at point O when the part is slewed at the free precession rate. (8 marks)