path: root/tutorials/module_3/Fourbar.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6e81f53e-d5d7-45d9-b596-5b5aaea1afb6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<link rel=\"stylesheet\"\n",
       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/css/font-awesome.min.css\">\n",
       "<script language=\"javascript\">\n",
       "  function isInternetExplorer() {\n",
       "    ua = navigator.userAgent;\n",
       "    /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
       "    return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
       "  }\n",
       "\n",
       "  /* Define the Animation class */\n",
       "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
       "    this.img_id = img_id;\n",
       "    this.slider_id = slider_id;\n",
       "    this.loop_select_id = loop_select_id;\n",
       "    this.interval = interval;\n",
       "    this.current_frame = 0;\n",
       "    this.direction = 0;\n",
       "    this.timer = null;\n",
       "    this.frames = new Array(frames.length);\n",
       "\n",
       "    for (var i=0; i<frames.length; i++)\n",
       "    {\n",
       "     this.frames[i] = new Image();\n",
       "     this.frames[i].src = frames[i];\n",
       "    }\n",
       "    var slider = document.getElementById(this.slider_id);\n",
       "    slider.max = this.frames.length - 1;\n",
       "    if (isInternetExplorer()) {\n",
       "        // switch from oninput to onchange because IE <= 11 does not conform\n",
       "        // with W3C specification. It ignores oninput and onchange behaves\n",
       "        // like oninput. In contrast, Microsoft Edge behaves correctly.\n",
       "        slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
       "        slider.setAttribute('oninput', null);\n",
       "    }\n",
       "    this.set_frame(this.current_frame);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.get_loop_state = function(){\n",
       "    var button_group = document[this.loop_select_id].state;\n",
       "    for (var i = 0; i < button_group.length; i++) {\n",
       "        var button = button_group[i];\n",
       "        if (button.checked) {\n",
       "            return button.value;\n",
       "        }\n",
       "    }\n",
       "    return undefined;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.set_frame = function(frame){\n",
       "    this.current_frame = frame;\n",
       "    document.getElementById(this.img_id).src =\n",
       "            this.frames[this.current_frame].src;\n",
       "    document.getElementById(this.slider_id).value = this.current_frame;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.next_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.previous_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.first_frame = function()\n",
       "  {\n",
       "    this.set_frame(0);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.last_frame = function()\n",
       "  {\n",
       "    this.set_frame(this.frames.length - 1);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.slower = function()\n",
       "  {\n",
       "    this.interval /= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.faster = function()\n",
       "  {\n",
       "    this.interval *= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_forward = function()\n",
       "  {\n",
       "    this.current_frame += 1;\n",
       "    if(this.current_frame < this.frames.length){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.first_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.last_frame();\n",
       "        this.reverse_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.last_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_reverse = function()\n",
       "  {\n",
       "    this.current_frame -= 1;\n",
       "    if(this.current_frame >= 0){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.last_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.first_frame();\n",
       "        this.play_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.first_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.pause_animation = function()\n",
       "  {\n",
       "    this.direction = 0;\n",
       "    if (this.timer){\n",
       "      clearInterval(this.timer);\n",
       "      this.timer = null;\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.play_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = 1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_forward();\n",
       "    }, this.interval);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.reverse_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = -1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_reverse();\n",
       "    }, this.interval);\n",
       "  }\n",
       "</script>\n",
       "\n",
       "<style>\n",
       ".animation {\n",
       "    display: inline-block;\n",
       "    text-align: center;\n",
       "}\n",
       "input[type=range].anim-slider {\n",
       "    width: 374px;\n",
       "    margin-left: auto;\n",
       "    margin-right: auto;\n",
       "}\n",
       ".anim-buttons {\n",
       "    margin: 8px 0px;\n",
       "}\n",
       ".anim-buttons button {\n",
       "    padding: 0;\n",
       "    width: 36px;\n",
       "}\n",
       ".anim-state label {\n",
       "    margin-right: 8px;\n",
       "}\n",
       ".anim-state input {\n",
       "    margin: 0;\n",
       "    vertical-align: middle;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<div class=\"animation\">\n",
       "  <img id=\"_anim_img0446d4a161904fb49b837c3f452eb604\">\n",
       "  <div class=\"anim-controls\">\n",
       "    <input id=\"_anim_slider0446d4a161904fb49b837c3f452eb604\" type=\"range\" class=\"anim-slider\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           oninput=\"anim0446d4a161904fb49b837c3f452eb604.set_frame(parseInt(this.value));\">\n",
       "    <div class=\"anim-buttons\">\n",
       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"anim0446d4a161904fb49b837c3f452eb604.slower()\">\n",
