$4\mathrm{.}1$ It is required to plan the motion of a line gantry robot shown in Figure $3($a$)$ as follows:

Distance travelled during constant velocity $=1m$

Acceleration time $=0\mathrm{.}1s$

Deceleration time $=0\mathrm{.}25s$

$($a$)$

Figure $3.($a$)$ Line gantry robot and $($b$)$ Trapezoidal velocity profile

$|$

ROBO$202/$ROBT$202$: June, $2024$: Supplementary Examination

Assuming the motion follows a trapezoidal velocity profile $($shown in Figure $3($b$)),$ find

the following performance variables, given that $v_m=1\mathrm{.}6m{s}^{-1}$ :

a$)$ Total move time

b$)$ Total distance travelled

c$)$ Acceleration

d$)$ Deceleration