Problem $1$ Trajectory

Derive the trajectory for an end$-$effector located at Frame $\{A\}$ to Frame $\{B\}$ shown

in Fig. $11$ in a $10$ second duration.

$x(s)=(1-s)x_0+s{x}_1,s(t)in[0,1]$

Figure $1$: Reference frames and homogeneous transformations for Frame $\{A\}$ and

Frame $\{B\}.$

a$)$ Determine the quintic polynomial coefficients for $s.$

b$)$ What is the position of the end$-$effector at $7$ seconds?

c$)$ What is the orientation of the end$-$effector at $7$ seconds?