Meriam, Kraige & Bolton — Introduction to Three-Dimensional Dynamics of Rigid Bodies: Problem 7_39

7/39 For the conditions described in Prob. 7/32, determine the velocity $\mathbf{v}$ and acceleration $\mathbf{a}$ of the center $A$ of the ball tool in terms of $\beta$. Conditions from Problem 7/32: The small motor $M$ is pivoted about the $x$-axis through $O$ and gives its shaft $OA$ a constant speed $p$ rad/s in the direction shown relative to its housing. The entire unit is then set into rotation about the vertical $Z$-axis at the constant angular velocity $\Omega$ rad/s. Simultaneously, the motor pivots about the $x$-axis at the constant rate $\dot{\beta}$ for an interval of motion. Let $R$ be the horizontal distance from the vertical $Z$-axis to the pivot $O$, and let $b$ be the length of the shaft $OA$.