Commented jupytr notebook

inv_kin_testing.ipynb

@@ -1,5 +1,12 @@
 {
  "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Inverse Kinematics Simulation"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 1,
@@ -12,6 +19,13 @@
     "import numpy as np"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Polar coordinate functions"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 2,
@@ -29,9 +43,16 @@
     "    return x, y"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Calculate end-joint values from xyz position"
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 141,
+   "execution_count": 157,
    "metadata": {},
    "outputs": [
     {
@@ -93,9 +114,16 @@
     "print([math.degrees(deg) for deg in get_joints_from_xyz_abs(0.3, 0.3, 0.3)])"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Simulate arm and joint angles"
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 142,
+   "execution_count": 164,
    "metadata": {},
    "outputs": [
     {
@@ -112,7 +140,7 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -123,14 +151,18 @@
    ],
    "source": [
     "def draw_arm(x, y, z):\n",
-    "    #(.422864, .359041, .092124)\n",
+    "\n",
+    "    # Get joint angles\n",
     "    l1, l2, l3 = (.422864, .359041, .092124)\n",
     "    r, theta = cartesian_to_polar(x, y)\n",
-    "    base, shoulder, elbow, wrist = get_joints_from_xyz_rel(x, y, z, limbs=(l1, l2, l3))\n",
+    "    base, shoulder, elbow, wrist = get_joints_from_xyz_rel(x, y, z)\n",
+    "\n",
+    "    # Print angles\n",
     "    print('Target position (x,y,z):', x, y, z)\n",
     "    print('Angles (base, shoulder, elbow, wrist):', [round(math.degrees(i), 4) for i in [base, shoulder, elbow, wrist]])\n",
     "    print('Robot Angles:', [round(math.degrees(i), 4) for i in get_joints_from_xyz_abs(x, y, z)])\n",
     "\n",
+    "    # Calculate each joint's endpoint position\n",
     "    x1, y1 = polar_to_cartesian(l1, shoulder)\n",
     "    x2, y2 = polar_to_cartesian(l2, shoulder-elbow)\n",
     "    x2 += x1\n",
@@ -139,6 +171,7 @@
     "    x3 += x2\n",
     "    y3 += y2\n",
     "\n",
+    "    # Print each joint's endpoint position\n",
     "    print('elbow (x,y):', round(x1,3), round(y1,3))\n",
     "    print('wrist (x,y):', round(x2,3), round(y2,3))\n",
     "    print('tool  (x,y):', round(x3,3), round(y3,3))\n",
@@ -148,20 +181,20 @@
     "    plt.plot([x1, x2], [y1, y2], color='orange', linewidth=7)\n",
