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- Consider the same motion as in HW-04. Draw figures from previous homework to the pdf report.
- Find the axis of motion $a_0$ for ($R$,$\vec{o}_{\beta'} = [0; 0; 0]$) and $a_1$ for ($R$,$\vec{o}_{\beta'}=[1; 1; 1]$). (By $\vec{o}_{\beta'}$ we understand $\overrightarrow{O'O}_{\beta'}$).
- Draw the coordinate systems and motion axes.
- Find and draw the rotation axis $r$. What is the relationship beween $r$, $a_0$, and $a_1$?
- Find the generators of the plane $\sigma$ which is perpendicular to the rotation axis $r$ and draw them into the figure.
- Consider next only motion defined by ($R$, $\vec{o}_{\beta'}=[1; 1; 1]$) and the corresponding $a_1$.
- What is the relationship between the generators of $\sigma$ and the matrix $R-I$?
- Find the point $P$ where the motion axis $a_1$ intersects the plane $\sigma$, and draw it.
- Find and draw the point $P'$, which is obtained by rotating $P$ by rotation $R$.
- Find and draw the point $P''$, which is obtained by translating $P'$ along $\vec{o}'_{\beta}$.
- What is the relationship between $P$, $P'$, $P''$ and the axis $a_1$?
- What is the relationship between the rotation axis $r$ and the motion axis $a_1$ when:
- $R = I$
- $\vec{o}'_{\beta} = \vec{0}$
- $\vec{o}'_{\beta}$ is an eigenvector of $R$

Create an empty dictionary in Python:

solution = {}

The keys for this dictionary will be:

`“a_0_dir”`

(3×1) and`“a_0_point”`

(3×1) containing the description of the motion axis a_0: a_0 = x * a_0_dir + a_0_point.`“a_1_dir”`

(3×1) and`“a_1_point”`

(3×1) containing the description of the motion axis a_1: a_1 = x * a_1_dir + a_1_point.`“sigma1”`

(3×1) and`“sigma2”`

(3×1) containing the generators of the plane $\sigma$.`“p”`

(3×1),`“p_pr”`

(3×1) and`“p_pr_pr”`

(3×1) containing the points $P$, $P'$ and $P''$.

Finally, save `solution`

to `hw05.json`

:

import json with open("hw05.json", "w") as outfile: json.dump(solution, outfile)Upload a zip archive

`hw05.zip`

(via the course ware) containing the following files:
`hw05.py`

- python script used for computation`hw05.pdf`

- report file describing your solution with all the figures and explanatory text. Please mark the discussion of 4, 7, 11, 12 so it is easy to find`hw05.json`

courses/pro/labs/hw05.txt · Last modified: 2021/10/28 16:10 by korotvik