jbradberry/KeplerGears.ipynb

## KeplerGears.ipynb
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  {
   "cell_type": "markdown",
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   "source": [
    "# Kepler's Gears\n",
    "\n",
    "The goal of this project is to construct non-circular gear geometries that result in output that obeys Kepler's Law orbits.\n",
    "\n",
    "The sources for this notebook include Noncircular Gears: Design and Generation by Litvin and Fuentes-Aznar, and the Wikipedia page for Kepler's Laws of Planetary Motion."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a2be7b4-492a-49b6-8d97-d231f0126a9c",
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   "source": [
    "## Kepler's 2nd Law\n",
    "\n",
    "A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.\n",
    "\n",
    "$$ \\frac{dA}{dt} = \\frac{r^2}{2} \\frac{d \\theta}{dt} = \\frac{abn}{2} = \\frac{\\pi ab}{T} = \\mbox{constant} $$\n",
    "\n",
    "Where\n",
    "\n",
    "- $A$ : area swept out by a line from the sun to the planet\n",
    "- $t$ : time\n",
    "- $r$ : distance of the planet from the sun\n",
    "- $\\theta$ : angle of the planet's location in orbit compared to its location at perihelion\n",
    "- $a$ : length of the semi-major axis of the ellipse of the planet's orbit\n",
    "- $b$ : length of the semi-minor axis of the ellipse of the planet's orbit\n",
    "- $T$ : period of the planet's orbit\n",
    "\n",
    "We shall rename $\\theta$ to $\\phi_2$ to begin to change into the format that we need to design the gearing:\n",
    "\n",
    "$$ \\frac{d \\theta}{dt} = \\frac{d \\phi_2}{dt} = \\frac{2\\pi ab}{T} \\frac{1}{r^2} $$\n",
    "\n",
    "We also want to convert time $t$ into the angle of the input gear, $\\phi_1$, so:\n",
    "\n",
    "$$ \\frac{dt}{d\\phi_1} = \\frac{T}{2\\pi} $$\n",
    "\n",
    "$$ \\frac{d\\phi_2}{d\\phi_1} = \\frac{d \\phi_2}{dt} \\cdot \\frac{dt}{d\\phi_1} = \\frac{\\cancel{2\\pi} ab}{\\cancel{T}} \\frac{1}{r^2} \\cdot \\frac{\\cancel{T}}{\\cancel{2\\pi}} = \\frac{ab}{r^2} $$\n",
    "\n",
    "$$ \\frac{d\\phi_1}{d\\phi_2} = \\frac{r^2}{ab} $$"
   ]
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  {
   "cell_type": "markdown",
   "id": "99a6afaf-3372-47ce-b489-8cb6fa34dbf1",
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   "source": [
    "## Non-Circular Gears\n",
    "\n",
    "Given the derivative function $m_{12}(\\phi_1) = \\frac{d\\phi_1}{d\\phi_2}$,\n",
    "\n",
    "$$ m_{12}(\\phi_1) = \\frac{d\\phi_1}{d\\phi_2} = \\frac{r_2}{r_1} = \\frac{E - r_1}{r_1} $$\n",
    "\n",
    "where,\n",
    "\n",
    "- $\\phi_1$: angle of rotation of the input gear\n",
    "- $\\phi_2$: angle of rotation of the output gear\n",
    "- $r_1$: parametric function representing the centroid (idealized perimeter before adding teeth) of the input gear\n",
    "- $r_2$: parametric function of the centroid of the output gear\n",
    "- $E$: fixed distance between the pivot points of the input and output gears\n",
    "\n",
    "We can find the equations for the gear centrodes:\n",
    "\n",
    "$$ r_1(\\phi_1) = \\frac{E}{1 + m_{12}(\\phi_1)} $$\n",
    "\n",
    "$$ r_2(\\phi_1) = E \\frac{m_{12}(\\phi_1)}{1 + m_{12}(\\phi_1)} $$\n",
    "\n",
    "And also the function of the output angle with respect to the input gear's angle:\n",
    "\n",
    "$$ \\phi_2(\\phi_1) = \\int^{\\phi_1}_0 \\frac{d\\phi_1}{m_{12}(\\phi_1)} $$"
   ]
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  {
   "cell_type": "markdown",
   "id": "a45b0fba-7480-4013-88d0-1ebde5c71652",
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   "source": [
    "## Kepler position as a function of time\n",
    "\n",
    "### Mean motion\n",
    "\n",
    "$$ n = \\frac{2\\pi}{P} $$\n",
    "\n",
    "We don't actually care about orbital period, everything needs to scale to $P = 1\\mbox{ year}$.\n",
    "\n",
    "### Mean anomaly, $M$\n",
    "\n",
    "$$ M = nt = 2\\pi t $$\n",
    "\n",
    "### Eccentric anomaly, $E$\n",
    "\n",
    "$$ M = E - \\varepsilon \\sin E $$\n",
    "\n",
    "$$ E = \\mbox{???} $$\n",
    "\n",
    "Unfortunately, $E$ is not solvable analytically and so has to be done numerically.\n",
