Solve the question by writing a matlab code:

P$1\mathrm{.}2.$ Frames $M$ and $C$ are attached rigidly to a cuboid as shown in Fig. $3.$ Frame

$U$ is fixed and serves as the universe frame of reference. The cube undergoes the

following motion in the indicated sequence:

Rotation about the $z$ axis of Frame $C$ by $30,$ then

Translation of $(1,2,3)$ along Frame C$,$ then

Rotation about the $x$ axis of Frame $M$ by $45,$ and then

Rotation about the $y$ axis of Frame $U$ by $60.$

Let ${?}^U{T}_{C_i}$ and ${?}^U{T}_{M_i}$ be the $44$ homogeneous transformation matrices that describes

the position and orientation of Frames $C$ and M$,$ respectively, in $U$ after motion $i.$

Find

i$.,{?}^U{T}_{C_1}$

ii$.,{?}^U{T}_{C_2}$

iii. ${?}^U{T}_{C_3}$

iv$.{?}^U{T}_{C_4}$

v$.{?}^U{T}_{M_4}$

line segment lengths:

$AD=1$

$DC=3$

$DE=2$