Consider a two$-$axis spinning device as shown, where a primary shaft can rotate about the

horizontal axis $($turning up or down$).$ A secondary rotating device is fixed on the primary

shaft that apins a circular panel about an axis passing through the circle's geometric center

also perpendicular to it$.$

We are interested in the motion of a particle $P$ fixed on the edge of the panel while it spins

around. Inertial frame $E$ is given, frame $a$ is fixed on the primary shaft such that hat$(a{)}_2$ is

perpendicular to the panel and passes through the disk center, and frame $d$ is fixed in the

circular disk such that $d_3^{}$ points towards $P$ from its center.

You can use $L$ for the total shaft length. Primary tilt angle $$ measures between disk per$-$

pendicular direction $a_2^{`}$ and the front $(e_2^{}).$ Thrning up is defined as positive. From the side

view, the secondary rotation's spin axis coincide with the shaft axis. 'The disk is at a fixed

distance $D$ relative to it$.$ The disk also have a radius $R.$ Disk spin angle $$ is defined.