Chapter 1.5, Problem 1SA

Write a M_ATLAB function file for $f\left(\theta \right)$ . The parameters

$L_1$ ,

$L_2$ ,

$L_3$ ,

$\gamma$ ,

$x_1$ ,

$x_2$ ,

$y_2$ are fixed constant, and the struct lengths

$p_1$ ,

$p_2$ ,

$p_3$ will be known for a given pose. Check Appendix B.5 If you are new to M_ATLAB function files. Here for free are the first and last lines.

To test your code, set the parameters

$L_1=2$ ,

$L_2=L_3=\sqrt{2}$ ,

$\gamma =\pi /2$ , $p_1=p_2=p_3=\sqrt{5}$ from figure 1.15. Then substituting $\theta =-\pi /4$ or $\theta =\pi /4$ , corresponding to figures 1.15 (a, b)m respectively, should make $f\left(\theta \right)=0$ .

Figure 1.15 Two poses of the planar Stewart platform with identical arm lengths.

Each pose corresponds to a solution of (1.38) with strut lengths $p_1=p_2=p_3=\sqrt{5}$ . The shape of the triangle is defined by $L_1=2$ , $L_2=L_3=\sqrt{2}$ , $\gamma =\pi /2$ .