{ "cells": [ { "cell_type": "markdown", "metadata": { "id": "txzjCkPddNYW" }, "source": [ "> Marcos Duarte \n", "> Laboratory of Biomechanics and Motor Control ([http://pesquisa.ufabc.edu.br/bmclab](http://pesquisa.ufabc.edu.br/bmclab)) \n", "> Federal University of ABC, Brazil# Angular kinematics in a plane (2D)\n" ] }, { "cell_type": "markdown", "metadata": { "id": "gORkllQRhF6w" }, "source": [ "

Contents

\n", "
" ] }, { "cell_type": "markdown", "metadata": { "id": "-j8tXrk1dSIc" }, "source": [ "Human motion is a combination of linear and angular movement and occurs in the three-dimensional (3D) space. For certain movements and depending on the desired or needed degree of detail for the motion analysis, it's possible to perform a two-dimensional (2D, planar) analysis at the main plane of movement. Such simplification is appreciated because the instrumentation and analysis are much more complicated in order to measure 3D motion than for the 2D case." ] }, { "cell_type": "markdown", "metadata": { "id": "-Wb-NcroiILC" }, "source": [ "## Python setup" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "id": "o2Ger3R_iXqq" }, "outputs": [], "source": [ "# Import the necessary libraries\n", "import numpy as np\n", "from IPython.display import display, Latex\n", "import matplotlib\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "import seaborn as sns\n", "sns.set_context(\"notebook\", font_scale=1.2, rc={\"lines.linewidth\": 2, \"lines.markersize\": 8})" ] }, { "cell_type": "markdown", "metadata": { "id": "jiqckVRriY7j" }, "source": [ "## Angles in a plane" ] }, { "cell_type": "markdown", "metadata": { "id": "9tzd9_9Xincq" }, "source": [ "For the planar case, the calculation of angles is reduced to the application of trigonometry to the kinematic data. For instance, given the coordinates in a plane of markers on a segment as shown in the figure below, the angle of the segment can be calculated using the inverse function of $\\sin,\\cos$ , or $\\tan$ .\n", "\n", "
Figure. A segment in a plane and its coordinates.
" ] }, { "cell_type": "markdown", "metadata": { "id": "CeGV6Zp5jrKl" }, "source": [ "For better numerical accuracy (and also to distinguish values in the whole quadrant), the inverse function of $\\tan$ is preferred. \n", "For the data shown in the previous figure: \n", "\n", "\n", "$$ \\theta = arctan\\left(\\frac{y_2-y_1}{x_2-x_1}\\right) $$\n", "" ] }, { "cell_type": "markdown", "metadata": { "id": "rdDtjZZzjsTa" }, "source": [ "In computer