Perform the forward kinematics on the robot. Write down all your work. for the matrix mutiplications, By hand, calculate T$3\_0$ and T$6\_33)$ Denso $4-$axis $($SCARA$)$ robots: HS$-$G$,$ HM$-$G series

DENSO

CEILING$-$MOUNT OPTION $\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline $\backslash$multicolumn$\{2\}\{|$l$|\}\{\}$ & HS $\backslash (4535^\{*\}\backslash$mathrm$\{$G$\}\backslash )$ & HS$-4545*4$ & H$5-4555\backslash (\{\}^\{*\}\backslash$mathrm$\{$G$\}\backslash )\backslash \backslash$

$\backslash$hline $\backslash$multicolumn$\{2\}\{|$l$|\}\{$Number of axas$\}$ & $\backslash$multicolumn$\{3\}\{|$c$|\}\{4\}\backslash \backslash$

$\backslash$hline $\backslash$multicolumn$\{2\}\{|$l$|\}\{$Maximum arm reach $($mm$)\}$ & $350$ & $450$ & $550\backslash \backslash$

$\backslash$hline $\backslash$multicolumn$\{2\}\{|$l$|\}\{$First$-$arm reach $($ mm $)\}$ & $125$ & $225$ & $325\backslash \backslash$

$\backslash$hline $\backslash$multicolumn$\{2\}\{|$l$|\}\{$Second$-$arm reach $($ mm $)\}$ & $\backslash$multicolumn$\{3\}\{|$c$|\}\{275\}\backslash \backslash$

$\backslash$hline $\backslash$multirow$\{4\}\{*\}\{$Range of mation $(\backslash \%)\}$ & $$ & $\backslash$multicolumn$\{3\}\{|$c$|\}\{\backslash (\backslash$pm $155\backslash )\}\backslash \backslash$

$\backslash$hline & $12$ & $\backslash$multicolumn$\{3\}\{|$c$|\}\{\backslash (\backslash$pm $145\backslash )\}\backslash \backslash$

$\backslash$hline & $\backslash (2(\backslash$mathrm$\{$~mm$\})\backslash )$ & $\backslash$multicolumn$\{3\}\{|$c$|\}\{200,320\}\backslash \backslash$

$\backslash$hline & T & $\backslash$multicolumn$\{3\}\{|$c$|\}\{\backslash (\backslash$pm $360\backslash )\}\backslash \backslash$

$\backslash$hline $\backslash$multicolumn$\{2\}\{|$l$|\}\{$Positian detection$\}$ & $\backslash$multicolumn$\{3\}\{|$c$|\}\{$Absolute encoder$\}\backslash \backslash$

$\backslash$hline $\backslash$multicolumn$\{2\}\{|$l$|\}\{$Minimum motion area $($m$)\}$ & $143$ & $136$ & $191\backslash \backslash$

$\backslash$hline $\backslash$multicolumn$\{2\}\{|$l$|\}\{$Maximum payjoad $($kg$)\}$ & $\backslash$multicolumn$\{3\}\{|$c$|\}\{5\}\backslash \backslash$

$\backslash$hline $\backslash$multicolumn$\{2\}\{|$l$|\}\{$Weight$,$ approx. $($kgi$)\}$ & $\backslash$multicolumn$\{3\}\{|$c$|\}\{25\}\backslash \backslash$

$\backslash$hline $\backslash$multicolumn$\{2\}\{|$l$|\}\{$Fooprint $($ mm $)\}$ & $\backslash$multicolumn$\{3\}\{|$c$|\}\{\backslash (150\backslash$times $150\backslash )\}\backslash \backslash$

$\backslash$hline $\backslash$multicolumn$\{2\}\{|$l$|\}\{$Cycle time $($sec$.)\}$ & $\backslash$multicolumn$\{3\}\{|$c$|\}\{0\mathrm{.}35($with $2-$kg weight$)\}\backslash \backslash$

$\backslash$hline $\backslash$multicolumn$\{2\}\{|$l$|\}\{$Maximum composite speed $($mm$/$sec$.)\}$ & $7,200$ & $6,300$ & $7,100\backslash \backslash$