    "\n",
    "### True anomaly, $\\theta$\n",
    "\n",
    "$$ \\cos E = \\frac{\\varepsilon + \\cos \\theta}{1 + \\varepsilon \\cos \\theta} $$\n",
    "\n",
    "### Distance, $r$\n",
    "\n",
    "$$ r(1 + \\varepsilon \\cos \\theta) = a(1 - \\varepsilon^2) $$\n",
    "\n",
    "$$ r = a(1 - \\varepsilon \\cos E) $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0706cb37-2d21-4fc9-9a96-fa63925c062c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3c6cb45b-167d-4e93-bce9-e5899e7c0086",
   "metadata": {},
   "outputs": [],
   "source": [
    "# orbit eccentricity\n",
    "epsilon = 0.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e69edaa8-21e2-4090-84d1-b8b6a2b23f8f",
   "metadata": {},
   "outputs": [],
   "source": [
    "t = pd.Series(np.arange(0, 1000)) / 1000."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c8cb7a84-3b98-4666-9b7b-c9b4181a516b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# note: M = \\phi_1\n",
    "df = pd.DataFrame({'M': (2 * np.pi * t).array}, index=t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "9d5785a8-e1ab-4d79-b5ec-72db45c18eae",
   "metadata": {},
   "outputs": [],
   "source": [
    "def fixedpoint(e, M, n):\n",
    "    # Numerically solves for the Eccentric Anomaly using a fixed-point iteration method.\n",
    "    # See: https://en.wikipedia.org/wiki/Kepler%27s_equation#Fixed-point_iteration\n",
    "    En = M\n",
    "    for _ in range(n):\n",
    "        En = M + e * np.sin(En)\n",
    "    return En"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "df7a15a4-6fa6-4477-aede-3db2ca56306c",
   "metadata": {},
   "outputs": [],
   "source": [
    "df['E'] = df['M'].map(lambda x: fixedpoint(epsilon, x, 100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "453905b7-019f-4d7b-b69b-e77230195e9d",
   "metadata": {},
   "outputs": [],
   "source": [
    "df['r'] = 1 - epsilon * np.cos(df['E'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "8b53ff59-b1f0-4712-8d75-757047c3d970",
   "metadata": {},
   "outputs": [],
   "source": [
    "df['m12'] = np.pow(df['r'], 2) / np.sqrt(1 - np.pow(epsilon, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "66dbd8d9-fea3-404b-bae6-2f05d562b8fb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# E = 100 mm\n",
    "df['r1'] = 100 / (1 + df['m12'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "9fc517b6-2d7a-4583-927e-70bb53f5386e",
   "metadata": {},
   "outputs": [],
   "source": [
    "df['r2'] = 100 * df['m12'] / (1 + df['m12'])"
   ]
  },
  {
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   "execution_count": 11,
   "id": "d24766f2-5b37-4acf-a359-06ca974f3e4a",
   "metadata": {},
   "outputs": [
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       "              M         E         r       m12         r1        r2\n",
       "0.000  0.000000  0.000000  0.200000  0.066667  93.750000  6.250000\n",
       "0.001  0.006283  0.031395  0.200394  0.066930  93.726883  6.273117\n",
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       "0.004  0.025133  0.124382  0.206180  0.070851  93.383711  6.616289\n",
       "...         ...       ...       ...       ...        ...       ...\n",
       "0.995  6.251769  6.128567  0.209544  0.073181  93.180933  6.819067\n",
       "0.996  6.258053  6.158803  0.206180  0.070851  93.383711  6.616289\n",
       "0.997  6.264336  6.189486  0.203509  0.069027  93.543032  6.456968\n",
       "0.998  6.270619  6.220517  0.201570  0.067718  93.657715  6.342285\n",
       "0.999  6.276902  6.251790  0.200394  0.066930  93.726883  6.273117\n",
       "\n",
       "[1000 rows x 6 columns]"
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     "metadata": {},
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    "df"
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   "cell_type": "code",
   "execution_count": 12,
   "id": "91e07dd2-4321-4f25-bab7-0feb279eba03",
   "metadata": {},
   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>M</th>\n",
       "      <th>E</th>\n",
       "      <th>r</th>\n",
       "      <th>m12</th>\n",
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       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