programming (here, Python/Numpy) this is calculated using: `numpy.arctan((y2-y1)/(x2-x1))`. However, for the previous figure the function `arctan` can not distinguish if the segment is at 45o or at 225o, `arctan` will return the same value. Because this, the function `numpy.arctan2(y, x)` is used, but be aware that `arctan2` will return angles between $[-\\pi,\\pi]$: " ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 84 }, "id": "1Z-GtDVmjxBk", "outputId": "1afd9589-d253-4913-a468-0b8887234514" }, "outputs": [ { "data": { "text/latex": [ "Segment at 45o:" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "Using arctan: 45.0$\\quad$Using arctan2: 45.0" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "Segment at 225o:" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "Using arctan: 45.0$\\quad$Using arctan2: -135.0" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x1, y1 = 0, 0\n", "x2, y2 = 1, 1\n", "\n", "display(Latex('Segment at 45o:'))\n", "angs = [ np.arctan((1-0)/(1-0))*180/np.pi, np.arctan2(1-0, 1-0)*180/np.pi ]\n", "display(Latex('Using arctan: '+str(angs[0])+'$\\quad$'+'Using arctan2: '+str(angs[1])))\n", "display(Latex('Segment at 225o:'))\n", "angs = [ np.arctan((-1-0)/(-1-0))*180/np.pi, np.arctan2(-1-0, -1-0)*180/np.pi ]\n", "display(Latex('Using arctan: '+str(angs[0])+'$\\quad$'+'Using arctan2: '+str(angs[1])))" ] }, { "cell_type": "markdown", "metadata": { "id": "NykbWZxWj2Yz" }, "source": [ "And Numpy has a function to convert an angle in rad to degrees and the other way around:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 50 }, "id": "IdUVzjKGj3OJ", "outputId": "0c3b153b-1b1c-4e6d-ca5e-2921a37ed084" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "np.rad2deg(np.pi/2) = 180.0\n", "np.deg2rad(180) = 3.141592653589793\n" ] } ], "source": [ "print('np.rad2deg(np.pi/2) =', np.rad2deg(np.pi))\n", "print('np.deg2rad(180) =', np.deg2rad(180))" ] }, { "cell_type": "markdown", "metadata": { "id": "7kc6Bi3Dj6eL" }, "source": [ "Let's simulate a 2D motion of the arm performing two complete turns around the shoulder to exemplify the use of `arctan2`:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 288 }, "id": "GbTRsYVoj8GL", "outputId": "9ae49c3e-87dc-44ad-be7f-0e11d6880793" }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t = np.arange(0, 2, 0.01)\n", "x = np.cos(2*np.pi*t)\n", "y = np.sin(2*np.pi*t)\n", "ang = np.arctan2(y, x)*180/np.pi\n", "\n", "plt.figure(figsize=(12, 4))\n", "hax1 = plt.subplot2grid((2, 