     "    plt.plot([x2, x2+l3], [y2, y2], color='red', linewidth=7)\n",
     "\n",
-    "    # angles\n",
+    "    # Display angles\n",
     "    plt.text(0, 0.02, f'{round(math.degrees(shoulder), 2)}°')\n",
     "    plt.text(x1, y1+0.02, f'{round(math.degrees(elbow), 2)}°')\n",
     "    plt.text(x2, y2+0.02, f'{round(math.degrees(wrist), 2)}°')\n",
     "\n",
-    "    # r arrow\n",
+    "    # Display r arrow\n",
     "    plt.annotate(f'', xy=(0, 0), xycoords='data', xytext=(x3, 0), textcoords='data', arrowprops={'arrowstyle': '<->'})\n",
-    "    plt.annotate(f'r={round(r,4)}', xy=(x2/4, 0.01), xycoords='data', xytext=(x2/2, 0), textcoords='offset points')\n",
+    "    plt.annotate(f'r={round(r,4)}', xy=(x2/2, 0.01), xycoords='data', xytext=(x2/2, 0), textcoords='offset points')\n",
     "\n",
-    "    # z arrow\n",
+    "    # Display z arrow\n",
     "    plt.annotate(f'', xy=(x3, 0), xycoords='data', xytext=(x3, y3), textcoords='data', arrowprops={'arrowstyle': '<->'})\n",
     "    plt.annotate(f'z={round(y2,4)}', xy=(x3+0.01, y2/2), xycoords='data', xytext=(x3/2, 0), textcoords='offset points')\n",
     "   \n",
-    "    # Display\n",
+    "    # Display plot\n",
     "    ax = plt.subplot(111)\n",
     "    ax.spines[['right', 'top']].set_visible(False)\n",
     "    plt.axis('equal')\n",
@@ -172,7 +205,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 144,
+   "execution_count": 165,
    "metadata": {},
    "outputs": [
     {
@@ -189,7 +222,7 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "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 truncated
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -211,7 +244,7 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "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 truncated
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -233,7 +266,7 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjQAAAGoCAYAAABRx3+mAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAA9hAAAPYQGoP6dpAABOYklEQVR4nO3de3gU5fn/8fcmkIRjEozkQKMBo6ACiYCkQUDUQKBW4fetFmwVRCoWT7XxBFUJiDWIqNSC0oJUPEL1UrRWAxiFqoQghMhRBApy3HCoJCRIAtn5/RGzuJKQ2WUne/q8rmuusrP3PnvPmJKbeZ6Z22YYhoGIiIhIAAvzdQIiIiIiZ0sFjYiIiAQ8FTQiIiIS8FTQiIiISMBTQSMiIiIBTwWNiIiIBDwVNCIiIhLwVNCIiIhIwFNBIyIiIgFPBY2IiIgEPBU0ElL+85//cN1115GUlITNZmPRokUu7xuGwcSJE0lMTKRFixZkZWWxdetWl5ji4mIGDhxITEwM55xzDmPHjqWiouKM33vrrbdis9lctsGDB7vEFBYWkp6eTkpKCi+99JJXjldEJFSooJGQUllZSVpaGrNmzar3/WnTpvH8888ze/ZsioqKaNWqFdnZ2Rw/fhyAffv2kZWVRWpqKkVFReTn57Nx40ZuvfXWRr978ODB7N+/37m9+eabLu+PGTOGxx57jDfeeIO8vDx279591scrIhIqmvk6AZGmNGTIEIYMGVLve4ZhMGPGDB599FGGDh0KwCuvvEJ8fDyLFi1ixIgRfPDBBzRv3pxZs2YRFlb774HZs2fTvXt3tm3bRmpqaoPfHRkZSUJCQoPvV1ZW0qNHD9q3b09sbCxHjx49iyMVEQktukIj8oMdO3Zgt9vJyspy7ouOjiYjI4PCwkIAqqqqiIiIcBYzAC1atADg888/P+P4y5Yto3379nTu3Jlx48Zx+PBhl/cnTpzIxRdfTHR0ND//+c+55JJLvHVoIiJBTwWNyA/sdjsA8fHxLvvj4+Od71199dXY7Xaefvppqqur+e677xg/fjwA+/fvb3DswYMH88orr1BQUMBTTz3F8uXLGTJkCDU1Nc6YMWPGcPjwYQ4ePMhf//pXbx+eiEhQU0Ej4oZLL72U+fPn88wzz9CyZUsSEhLo2LEj8fHxLldtfmrEiBFcf/31dOvWjWHDhvHBBx/w5ZdfsmzZMpe4Vq1aERsba/FRiIgEHxU0Ij+oW99SWlrqsr+0tNRl7ctvfvMb7HY7e/fu5fDhw0yaNImDBw/SqVMn09/VqVMn4uLi2LZtm3eSFxEJcSpoRH7QsWNHEhISKCgocO4rLy+nqKiIzMzM0+Lj4+Np3bo1CxcuJCoqioEDB5r+rj179nD48GESExO9kruISKhTQSMhpaKigpKSEkpKSoDahcAlJSXs2rULm83GfffdxxNPPMH777/P+vXrGTlyJElJSQwbNsw5xsyZMykuLuabb75h1qxZ3H333eTl5RETE+OM6dKlC++++67zOx988EFWrlzJzp07KSgoYOjQoaSmppKdnd2ERy8iEryC4rZtwzA4evQobdq0wWaz+Tod8WOrV6/mqquucr7OyckBYNSoUbz88ss89NBDVFZWMnbsWI4cOULfvn3Jz88nKirK+ZlVq1aRm5tLRUUFXbp04W9/+xu33HKLy/ds2bKFsrIyAMLDw1m3bh3z58/nyJEjJCUlMWjQIKZMmUJkZGQTHLWISPCzGYZh+DqJs1VeXk50dDRlZWW0bdvW1+mIiIhIE9OUk4iIiAQ8FTQiIiIS8FTQiIiISMBTQSMiIiIBTwWNiIiIBDwVNCIiIhLwVNCIiIhIwFNBIyIiIgFPBY0Ev+/tvs5AREQspoJGgtZbwKaKnRgfdIZVv4eTlb5OSURELKKCRoLSceA2Rw2HC2/BdqIctv2N8o96UHZ4ta9TExERC6igkaD0OXDvpqn0O/i5c1/bo9/Qckkmszc+yRRHDauAGp9lKCIi3qSCRoLSxsNfMmn9pNP2NzdO8vuvHuHKgqv4dcVOHmn61ERExAIqaCT4nKzk+hU309w42WBI/4Of8dVHafx2x2sQ+A3nRURCngoaCToVxTl0PPpNo3HRJ8rpVngLrPgNVB+xPjEREbGMChoJLnveo/W2v7v3mW8XwIfdoXSZJSmJiIj1VNBI8HCchOIczz57bDcUXA1rH4aaau/mJSIilvOooJk1axYpKSlERUWRkZHBqlWrTH1uwYIF2Gw2hg0b5rLfMAwmTpxIYmIiLVq0ICsri61bt3qSmoSysGacuHopK+P6eDiAAZunwZKfQ9lmr6YmIiLWcrugWbhwITk5OeTm5lJcXExaWhrZ2dkcOHDgjJ/buXMnDzzwAP369TvtvWnTpvH8888ze/ZsioqKaNWqFdnZ2Rw/ftzd9CTEFbXuRN+s5TzW7XFO2sI9G+S7tZDfA76ZpQXDIiIBwmYY7v2NnZGRweWXX87MmTMBcDgcJCcnc8899zB+/Ph6P1NTU0P//v257bbb+Oyzzzhy5AiLFi0Caq/OJCUlcf/99/PAAw8AUFZWRnx8PC+//DIjRoxoNKfy8nKio6MpKyujbdu27hyOBJlHgT//8Ofeh4p4bcXNXFixzfMBk34BGfOgRbw30hMREYu4dYWmurqaNWvWkJWVdWqAsDCysrIoLCxs8HOPP/447du3Z8yYMae9t2PHDux2u8uY0dHRZGRkNDhmVVUV5eXlLpsIQP6P/rwqLoPLhqxlzgW/83zAfR/Ch91gz7/OOjcREbGOWwXNoUOHqKmpIT7e9V+r8fHx2O31NwD8/PPPeemll5gzZ06979d9zp0x8/LyiI6Odm7JycnuHIYEqQPAmp/sq2zemrEZcxjW710ORZ7j2cBVB+E/16sflIiIH7P0LqejR49yyy23MGfOHOLi4rw27oQJEygrK3Nuu3fv9trYEriWnOG995KH0e0X68lPzPb8C7b9DT7qAeoHJSLid5q5ExwXF0d4eDilpaUu+0tLS0lISDgtfvv27ezcuZPrrrvOuc/hcNR+cbNmbNmyxfm50tJSEhMTXcZMT0+vN4/IyEgiIyPdSV1CwEeNvG9vkcgvBnzI