Check if a is correct than help with b please..................... b$)$ Suppose the robot is commanded to move to a new position Pj $(=30,=-10,=15,$ L$=25),$ the maximum speed of any rotational joint is $10$o$/$s and the maximum speed for the linear joint is $2\mathrm{.}0$ in$/$s$.$ If the robot controller has joint interpolation routine, determine the time and speeds of each joint to move the robot to the new position.sConsider a TRL:R manipulator with the following setting $($Figure $1)$

Length of link $L_1=10\mathrm{.}0in.$

Length of the extension link $L=15\mathrm{.}0in.$

Length of link $4,L_4=3\mathrm{.}0in$

Base angle $=0$

Elevation angle $=20$

Pitch angle $=34$

a$)$ Determine the coordinates of the point that can be reached by the end $-$of$-$arm

$x=cos(Lcos\frac{O}{+}{L}_{4}cos)$

$y=sin(Lcos\frac{O}{+}{L}_{4}cos)$

$\{$:$z=L_1+$Lsin$+L_{4}sin)$

$x=cos(15cos20+3cos34)$

$x=(14\mathrm{.}09+2\mathrm{.}48),x=16\mathrm{.}578$

$z=10+5\mathrm{.}13+1\mathrm{.}677$

$z=16\mathrm{.}8$

$Pw=(16\mathrm{.}578,0,16\mathrm{.}8)$

b$)$ Suppose the robot is commanded to move to a new position

$,$ the maximum speed of any rotational joint is $10\%$ and the maximum speed for the linear

joint is $2\mathrm{.}0i\frac{n}{s}.$ If the robot controller has joint interpolation routine, determine the time and

speeds of each joint to move the robot to the new position.