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       "      <th>mean</th>\n",
       "      <td>3.138451</td>\n",
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       "      <td>68.816397</td>\n",
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       "      <th>std</th>\n",
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       "      <td>63.039670</td>\n",
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       "      <td>3.139847</td>\n",
       "      <td>1.478484</td>\n",
       "      <td>3.643191</td>\n",
       "      <td>21.536913</td>\n",
       "      <td>78.463087</td>\n",
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       "      <th>75%</th>\n",
       "      <td>4.707677</td>\n",
       "      <td>4.068070</td>\n",
       "      <td>1.722880</td>\n",
       "      <td>4.947192</td>\n",
       "      <td>36.960330</td>\n",
       "      <td>83.185342</td>\n",
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       "      <th>max</th>\n",
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       "      <td>6.251790</td>\n",
       "      <td>1.800000</td>\n",
       "      <td>5.400000</td>\n",
       "      <td>93.750000</td>\n",
       "      <td>84.375000</td>\n",
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      ],
      "text/plain": [
       "                 M            E            r          m12           r1  \\\n",
       "count  1000.000000  1000.000000  1000.000000  1000.000000  1000.000000   \n",
       "mean      3.138451     3.138451     1.320000     3.266667    31.183603   \n",
       "std       1.814706     1.300609     0.466710     1.769752    20.764797   \n",
       "min       0.000000     0.000000     0.200000     0.066667    15.625000   \n",
       "25%       1.569226     2.210867     1.011614     1.705604    16.814658   \n",
       "50%       3.138451     3.139847     1.478484     3.643191    21.536913   \n",
       "75%       4.707677     4.068070     1.722880     4.947192    36.960330   \n",
       "max       6.276902     6.251790     1.800000     5.400000    93.750000   \n",
       "\n",
       "                r2  \n",
       "count  1000.000000  \n",
       "mean     68.816397  \n",
       "std      20.764797  \n",
       "min       6.250000  \n",
       "25%      63.039670  \n",
       "50%      78.463087  \n",
       "75%      83.185342  \n",
       "max      84.375000  "
      ]
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     "execution_count": 12,
     "metadata": {},
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    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "2631031c-0e18-48b7-bf79-0b172c2c7807",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "850d5cb9-f57f-4a73-9e94-76cd5a1b78b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.polar(df['M'].values, df['r1'].values)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "814f8bf8-db83-4800-bceb-d43690b4fb4c",
   "metadata": {},
   "outputs": [],
   "source": [
    "df['phi2'] = (2 * np.pi / (1000 * df['m12'])).cumsum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "df1e9983-b9f5-4712-90e6-d93da2d97602",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>M</th>\n",
       "      <th>E</th>\n",
       "      <th>r</th>\n",
       "      <th>m12</th>\n",
       "      <th>r1</th>\n",
       "      <th>r2</th>\n",
       "      <th>phi2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.000</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.200000</td>\n",
       "      <td>0.066667</td>\n",
       "      <td>93.750000</td>\n",
       "      <td>6.250000</td>\n",
       "      <td>0.094248</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.001</th>\n",
       "      <td>0.006283</td>\n",
       "      <td>0.031395</td>\n",
       "      <td>0.200394</td>\n",
       "      <td>0.066930</td>\n",
       "      <td>93.726883</td>\n",
       "      <td>6.273117</td>\n",
       "      <td>0.188125</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.002</th>\n",
       "      <td>0.012566</td>\n",
       "      <td>0.062668</td>\n",
       "      <td>0.201570</td>\n",
       "      <td>0.067718</td>\n",
       "      <td>93.657715</td>\n",
