From d89036644494986ef904ff7a1c1915d476a8d44e Mon Sep 17 00:00:00 2001
From: Fabian Reister <fabian.reister@kit.edu>
Date: Wed, 8 Mar 2023 21:52:33 +0100
Subject: [PATCH] minor

---
 python/four_bar_mechanism/equations.ipynb | 123 ++++++----------------
 1 file changed, 32 insertions(+), 91 deletions(-)

diff --git a/python/four_bar_mechanism/equations.ipynb b/python/four_bar_mechanism/equations.ipynb
index 377d7f74c..5cdd1e7a2 100644
--- a/python/four_bar_mechanism/equations.ipynb
+++ b/python/four_bar_mechanism/equations.ipynb
@@ -16,7 +16,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 12,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -28,7 +28,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 13,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -41,7 +41,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 14,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -55,7 +55,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 15,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -73,58 +73,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 16,
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/latex": [
-       "$\\displaystyle \\left[ - i \\log{\\left(\\frac{k_{2} e^{2 i \\psi} + k_{2} - 2 k_{3} e^{i \\psi} - \\sqrt{- 4 k_{1}^{2} e^{2 i \\psi} + 4 k_{1} e^{3 i \\psi} + 4 k_{1} e^{i \\psi} + k_{2}^{2} e^{4 i \\psi} + 2 k_{2}^{2} e^{2 i \\psi} + k_{2}^{2} - 4 k_{2} k_{3} e^{3 i \\psi} - 4 k_{2} k_{3} e^{i \\psi} + 4 k_{3}^{2} e^{2 i \\psi} - 4 e^{2 i \\psi}}}{2 \\left(k_{1} e^{i \\psi} - 1\\right)} \\right)}, \\  - i \\log{\\left(\\frac{k_{2} e^{2 i \\psi} + k_{2} - 2 k_{3} e^{i \\psi} + \\sqrt{- 4 k_{1}^{2} e^{2 i \\psi} + 4 k_{1} e^{3 i \\psi} + 4 k_{1} e^{i \\psi} + k_{2}^{2} e^{4 i \\psi} + 2 k_{2}^{2} e^{2 i \\psi} + k_{2}^{2} - 4 k_{2} k_{3} e^{3 i \\psi} - 4 k_{2} k_{3} e^{i \\psi} + 4 k_{3}^{2} e^{2 i \\psi} - 4 e^{2 i \\psi}}}{2 \\left(k_{1} e^{i \\psi} - 1\\right)} \\right)}\\right]$"
-      ],
-      "text/plain": [
-       "⎡      ⎛                                ______________________________________\n",
-       "⎢      ⎜    2⋅ⅈ⋅ψ              ⅈ⋅ψ     ╱       2  2⋅ⅈ⋅ψ         3⋅ⅈ⋅ψ         \n",
-       "⎢      ⎜k₂⋅ℯ      + k₂ - 2⋅k₃⋅ℯ    - ╲╱  - 4⋅k₁ ⋅ℯ      + 4⋅k₁⋅ℯ      + 4⋅k₁⋅ℯ\n",
-       "⎢-ⅈ⋅log⎜──────────────────────────────────────────────────────────────────────\n",
-       "⎢      ⎜                                                                      \n",
-       "⎣      ⎝                                                                      \n",
-       "\n",
-       "______________________________________________________________________________\n",
-       "ⅈ⋅ψ     2  4⋅ⅈ⋅ψ       2  2⋅ⅈ⋅ψ     2            3⋅ⅈ⋅ψ            ⅈ⋅ψ       2 \n",
-       "    + k₂ ⋅ℯ      + 2⋅k₂ ⋅ℯ      + k₂  - 4⋅k₂⋅k₃⋅ℯ      - 4⋅k₂⋅k₃⋅ℯ    + 4⋅k₃ ⋅\n",
-       "──────────────────────────────────────────────────────────────────────────────\n",
-       "       ⎛    ⅈ⋅ψ    ⎞                                                          \n",
-       "     2⋅⎝k₁⋅ℯ    - 1⎠                                                          \n",
-       "\n",
-       "__________________⎞        ⎛                                __________________\n",
-       " 2⋅ⅈ⋅ψ      2⋅ⅈ⋅ψ ⎟        ⎜    2⋅ⅈ⋅ψ              ⅈ⋅ψ     ╱       2  2⋅ⅈ⋅ψ   \n",
-       "ℯ      - 4⋅ℯ      ⎟        ⎜k₂⋅ℯ      + k₂ - 2⋅k₃⋅ℯ    + ╲╱  - 4⋅k₁ ⋅ℯ      + \n",
-       "──────────────────⎟, -ⅈ⋅log⎜──────────────────────────────────────────────────\n",
-       "                  ⎟        ⎜                                                  \n",
-       "                  ⎠        ⎝                                                  \n",
-       "\n",
-       "______________________________________________________________________________\n",
-       "      3⋅ⅈ⋅ψ         ⅈ⋅ψ     2  4⋅ⅈ⋅ψ       2  2⋅ⅈ⋅ψ     2            3⋅ⅈ⋅ψ    \n",
-       "4⋅k₁⋅ℯ      + 4⋅k₁⋅ℯ    + k₂ ⋅ℯ      + 2⋅k₂ ⋅ℯ      + k₂  - 4⋅k₂⋅k₃⋅ℯ      - 4\n",
-       "──────────────────────────────────────────────────────────────────────────────\n",
-       "                           ⎛    ⅈ⋅ψ    ⎞                                      \n",
-       "                         2⋅⎝k₁⋅ℯ    - 1⎠                                      \n",
-       "\n",
-       "______________________________________⎞⎤\n",
-       "        ⅈ⋅ψ       2  2⋅ⅈ⋅ψ      2⋅ⅈ⋅ψ ⎟⎥\n",
-       "⋅k₂⋅k₃⋅ℯ    + 4⋅k₃ ⋅ℯ      - 4⋅ℯ      ⎟⎥\n",
-       "──────────────────────────────────────⎟⎥\n",
-       "                                      ⎟⎥\n",
-       "                                      ⎠⎦"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
-    "from sympy import Eq, solve\n",
+    "from sympy import Eq, solve, Function\n",
     "\n",
     "#  k1 * cos(theta) - k2 * cos(psi) + k3 = cos(psi - theta)\n",
     "#  k1 * cos(theta) - k2 * cos(0) + k3 = cos(0 - theta)\n",