       "          <i class=\"fa fa-minus\"></i></button>\n",
       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"anim0446d4a161904fb49b837c3f452eb604.first_frame()\">\n",
       "        <i class=\"fa fa-fast-backward\"></i></button>\n",
       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"anim0446d4a161904fb49b837c3f452eb604.previous_frame()\">\n",
       "          <i class=\"fa fa-step-backward\"></i></button>\n",
       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"anim0446d4a161904fb49b837c3f452eb604.reverse_animation()\">\n",
       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"anim0446d4a161904fb49b837c3f452eb604.pause_animation()\">\n",
       "          <i class=\"fa fa-pause\"></i></button>\n",
       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"anim0446d4a161904fb49b837c3f452eb604.play_animation()\">\n",
       "          <i class=\"fa fa-play\"></i></button>\n",
       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"anim0446d4a161904fb49b837c3f452eb604.next_frame()\">\n",
       "          <i class=\"fa fa-step-forward\"></i></button>\n",
       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"anim0446d4a161904fb49b837c3f452eb604.last_frame()\">\n",
       "          <i class=\"fa fa-fast-forward\"></i></button>\n",
       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"anim0446d4a161904fb49b837c3f452eb604.faster()\">\n",
       "          <i class=\"fa fa-plus\"></i></button>\n",
       "    </div>\n",
       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_select0446d4a161904fb49b837c3f452eb604\"\n",
       "          class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_0446d4a161904fb49b837c3f452eb604\"\n",
       "             >\n",
       "      <label for=\"_anim_radio1_0446d4a161904fb49b837c3f452eb604\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_0446d4a161904fb49b837c3f452eb604\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio2_0446d4a161904fb49b837c3f452eb604\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_0446d4a161904fb49b837c3f452eb604\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_0446d4a161904fb49b837c3f452eb604\">Reflect</label>\n",
       "    </form>\n",
       "  </div>\n",
       "</div>\n",
       "\n",
       "\n",
       "<script language=\"javascript\">\n",
       "  /* Instantiate the Animation class. */\n",
       "  /* The IDs given should match those used in the template above. */\n",
       "  (function() {\n",
       "    var img_id = \"_anim_img0446d4a161904fb49b837c3f452eb604\";\n",
       "    var slider_id = \"_anim_slider0446d4a161904fb49b837c3f452eb604\";\n",
       "    var loop_select_id = \"_anim_loop_select0446d4a161904fb49b837c3f452eb604\";\n",
       "    var frames = new Array(360);\n",
       "    \n",
       "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAeAAAAFoCAYAAACPNyggAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
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       "gg==\\\n",
       "\"\n",
       "\n",
       "\n",
       "    /* set a timeout to make sure all the above elements are created before\n",
       "       the object is initialized. */\n",
       "    setTimeout(function() {\n",
       "        anim0446d4a161904fb49b837c3f452eb604 = new Animation(frames, img_id, slider_id, 20.0,\n",
       "                                 loop_select_id);\n",
       "    }, 0);\n",
       "  })()\n",
       "</script>\n"
      ],
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x74b8413f9090>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.animation as animation\n",
    "from scipy.optimize import fsolve\n",
    "\n",
    "# Render animation in Jupyter Notebook\n",
    "%matplotlib inline\n",
    "plt.rcParams[\"animation.html\"] = \"jshtml\"\n",
    "plt.rcParams['figure.dpi'] = 75\n",
    "\n",
    "# Link lengths (arbitrary units)\n",
    "L1 = 4.0  # Ground link\n",
    "L2 = 2.0  # Input crank\n",
    "L3 = 3.0  # Coupler\n",
    "L4 = 3.5  # Output rocker\n",
    "\n",
    "# Fixed pivots\n",
    "A = np.array([0, 0])\n",
    "D = np.array([L1, 0])\n",
    "\n",
    "# Input crank angle range\n",
    "theta2_vals = np.linspace(0, 2 * np.pi, 360)\n",
    "\n",
    "# Store previous angles to ensure continuity\n",
    "previous_guess = [np.pi / 2, np.pi / 2]\n",
    "\n",
    "# Solve joint positions using loop closure equations\n",
    "def solve_positions(theta2):\n",
    "    global previous_guess\n",
    "    B = A + L2 * np.array([np.cos(theta2), np.sin(theta2)])\n",
    "\n",
    "    def loop_closure(vars):\n",
    "        theta3, theta4 = vars\n",
    "        eq1 = L2 * np.cos(theta2) + L3 * np.cos(theta3) - L4 * np.cos(theta4) - L1\n",
    "        eq2 = L2 * np.sin(theta2) + L3 * np.sin(theta3) - L4 * np.sin(theta4)\n",
    "        return [eq1, eq2]\n",
    "\n",
    "    theta3, theta4 = fsolve(loop_closure, previous_guess)\n",
    "    previous_guess = [theta3, theta4]  # update guess for continuity\n",
    "\n",
    "    C = B + L3 * np.array([np.cos(theta3), np.sin(theta3)])\n",
    "    return A, B, C, D\n",
    "\n",
    "# Set up plot\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "# Animation function\n",
    "def animate(i):\n",
    "    ax.cla()\n",
    "    A, B, C, D = solve_positions(theta2_vals[i])\n",
    "    x_vals = [A[0], B[0], C[0], D[0]]\n",
    "    y_vals = [A[1], B[1], C[1], D[1]]\n",
    "    ax.plot(x_vals, y_vals, 'o-', lw=2)\n",
    "    ax.set_xlim(-5, 8)\n",
    "    ax.set_ylim(-5, 5)\n",
    "    ax.set_aspect('equal')\n",
    "    ax.set_title(\"Four-Bar Linkage Simulation\")\n",
    "\n",
    "ani = animation.FuncAnimation(fig, animate, frames=len(theta2_vals), interval=20)\n",
    "ani"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1adaacdd-80ff-4f1d-bf5a-a9bb2b0b3dc5",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.2"
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 "nbformat": 4,
 "nbformat_minor": 5
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