       "      <td>6.342285</td>\n",
       "      <td>0.280910</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.003</th>\n",
       "      <td>0.018850</td>\n",
       "      <td>0.093700</td>\n",
       "      <td>0.203509</td>\n",
       "      <td>0.069027</td>\n",
       "      <td>93.543032</td>\n",
       "      <td>6.456968</td>\n",
       "      <td>0.371935</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.004</th>\n",
       "      <td>0.025133</td>\n",
       "      <td>0.124382</td>\n",
       "      <td>0.206180</td>\n",
       "      <td>0.070851</td>\n",
       "      <td>93.383711</td>\n",
       "      <td>6.616289</td>\n",
       "      <td>0.460618</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.995</th>\n",
       "      <td>6.251769</td>\n",
       "      <td>6.128567</td>\n",
       "      <td>0.209544</td>\n",
       "      <td>0.073181</td>\n",
       "      <td>93.180933</td>\n",
       "      <td>6.819067</td>\n",
       "      <td>5.916815</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.996</th>\n",
       "      <td>6.258053</td>\n",
       "      <td>6.158803</td>\n",
       "      <td>0.206180</td>\n",
       "      <td>0.070851</td>\n",
       "      <td>93.383711</td>\n",
       "      <td>6.616289</td>\n",
       "      <td>6.005498</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.997</th>\n",
       "      <td>6.264336</td>\n",
       "      <td>6.189486</td>\n",
       "      <td>0.203509</td>\n",
       "      <td>0.069027</td>\n",
       "      <td>93.543032</td>\n",
       "      <td>6.456968</td>\n",
       "      <td>6.096523</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.998</th>\n",
       "      <td>6.270619</td>\n",
       "      <td>6.220517</td>\n",
       "      <td>0.201570</td>\n",
       "      <td>0.067718</td>\n",
       "      <td>93.657715</td>\n",
       "      <td>6.342285</td>\n",
       "      <td>6.189308</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.999</th>\n",
       "      <td>6.276902</td>\n",
       "      <td>6.251790</td>\n",
       "      <td>0.200394</td>\n",
       "      <td>0.066930</td>\n",
       "      <td>93.726883</td>\n",
       "      <td>6.273117</td>\n",
       "      <td>6.283185</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1000 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "              M         E         r       m12         r1        r2      phi2\n",
       "0.000  0.000000  0.000000  0.200000  0.066667  93.750000  6.250000  0.094248\n",
       "0.001  0.006283  0.031395  0.200394  0.066930  93.726883  6.273117  0.188125\n",
       "0.002  0.012566  0.062668  0.201570  0.067718  93.657715  6.342285  0.280910\n",
       "0.003  0.018850  0.093700  0.203509  0.069027  93.543032  6.456968  0.371935\n",
       "0.004  0.025133  0.124382  0.206180  0.070851  93.383711  6.616289  0.460618\n",
       "...         ...       ...       ...       ...        ...       ...       ...\n",
       "0.995  6.251769  6.128567  0.209544  0.073181  93.180933  6.819067  5.916815\n",
       "0.996  6.258053  6.158803  0.206180  0.070851  93.383711  6.616289  6.005498\n",
       "0.997  6.264336  6.189486  0.203509  0.069027  93.543032  6.456968  6.096523\n",
       "0.998  6.270619  6.220517  0.201570  0.067718  93.657715  6.342285  6.189308\n",
       "0.999  6.276902  6.251790  0.200394  0.066930  93.726883  6.273117  6.283185\n",
       "\n",
       "[1000 rows x 7 columns]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "71b4b3e0-e541-4df1-ae7d-4ea1eb261a8f",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.polar(df['phi2'].values, df['r2'].values)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "0a869e9d-8c7b-40bc-b643-25182a0065c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x1</th>\n",
       "      <th>y1</th>\n",
       "      <th>x2</th>\n",
       "      <th>y2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.000</th>\n",
       "      <td>93.750000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>93.777738</td>\n",
       "      <td>5.881770e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.001</th>\n",
       "      <td>93.725033</td>\n",
       "      <td>0.588900</td>\n",
