$\backslash (7\backslash$cdot $5\backslash )$ It is desired to have the second joint of a $6-$axis robot go from an initial angle of $\backslash (0^\{\backslash$circ$\}\backslash )$ to a final angle of $\backslash (90^\{\backslash$circ$\}\backslash )$ in $1$ second. Calculate the coefficients for a third$-$order polynomial joint$-$space trajectory. Determine the joint angles, velocities, and accelerations at $\backslash (0\mathrm{.}1,0\mathrm{.}2,0\mathrm{.}5\backslash ),$ and $0\mathrm{.}9$ seconds. It is assumed that the motion starts at $\backslash (5^\{\backslash$circ$\}/\backslash$mathrm$\{$sec$\}\backslash )$ and stop. at the end of the motion.

$7\mathrm{.}6$ Repeat Problem $7\mathrm{.}5,$ but plot the position, velocity, and acceleration versus time.

$7-11$ A $2-$DOF planar robot is to follow a straight line in Cartesian space between the start point $\backslash ((2,6)\backslash )$ and the end point $\backslash ((12,3)\backslash )$ of the motion segment. Find the joint variables for the robot if the path is divided into $10$ sections. Each link is $9$ inches long.