@@ -134,7 +87,7 @@
     "#   (k3 - k2)/(1-k1) =  cos(theta)\n",
     "# theta = arccos( (k3 - k2) / (1-k1) )\n",
     "\n",
-    "solve(eqn, theta)\n"
+    "# solve(eqn, theta)\n"
    ]
   },
   {
@@ -152,21 +105,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 17,
    "metadata": {},
-   "outputs": [
-    {
-     "ename": "NameError",
-     "evalue": "name 'Function' is not defined",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
-      "\u001b[0;32m<ipython-input-8-b6bfc7ab0d40>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     10\u001b[0m \u001b[0mD\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msqrt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mB\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mB\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m4\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mA\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mC\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 12\u001b[0;31m \u001b[0mD_fn\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mFunction\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"D\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtheta\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     13\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     14\u001b[0m \u001b[0;31m# ankle\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;31mNameError\u001b[0m: name 'Function' is not defined"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "\n",
     "# some helpers\n",
@@ -193,7 +134,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 18,
    "metadata": {},
    "outputs": [
     {
@@ -209,7 +150,7 @@
        "      ⎝k₁⋅cos(θ) + k₂ + k₃ + cos(θ)⎠"
       ]
      },
-     "execution_count": 227,
+     "execution_count": 18,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -228,7 +169,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 19,
    "metadata": {},
    "outputs": [
     {
@@ -245,7 +186,7 @@
        "╲╱  - k₁ ⋅cos (θ) - 2⋅k₁⋅k₃⋅cos(θ) + k₂  + 2⋅k₂⋅cos(θ) - k₃  + 1 "
       ]
      },
-     "execution_count": 228,
+     "execution_count": 19,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -262,7 +203,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 20,
    "metadata": {},
    "outputs": [
     {
@@ -286,7 +227,7 @@
        "              "
       ]
      },
-     "execution_count": 229,
+     "execution_count": 20,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -307,7 +248,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 21,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -327,7 +268,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 22,
    "metadata": {},
    "outputs": [
     {
@@ -339,7 +280,7 @@
        "knee_base"
       ]
      },
-     "execution_count": 231,
+     "execution_count": 22,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -368,7 +309,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 23,
    "metadata": {},
    "outputs": [
     {
@@ -380,7 +321,7 @@
        "knee"
       ]
      },
-     "execution_count": 232,
+     "execution_count": 23,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -404,7 +345,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 24,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -420,7 +361,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 25,
    "metadata": {},
    "outputs": [
     {
@@ -442,7 +383,7 @@
        "                       ⎦"
       ]
      },
-     "execution_count": 267,
+     "execution_count": 25,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -478,7 +419,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 26,
    "metadata": {},
    "outputs": [
     {
@@ -508,7 +449,7 @@
        "               ⎦"
       ]
      },
-     "execution_count": 240,
+     "execution_count": 26,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -525,7 +466,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 27,
    "metadata": {},
    "outputs": [
     {
@@ -541,7 +482,7 @@
        "⎝⎣       0                 0          -shank⎦⎠        "
       ]
      },
-     "execution_count": 266,
+     "execution_count": 27,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -610,7 +551,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 28,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -627,7 +568,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "simox_control",
+   "display_name": "armarx",
    "language": "python",
    "name": "python3"
   },
@@ -641,12 +582,12 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.13"
+   "version": "3.7.11"
   },
   "orig_nbformat": 4,
   "vscode": {
    "interpreter": {
-    "hash": "e4599465d50e71b5ac4fe67b3a4b0cd1869600672e1938bc9720f881263763f9"
+    "hash": "edf8927144584185110aeeacb4ee22a221f99c19957d335f96fa1b4f8f5621f4"
    }
   }
  },
-- 
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