$\backslash$hline $\backslash$multirow$\{4\}\{*\}\{$Maximum joint speed$\}$ & $11("5$ec$.)$ & $720$ & $\backslash$multicolumn$\{2\}\{|$c$|\}\{450\}\backslash \backslash$

$\backslash$hline & $12("$ sec $)$ & $\backslash$multicolumn$\{3\}\{|$c$|\}\{720\}\backslash \backslash$

$\backslash$hline & $2($mmsec$)$ & $\backslash$multicolumn$\{3\}\{|$c$|\}\{2,050\}\backslash \backslash$

$\backslash$hline & T$(9)$ & $\backslash$multicolumn$\{3\}\{|$c$|\}\{2,400\}\backslash \backslash$

$\backslash$hline $\backslash$multirow$\{3\}\{*\}\{$Repeatability$\text{'}\}$ & $(1)\backslash (+12($m $\backslash$mathrm$\{$~m$\})\backslash )$ & $10\mathrm{.}915$ & $\backslash$multicolumn$\{2\}\{|$c$|\}\{10\mathrm{.}02\}\backslash \backslash$

$\backslash$hline & $\backslash (2(\backslash$mathrm$\{$~mm$\})\backslash )$ & $\backslash$multicolumn$\{3\}\{|$c$|\}\{\backslash (\backslash$pm $0\mathrm{.}01\backslash )\}\backslash \backslash$

$\backslash$hline & $(9)$ & $\backslash$multicolumn$\{3\}\{|$c$|\}\{\backslash (\backslash$pm $0\mathrm{.}005\backslash )\}\backslash \backslash$

$\backslash$hline $\backslash$multicolumn$\{2\}\{|$l$|\}\{$Maximum force fiti $(1$ sec or less, Ni$)\}$ & $\backslash$multicolumn$\{3\}\{|$c$|\}\{98\}\backslash \backslash$

$\backslash$hline $\backslash$multicolumn$\{2\}\{|$l$|\}\{$Maximum allowable moment of inertia $($ kgm $)\}$ & $\backslash$multicolumn$\{3\}\{|$c$|\}\{0\mathrm{.}1($with $5-$kg weight$)\}\backslash \backslash$

$\backslash$hline $\backslash$multicolumn$\{2\}\{|$l$|\}\{$Wring $($in$-$arm integrated$)\}$ & $\backslash$multicolumn$\{3\}\{|$c$|\}\{19$ lines $($max$.1$ A per line$)\}\backslash \backslash$

$\backslash$hline $\backslash$multicolumn$\{2\}\{|$l$|\}\{$Ait piping $($in$-$arm integrated$)\}$ & $\backslash$multicolumn$\{3\}\{|$c$|\}\{4$ ystems $\backslash ((04\backslash$times $2,06\backslash$times $2)\backslash )\}\backslash \backslash$

$\backslash$hline $\backslash$multicolumn$\{2\}\{|$l$|\}\{$Protection class$\}$ & $\backslash$multicolumn$\{3\}\{|$l$|\}\{\backslash$begin$\{$tabular$\}\{$l$\}$

Standart P$50\backslash \backslash$

Options: P$40/65,$ IP$65($dust$-$ and mistsroof$),$ deanroom dass $\backslash (10(0\mathrm{.}1\backslash$mu $\backslash$mathrm$\{$~m$\})^\{2\}\backslash )$

$\backslash$end$\{$tabular$\}\}\backslash \backslash$

$\backslash$hline $\backslash$multicolumn$\{2\}\{|$l$|\}\{$Ceiling$-$mount$\}$ & $*$ & $\backslash (\backslash$checkmark $\backslash )$ & $\backslash (\backslash$checkmark $\backslash )\backslash \backslash$

$\backslash$hline $\backslash$multicolumn$\{2\}\{|$l$|\}\{$UL spedifications $\backslash (\{\}^\{2\}\backslash )\}$ & $\backslash$multicolumn$\{3\}\{|$c$|\}\{\backslash (\backslash$checkmark $\backslash )\}\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$