Problem$-2$

The mechanism shown below has disconnecting revolute joints at A and $B$ for the assigned joint

variables such as ${}_{12},{}_{14},{}_{16},s_{43},s_{65}.$

The position loop equations are given as follows,

vec$(A_{0}A)=$vec$(A_0{B}_0)+$vec$(B_{0}A),in$ complex form: $a_2{e}^{i{}_{12}}=-a_1+s_{43}{e}^{i{}_{14}}$

vec$(B_{0}B)=$vec$(B_{0}Q)+$vec$(Q{C}_0)+$vec$(C_{0}B),in$ complex form: $-(a_3-s_{43})e^{i{}_{14}}=i{b}_1-c_1+s_{65}{e}^{i{}_{16}}$

a$)$ Obtain the velocity loop equations with real and imaginary parts.

b$)$ If the input is ${}_{14}^{},$ determine the velocities $s_{43}^{},{}_{12}^{},{}_{16}^{}$ and $s_{65}^{}$ in terms of input and

other variables.