0m9mcs3ah8BR5f6XHP0GlmRC98lw8cMQ5uHCYxER8Sq3rtBERETQs2dPCgoKnPscDgcFBQVkZmaeFt+lSxfWr19PSUmJc7v++uu56qqrKCkpITk5mY4dO5KQkOAyZnl5OUVFRfWOKVKfGmCxiTjDFkb7zvfC4DUQ092zLzNOwlePQMFVULHTszFERMSr3LpCA5CTk8OoUaPo1asXvXv3ZsaMGVRWVjJ69GgARo4cSYcOHcjLyyMqKoquXbu6fD4mJgbAZf99993HE088wYUXXkjHjh157LHHSEpKOu15NSINKQYOm4hLAroCxFwK2atqC5Ovn/HsSw9+Bh+lQa9ZkPJbsNk8G0dERM6a2wXN8OHDOXjwIBMnTsRut5Oenk5+fr5zUe+uXbsIC3Nvac5DDz1EZWUlY8eO5ciRI/Tt25f8/HyioqLcTU9CVH7jIQAMBpxlR3gk9JgOSUOgcBR8v9f9Lz5RDoW3wL5/w+UvQkSM+2OIiMhZc/s5NP5Iz6GRK4AVJuL+CdxY3xtV/4Mvfw+73vI8iZbJkPkKxA/wfAwREfGIejlJwPsOWGkiLgzIaujNyHZwxUL4+cvQrLVniagflIiIz6igkYD3MeAwEfdzIPZMATYbdBoFv/gK1A9KRCSgqKCRgOfO+hlTWneCrOXQ7XFQPygRkYCggkYCmoEFBQ1AWDPo9hgM/AJap7qfGEDNcVh9Nyz/JXxf2ni8iIh4TAWNBLQNwD4TcXFAT0++IC4DhqwF9YMSEfFrKmgkoJm9OjOIs/hhb94aMuZAv3dB/aBERPySChoJaJZMNzUkeRj8Yj2oH5SIiN9RQSMBqwL4zGTsIG99aYtEGPAh9PwLhHnYT6yuH9TGJ8FR463MRERCmgoaCVifAidMxPUA4r35xbYwUD8oERG/ooJGAlaTTjfVp64fVJf7PR+jrh/Ujtd0e7eIyFlQQSMByQA+MhlrWUEDp/pBXf0xtOjg2Rh1/aBW/Aaqj3g1PRGRUKGCRgLSNmCHibi21D4h2HIJ18Av1sF59XaKMufbBfBhdyhd5rW0RERChQoaCUhmp5uygOZWJvJj6gclIuIzKmgkIPl8/UxD1A9KRMQnVNBIwDlO7R1OZpzFE2POjvpBiYg0KRU0EnA+A743EXcJcJ7FuZyR+kGJiDQZFTQScPx2uqkh6gclImI5FTQScMzerj3E0izcpH5QIiKWUkEjAeVbwMwy2ZZAX4tz8Yj6QYmIWEIFjQSUxSbjrgKirEzkbKgflIiI16mgkYAScOtnGqJ+UCIiXqWCRgLGCeBjk7F+X9DUUT8oERGvUEEjAaMQOGoi7gLAw5ukfUP9oEREzpoKGgkYQTPd1BD1gxIR8ZgKGgkYQV/QgPpBiYh4yGYYgT/pXl5eTnR0NGVlZbRt29bX6YgF7ECiibgI4DDgYSngXyr+CytugUMrPB8j9jLo8zpEX+y9vERE/JCu0EhAWGIyrh9BUsyA+kGJiLhBBY0EhJCYbqqP+kGJiJiigkb8Xg3mr9AEXUFTR/2gRETOSAWN+L011K6LaUwH4FKLc/Ep9YMSEWmQRwXNrFmzSElJISoqioyMDFatWtVg7DvvvEOvXr2IiYmhVatWpKen8+qrr7rE3HrrrdhsNpdt8OCg/be2uMmd6SablYn4C/WDEhE5jdsFzcKFC8nJySE3N5fi4mLS0tLIzs7mwIED9ca3a9eORx55hMLCQtatW8fo0aMZPXo0ixe7duUZPHgw+/fvd25vvvmmZ0ckQSdk18+cifpBiYi4cPu27YyMDC6//HJmzpwJgMPhIDk5mXvuuYfx48ebGqNHjx5ce+21TJkyBai9QnPkyBEWLVrkXvY/0G3bwet/wLmAo5G4cOAQEGNLine truncated
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -257,13 +290,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 150,
+   "execution_count": 160,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "846c528ad814490d90a400348b6ae20c",
+       "model_id": "5617bc9f737949c4bc84c787ff88ce16",
        "version_major": 2,
        "version_minor": 0
       },
@@ -280,7 +313,7 @@
        "<function __main__.draw_arm(x, y, z)>"
       ]
      },
-     "execution_count": 150,
+     "execution_count": 160,
      "metadata": {},
      "output_type": "execute_result"
     }