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 w₁. The arm O₁O₂ rotates about the x-axis at the rate w₂ = θ˙. The control arm O₂A rotates about axis O₁-O₂ at the rate w₃ and about a perpendicular axis through O₂ which is momentarily parallel to the x-axis at the rate w₄ = β˙ . Finally, the jaws rotate about axis O₂-A at the rate w₅. The magnitudes of all angular rates are constant. For the configuration shown, determine the magnitude w of the total angular velocity of the jaws for θ = 60° and β = 45° if w₁ = 2 rad/s, θ ˙ = 1.5 rad/s, and w₃ = w₄ = w₅ = 0. Also express the angular acceleration a of arm O₁O₂ as a vector.

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