       "      <td>93.837562</td>\n",
       "      <td>1.173182e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.002</th>\n",
       "      <td>93.650320</td>\n",
       "      <td>1.176907</td>\n",
       "      <td>93.906310</td>\n",
       "      <td>1.758273e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.003</th>\n",
       "      <td>93.526415</td>\n",
       "      <td>1.763140</td>\n",
       "      <td>93.984523</td>\n",
       "      <td>2.346586e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.004</th>\n",
       "      <td>93.354219</td>\n",
       "      <td>2.346742</td>\n",
       "      <td>94.073273</td>\n",
       "      <td>2.940951e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.995</th>\n",
       "      <td>93.134954</td>\n",
       "      <td>-2.926884</td>\n",
       "      <td>93.633488</td>\n",
       "      <td>-2.442785e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.996</th>\n",
       "      <td>93.354219</td>\n",
       "      <td>-2.346742</td>\n",
       "      <td>93.637168</td>\n",
       "      <td>-1.813741e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.997</th>\n",
       "      <td>93.526415</td>\n",
       "      <td>-1.763140</td>\n",
       "      <td>93.655196</td>\n",
       "      <td>-1.198285e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.998</th>\n",
       "      <td>93.650320</td>\n",
       "      <td>-1.176907</td>\n",
       "      <td>93.685641</td>\n",
       "      <td>-5.945226e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.999</th>\n",
       "      <td>93.725033</td>\n",
       "      <td>-0.588900</td>\n",
       "      <td>93.726883</td>\n",
       "      <td>5.716356e-11</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1000 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "              x1        y1         x2            y2\n",
       "0.000  93.750000  0.000000  93.777738  5.881770e-01\n",
       "0.001  93.725033  0.588900  93.837562  1.173182e+00\n",
       "0.002  93.650320  1.176907  93.906310  1.758273e+00\n",
       "0.003  93.526415  1.763140  93.984523  2.346586e+00\n",
       "0.004  93.354219  2.346742  94.073273  2.940951e+00\n",
       "...          ...       ...        ...           ...\n",
       "0.995  93.134954 -2.926884  93.633488 -2.442785e+00\n",
       "0.996  93.354219 -2.346742  93.637168 -1.813741e+00\n",
       "0.997  93.526415 -1.763140  93.655196 -1.198285e+00\n",
       "0.998  93.650320 -1.176907  93.685641 -5.945226e-01\n",
       "0.999  93.725033 -0.588900  93.726883  5.716356e-11\n",
       "\n",
       "[1000 rows x 4 columns]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2 = pd.DataFrame({'x1': df['r1'] * np.cos(df['M']), 'y1': df['r1'] * np.sin(df['M']),\n",
    "                    'x2': 100 - df['r2'] * np.cos(df['phi2']), 'y2': df['r2'] * np.sin(df['phi2'])}, index=df.index)\n",
    "df2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "b891ee78-d705-4c77-9dd0-ecd62674fdec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x1', ylabel='y1'>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = df2.plot.scatter(x='x1', y='y1', marker='.')\n",
    "ax.set_aspect('equal')\n",
    "ax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "4d78e9a5-e327-48c6-a362-16767cf72da9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x2', ylabel='y2'>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = df2.plot.scatter(x='x2', y='y2', marker='.')\n",
    "ax.set_aspect('equal')\n",
    "ax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "69c412f7-5cd4-400f-8a21-d99cdc95204d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x1</th>\n",
       "      <th>y1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>93.725033</td>\n",
       "      <td>-0.588900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>93.750000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>93.725033</td>\n",
       "      <td>0.588900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>93.650320</td>\n",
       "      <td>1.176907</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>93.526415</td>\n",
       "      <td>1.763140</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>996</th>\n",
