The robot shown has five degrees of rotational freedom. The x-y-z axes are attached to t...

The robot shown has five degrees of rotational freedom. The x-y-z axes are attached to the base ring, which rotates about the z-axis at the rate ω₁. The arm O₁O₂ rotates about the x-axis at the rate The control arm O₂A rotates about axis O₁-O₂ at the rate ω₃ and about a perpendicular axis through O₂ which is momentarily parallel to the x-axis at the rate ω₄ = Finally, the jaws rotate about axis O₂-A at the rate ω₅. The magnitudes of all angular rates are constant. For the configuration shown, determine the magnitude ω of the total angular velocity of the jaws for θ = 60° and β = 45° if ω₁ = 2 rad/s, 1.5 rad/s, and ω₃ = ω₄ = ω₅ = 0. Also express the angular acceleration α of arm O₁O₂ as a vector.