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| Figure 1.14 Numerical Analysis: 2nd Edition |
A Stewart platform consists of six variable length struts supporting a payload. By changing the lengths of these struts, the payload can be moved around, but is subject to certain constraints. For Project 1, we studied a 2-D three strut version of the Stewart platform.
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| Figure 1.14 Numerical Analysis: 2nd Edition |
Given the three strut lengths, finding the position of the platform is called solving the forward kinematics problem. The dependency of the variables can be seen in the Matlab file here. Given L1, L2, L3, x1, x2, y2,γ, p1, p2, and p3, f(θ) plotted over the interval -θ to θ shows how many roots exist. The number of roots is equal to how many positions our 2-D payload can have given our constraints. Using Matlab to visually approximate the roots, we then used bisect.m to discover the roots more precisely.
With MatlabDraw(θ), we used the given parameters of L1, L2, L3,, x1, x2, y2,and γ as well as the strut lengths p1, p2, p3. Given the known roots of -π/4 and π/4, we were able to generate the following two images:
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| a) root = -π/4 | b) root = π/4 |