       "      <td>93.134954</td>\n",
       "      <td>-2.926884</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>997</th>\n",
       "      <td>93.354219</td>\n",
       "      <td>-2.346742</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>998</th>\n",
       "      <td>93.526415</td>\n",
       "      <td>-1.763140</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999</th>\n",
       "      <td>93.650320</td>\n",
       "      <td>-1.176907</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1000</th>\n",
       "      <td>93.725033</td>\n",
       "      <td>-0.588900</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1001 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             x1        y1\n",
       "0     93.725033 -0.588900\n",
       "1     93.750000  0.000000\n",
       "2     93.725033  0.588900\n",
       "3     93.650320  1.176907\n",
       "4     93.526415  1.763140\n",
       "...         ...       ...\n",
       "996   93.134954 -2.926884\n",
       "997   93.354219 -2.346742\n",
       "998   93.526415 -1.763140\n",
       "999   93.650320 -1.176907\n",
       "1000  93.725033 -0.588900\n",
       "\n",
       "[1001 rows x 2 columns]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gear1 = pd.concat([df2[['x1', 'y1']].iloc[-1:], df2[['x1', 'y1']]]).reset_index(drop=True)\n",
    "gear1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "7c5e3f09-519c-4edc-8b1a-33950bfada8c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(262.0373286141903)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(np.linalg.norm(gear1.diff().drop(0), axis=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "5812f0f3-4d51-41bf-bcd9-207f2927e395",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x2</th>\n",
       "      <th>y2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>93.726883</td>\n",
       "      <td>5.716356e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>93.777738</td>\n",
       "      <td>5.881770e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>93.837562</td>\n",
       "      <td>1.173182e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>93.906310</td>\n",
       "      <td>1.758273e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>93.984523</td>\n",
       "      <td>2.346586e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>996</th>\n",
       "      <td>93.633488</td>\n",
       "      <td>-2.442785e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>997</th>\n",
       "      <td>93.637168</td>\n",
       "      <td>-1.813741e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>998</th>\n",
       "      <td>93.655196</td>\n",
       "      <td>-1.198285e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999</th>\n",
       "      <td>93.685641</td>\n",
       "      <td>-5.945226e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1000</th>\n",
       "      <td>93.726883</td>\n",
       "      <td>5.716356e-11</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1001 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             x2            y2\n",
       "0     93.726883  5.716356e-11\n",
       "1     93.777738  5.881770e-01\n",
       "2     93.837562  1.173182e+00\n",
       "3     93.906310  1.758273e+00\n",
       "4     93.984523  2.346586e+00\n",
       "...         ...           ...\n",
       "996   93.633488 -2.442785e+00\n",
       "997   93.637168 -1.813741e+00\n",
       "998   93.655196 -1.198285e+00\n",
       "999   93.685641 -5.945226e-01\n",
       "1000  93.726883  5.716356e-11\n",
       "\n",
       "[1001 rows x 2 columns]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gear2 = pd.concat([df2[['x2', 'y2']].iloc[-1:], df2[['x2', 'y2']]]).reset_index(drop=True)\n",
    "gear2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "1c4c693e-85c6-4474-9b73-191fed5c44ef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(262.0470417027336)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(np.linalg.norm(gear2.diff().drop(0), axis=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "257a18f1-38bf-4edd-ab72-ae6854fadf6d",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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