3), (0, 0), rowspan=2)\n", "hax1.plot(x, y, 'go')\n", "hax1.plot(0, 0, 'go')\n", "hax1.set_xlabel('x [m]')\n", "hax1.set_ylabel('y [m]')\n", "hax1.set_xlim([-1.1, 1.1])\n", "hax1.set_ylim([-1.1, 1.1])\n", "hax2 = plt.subplot2grid((2, 3), (0, 1), colspan=2)\n", "hax2.plot(t, x, 'bo', label='x')\n", "hax2.plot(t, y, 'ro', label='y')\n", "hax2.legend(numpoints=1, frameon=True, framealpha=.8)\n", "hax2.set_ylabel('Position [m]')\n", "hax2.set_ylim([-1.1, 1.1])\n", "hax3 = plt.subplot2grid((2, 3), (1, 1), colspan=2)\n", "hax3.plot(t, ang, 'go')\n", "hax3.set_yticks(np.arange(-180, 181, 90))\n", "hax3.set_xlabel('Time [s]')\n", "hax3.set_ylabel('Angle [ o]')\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": { "id": "LAJn4ll4j-lz" }, "source": [ "Because the output of the `arctan2` is bounded to $[-\\pi,\\pi]$, the angle measured appears chopped in the figure. This problem can be solved using the function `numpy.unwrap`, which detects sudden jumps in the angle and corrects that:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 216 }, "id": "E3V-Ynh3kAS3", "outputId": "b57bcd7c-b170-4721-a661-2c488428eb0b" }, "outputs": [ { "data": { "image/png": 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Ol7Rp4YriksaSFu3M6xxOXc2scZylMbPhKDXA2Q54qcj2rUmPjEom6R9JC2ZuCdwPfCjb1QUcmO17P7A/cLOk90bE/aRHWoULfy4GOoBxwMKCfVNJK5KbWQtxlsbMqqHUAOchUr+YwrWp/pkUpJTjx6RMzY7AWaSA5nBgFLAA+GJEBPCwpP2Bz2XXUPHTDWgWMLtgWycwt8zzmFkdNGIod7/xY8Y7S2PWZkoNcM4CfiSpk5QxmSLpHaSVvSeXc8GIeAV4BfiTpD8CCyS9HVgEvJoFN/3+COyW/XkRKYuTN4HUN2ijf+ZFxDLSSKvXFTxeM7MGaWSWBhzQmI0EJQU4EfFzSX8HfJX0SOpUYB7w/oj49aAHD64/4lgH3Ad8TJJyQc7OpL44kLI+XZK6I6In2zYZeKSw/42ZNadGZmn8+MlsZCl5HpyIuJM0jHtYJG0CnAn8iNSXZkfga6THX38izW/zBeDrkq4h9cE5lDQknIh4VNI9wNWSTiT12TkxO8bMmpQ7CZtZI9RzJuMA3kbqU7Md8DxwBzAtmyjwaUkfAS4gdRD+E3B4RMzLneNTpD47vwFeBr7uOXDMmos7CZtZMxgwwJH0J1JQMqSI2KWEMmuBw4YoMwd41yD7nyf1+zGzJuP1nsysmQyWwfle3WphZi3FWRoza3YDBjgRcVY9K2Jmzc9Duc2sVXg1cTMrykO5zayVlbrY5kD9cQJYRVqy4TsRcUcV62ZmDeAsjZm1g1IzODcDxwF/II1gAtiLNCpqNmkyvtslfSwiflLtSppZ7TUisHFAY2a1UmqAsw1waUScnt8oaQYwNiIOkvQN4N8ABzhmTc6dhM2s3Y0qsdyngWuLbP8uaUVwgOuBvxroBJLOkPSIpFclLZD0bUlb5fYfKSmKvG7LlRkt6QJJL0paLulaSVuW2AazEa9vTR+n/eI0xp43lrPvObuuwc34MeOZtt80ln1lGecefK6DGzOrqVIzOB3ALqTJ9/J2YUOQtJrBVxbfBzgf+C3wJuBK0mrkn8323wT8NFd+E+Bx0szH/b5KCrYOB/pIQdfFpMkDzSzHnYTNbCQrNcD5AXCVpNNIK3sHsDcwA7gxK7M38ORAJ4iID+fe/lHSV0mzEvfvXwms7H8v6WPAZtm1kTSK1A/olGzZCCQdD/xM0peyxTXNRjx3EjYzKz3AOYE0WupyUmZFwBpSgHJKVuYh4Ogyrj2egtW+C0wBfpILXN6SHZNfD+uXWV32AObkD5Y0FhhbcM7OMupn1vScpTEzK67U1cRXASdI+gpphW+ApyJiRa7M46VeVNI2wEnANQPs3xb4MPDJ3OaJ2c8XctdcJ2lpbl/eVGB6qXUyayXO0piZDa6sif6ygObRSi4oaTPgVmA+cN4AxT4FvALcnj+0zEvNIg1hz+sE5pZ5HrOm0YjAxqOezKwVlTrRn4AjgENIHYTfMPoqIiaXeJ7RpD47WwMHZQtwFjMFuDEiXsttW5T9nAg8k52vg7Qy+QsUyB5tveERWGqGWWvw4yczs+ErNYNzPumRzy+AXkpcZTwv6yR8HekR1/4R0TdAuZ1II66mFuyaDywBDmRDZma/rC4PlVsfs2blx09mZpUrNcCZAnwmIm6u4FpXAgcAHwI2lbR9tn1xxBu+xacAT0bEg/mDI2K9pMuAcyQ9A7wKfBu4PiJeqqBeZg3jLI2ZWW2UGuBsQuVZkqOynw8XbO8mZYX6/RMDdD4GziY93ro1q9OtwPEV1sus7pylMTOrrVIDnOuBvyc9qhqWiCipA0xE7DzIvrXAidnLrCX0Z2kunXcpS1YsYfOOzVm9bjVR/pPeYXFAY2YjUakBzsvAqZL2AR4hzYHzuoj4erUrZtbqBsrSrFq3qubXdlBjZiNdqQHOEcBy4F3ZKy8ABzhmGQ/lNjNrvFIn+uuudUXMWpE7CZuZNaeyJvorJOnNwNERMa1K9TFrCe4kbGbW3MoOcLL5bA4FPk+a+O8FwAGOtS13EjYzaz0lBziSukiLaX6ONJvx94G/JS14adZ23EnYzKx1DRrgZEshfBQ4hjRJ389JMwx/HzgvIp6odQXN6qHRWRp3EjYzq66hMjj/C7xIWmLhnyPieQBJ3x/OxSQdBvwrsCfwZ4Vz40g6irTKeBfwPHA1cE5ERLZ/K+DfgcOA10hLNpxSMBOyWckakaURYovRW7By7UrGjxnPsXse60yNmVmVDRXgbAf8GniCIgtaDsMY4E7SmlZvGFouaT/gMtJjsHtIw9GvB54Drs2KXUIKjg4GtgK+R5qj5+wq1M1GEA/lNjNrb0MFOH9B6nNzMTBG0vdI2Zxh5e0j4nsAkg4osvs9wKMRcV32vlfSz4E9gGslbQv8I/C3EfFAdp5/A86VNCMi1udPJmksMLbgGp3Dqbe1Ng/lNjMbeQYNcCJiESmAOA94P2nk1DygA/i0pCsjYkGV6nIfMF3SPhFxr6S3k1YVPybbvwcpsLond8wcYCJpPaunC843FZhepbpZC/JQbjOzkavUif4C+Cnw02wV8KNJi2eeLum+iHhfpRWJiLmSjgPuzDo3dwCnRcSPsyITgaUF/W0W5/YVBjizSH108jqBuZXW1ZqPOwmbmVle2fPgZB2NZ0g6B/ggKatTMUnvJPXLOQH4DbArcJGkpyPiFqDYYp0D/vaKiGXAsoJrVKOq1kTcSdjMzIoZ9kzGWVbntuxVDacCt0XEldn7xyR1AycDtwCLgO0kdeSyOBOzn9XoAG1NzlkaMzMrVUVLNVTZGOCVgm3rgVHZnx8iZXH2Be7Otk0mBTc9daifNYizNGZmVq66BjiStgPeDOycvd892/UEKRN0kaS5bHhE9SXSvDdExFJJ/wFcnM2XsyUwA7ikcASVtQcP5TYzs+GqdwbnUDbMaQPwcPazOyKuyoZ2nwnsSJro7zvAubnyx5HmwpnDhon+zqltla0eGv34yaOezMzai7JJgkeEbD2tnp6eHrq6uhpbGQM8lNvMzIavt7eX7u5uSImS3vy+ZuqDY22u0VkaP34yMxs5HOBYzbmTsJmZ1ZsDHKu6Ri6N4CyNmZmBAxyrkkYENc7SmJnZQBzg2LA4S2NmZs3MAY6VrNGrcjuwMTOzUjVdgJPNhTMT+AiwFWkCwOMi4sVs/3tIc+HsCswHvhwRtzeouiNCI4Zy+/GTmZlVoukCHOAaYAdSgLMG+BZwA3CIpHHA7cD1wBHAR4EfSnpnRPypQfVtKx7KbWZm7aCpAhxJW5CCln0j4rfZtuOBJyW9HTgYWA5MzRb7fELSB4FjgJMaVO224KHcZmbWTpoqwAE2IS2umf+tujL7uRcwCbgr3jj98hxS4PMG2aOusQWbO6tX1dbmTsJmZtbOmirAiYjlkuYB0yQdSVpv6mvZ7jcBE9mwflW/xdn2QlOB6TWqaktqVFAjBMC4MeO8NIKZmdVFUwU4mSnA94GlwDrgctLCm+sh+01ZmlmkxTjzOoG5lVexNThLY2ZmI1XTBTgR8SSwh6RtgQBWk1YR7wUWsXG2ZgLwQpHzLAOW5bdJ5cRHrclZGjMzsyYMcPpFxEsAkv6B9KhqDukx1YkFRScD99e3ds2nEUO5naUxM7Nm1XQBTjYqahXwLPA+4GJgRkQskfR94ExJs4ArgEOB9wBHN6q+jeLHT2ZmZgNrugAHGA/MIM2F8ywwLSJmAUTEi5I+RJro71jSRH+HjZQ5cLzek5mZWWmaLsCJiOtJE/kNtP8+YI/61ahxnKUxMzMbnqYLcEY6dxI2MzOrnAOcBnOWxszMrPoc4DRIoxawBGdpzMys/TnAqaNGZGucpTEzs5HIAU4N+fGTmZlZYzjAqTJ3EjYzM2s8BzgVcpbGzMys+bRkgCPpNOB4YCxwB/D5iNhoPapa61vTx15X7cVTS59i9brVNb+eszRmZmalabkAR9JngdOBI4Ae0qrhNwAH1bsuM389k6dferqmwY2zNGZmZuVruQCHlLm5ICJ+CCDpc8DTknaNiMf7C0kaS8rw5HVWsyKXzruUVWtXVfOUrxs/ZryzNGZmZsPUUgGOpM2Ad5FbUTwi5kvqJS26+Xiu+FRgei3r8+KK6vW5cUBjZmZWPS0V4ADjgFFAYX+bxcDEgm2zgNkF2zqBuVWrzJhxLFmxZNjH+/GTmZlZbbRagKNSC0bEMmDZGw5WyYeX5Lg9j+P8e88v+TGVOwmbmZnVR6sFOEuA9aRszR9y2yewcVan5k5+78nc+odbBx1F5SyNmZlZ/Y1qdAXKERGrgd8BB/Zvk9QNdAH317s+W226FfcdfR+nvvdUxm8xPtUn+2/8mPFM228ay76yjHMPPtfBjZmZWR0pIhpdh7Jko6ZmAVOAXuBCgIiYXMKxXUBPT08PXV1dNaujmZmZ1V5vby/d3d0A3RHRm9/Xao+oiIhrJL0JuBzYBvg58PkSD+8AWLBgQY1qZ2ZmZvWS+33eUbiv5TI4lZD0Pqo4isrMzMyawr4R8av8hpEW4GwG/A2wEFhX5dP3D0HfF2jXFJHb2D5GQjvdxvYxEtrpNg5PB7AD8GDWT/d1LfeIqhJZ4381ZMFhyA1BX1D4HLBduI3tYyS0021sHyOhnW5jRZ4utrGlRlGZmZmZlcIBjpmZmbUdBzhmZmbWdhzgVM8y4CwKlodoM25j+xgJ7XQb28dIaKfbWGUjahSVmZmZjQzO4JiZmVnbcYBjZmZmbccBjpmZmbUdBzhmZmbWdhzgDELSaZL+T9IKST+SNHGQsrtIulvSSkk9ko4s2D9a0gWSXpS0XNK1kraseSOGUGobJe0u6WZJCyX1SbpP0sEFZWZLioLX1Pq0ZHBltLOrSBuWFZTZKmvr8uzz/JakjRZ6q7cy2nhkkTaGpNtyZe4usv9j9WtN0XofJmmOpJclDTk6ohXvyXLa2Kr3ZJltbOX7sZx2ttw9KekMSY9IelXSAknflrTVEMdsn303rci+q04tUqbk37tDcYAzAEmfBU4H/hXYBxgL3DBA2U2A/wYWkda6mgFcKWn/XLGvAp8GDgcOBiYBF9eq/qUop43AXwPPAJ8Adgd+BvxE0l8VlPsBaV2Q/teV1a95ecpsZ79JbGjDLgX7LiF9zgeTPs9/AM6oYpXLVmYbb+KNn9GbgeXAjwrKfaug3O1Vr3h5xgB3AucNVbBV70nKaCOte0+W08Z+LXU/ZsppZyvek/sA5wPvBj4DHMLQ989NwDbZsf8K/JukI/p3DvO7emAR4VeRF/AQcFbu/VuAAHYtUvZQYAWwZW7bdcAt2Z9HAYuBz+b2TwZeA8a2QhsHOP73wAm597OB2Y3+7Cr8LLuyfV0DnGtbYC1wYG7b50i/SEe1QhuLHPsxYFX+7yJwN3Bmoz+7Aep7QPrqGrRMS96T5bRxgONa4p4s43Nsyfux0s+y1e7JrH6HA0sH2b9b9lm+JbftbGBe7n1Fv5MKX87gFKG06vi7SNE3ABExH+gF3lPkkEnA/RHxam7bnFzZtwDj8+cDfgkI2KNqFS/DMNpYeLyAcWw8YdOhkhZLejRLNTZ0QdcK2nlPlib9b0m75rbvQbrh7sltmwNMBLqrVe9yVPpZAlOAn0RE4Wd5nKQlkn4r6V+qVd86abl7slKtck8OU8vcj1XSivfkeAafwG8S0Jt9N/WbA+wuadMqfI9tpBX/otfDONK/8F4o2L6YdOMUmjhE2f6fr5eJiHWSlg5wvnoot42FvkBapv4nuW23ATcCz5G+eGYCW5NSjo1Sbjv7gBOAe4HNgKmkL9e3RcSi7JilEbGu4Fxk+4qualtjw/4sJW0LfBj4ZMGu64H5wFJgf+AiSYqIRj/eKFUr3pOVapV7shyteD9WpBXvSUnbACcB1wxSbKB7soP0HSYq+520EQc4xWnoImWVL/d89TDsOkn6AOm58scj4qX+7RHxg1yxxyStAy6TdEZk+cYGKKudEbGE3HNkSfcDTwBHkH45FDtfo6cDr+Tv16eAVyh4lh8RV+fe/i77Avsije+/UapWvCeHrcXuyZK16P1YqZa6J7PMy62k4Guw/kZ1vyf9iKq4JcB6No4aJ7BxdAnpee9gZRdlP18vk/Xy326A89VDuW0EQNK+wM3AURFxxxDXeAjYkpS6bJRhtbNf9i/DR0l9AXoH11MAAAVZSURBVCB9ltsVjNLYKBtQZ5W0cQpwY0S8NkS5h9jw/6AVtOI9OSwteE8OW4vcj5VqmXsye9x5Iykr+PGIWDtI8YHuyXXAi1T4XV2MA5wiImI18DvgwP5tkrpJf5nuL3LIA8B7JI3JbZucKzuf9OEdmNu/H+lfGg9VreJlGEYbkTQJ+C/gyxFxYwmX2ZXU0XNJpfUdruG0My/r1/B20mgVSJ+XgH1zxSaTbsCeqlS6TMNto6SdSCMVrivhMruy4f9BK2i5e3I4WvGerEQr3I+VaKV7UtIoUj13Bj4YEX1DHPIA0JV9N/WbDDwSEWsq/a4uqtE9r5v1ReqJvxz4KBs6Pt2Z7ZsEPAn8efZ+U+Ap0nC2d2THrgH2z53vbNJz8AOz4x8DrmmhNr6T9Oz3fGD73Gub3PkuIHUG6wIOy9p7QYt9lv3DTHfJ2nwV8DLQmTvfddnnNyn7PJ8DprVKG3PHnAn8oci5ts/2vZvUGffI7P/BCbVuxxBt3I40HPpoUiCye/batI3uyXLa2JL3ZJltbMn7sdx25o5pmXsy+yz+L2tT/u9fR7b/z7M2Tsod80vSd9O7SN9Vy4EjcvsH/B4bVh0b/ZegmV/AacBC0r94/hN4U7b9AAqGLgJvJQ3jW0Xq9X1kwblGAxdmX0ivkIZvblmvtlTaxuzmiiKv2blz/ZTUIWw18CdgGrBZo9tYZjs/QXrGv4KUNr0D2KPgXFsB380+x6WkXyIdrdLGXPmngNOLnGdc9nd5KbCSNPT4CzR42C3pS73Y38Gudrkny2ljq96TZbaxle/Hsv6+Zse0zD05QNvyn11X9v6A3DHbk76bVpC+q75S5LxFv8eG81J2QjMzM7O24T44ZmZm1nYc4JiZmVnbcYBjZmZmbccBjpmZmbUdBzhmZmbWdhzgmJmZWdtxgGNmTUHS3ZKuatC1j5QU2euWMo6blzvufbWso5mVx4ttmllNSRpqsq1nIqKLNNPuYGvZ1No6oJM0MWCp3k+aWfaBmtTIzIbNAY6Z1doOuT9PIs1OOgn432zbOoCIWFrnem0kIp4vs/yLkrauVX3MbPj8iMrMaioinu9/kaaaB1ic274YNn5Elb2/WtIMSS9IWibpHEmjJE2TtEjSYknn5K8nabSkMyX1SFol6feSjhlO3SW9Q9LPsmu/KukPkqYM9/+FmdWPMzhm1sw+AVwOvC97XQ38NfA4aQXpvYHZkn4VEbdnx1xFWpTwGNL6S5OAKyStjYiry7z+Ddm19iE9unor0FFRi8ysLhzgmFkz64mIU7M//4+kLwM7RsSHctu+BBwE3C6pGzgCeHtEPNl/DklvBY4nBUjl+AvS6ttPZO/nD7slZlZXDnDMrJn9ruD989mrcNvE7M97AgLmScqXGU3W16dM3wSuknQkaTXnH0fEQ8M4j5nVmfvgmFkze63gfQywrf+7rP/nPsDuudeuwG7lXjwivgbsAvwgO8d9kmaUex4zqz8HOGbWTn6b/XxzRDxV8Hp6OCeMiPkRcWlEfAKYBhxbtdqaWc34EZWZtY2IeErSNcB3JJ0C/AbYEtgDmBAR3yj1XJK2Ar4B3Ar0AGOBDwBPDHacmTUHBzhm1m4+D3wZOIM0Cd9y4PfAv5d5nrXAtqSOyTtk57kLOKlqNTWzmlHEUJOMmpm1t6wT8VURUfY/+iR1kTI8+0bEr6pbMzMbLvfBMTNLOiT1Sbq+1AMk3UPKDplZk3EGx8xGvGy5hTdlb/tKXbJBUiewefZ2QUSUs46VmdWQAxwzMzNrO35EZWZmZm3HAY6ZmZm1HQc4ZmZm1nYc4JiZmVnbcYBjZmZmbef/A/NZ23scDdXSAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ang = np.unwrap(np.arctan2(y, x))*180/np.pi\n", "\n", "hfig, hax = plt.subplots(1,1, figsize=(8,3))\n", "hax.plot(t, ang, 'go')\n", "hax.set_yticks(np.arange(start=0, stop=721, step=90))\n", "hax.set_xlabel('Time [s]')\n", "hax.set_ylabel('Angle [ o]')\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": { "id": "p0oq7S6TkB2_" }, "source": [ "If now we want to measure the angle of a joint (i.e., the angle of a segment in relation to other segment) we just have to subtract the two segment angles (but this is correct only if the angles are at the same plane):" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 216 }, "id": "DZnVaSq1kD8g", "outputId": "b9ddd327-48e7-4baf-b9e8-728a063aaadd" }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x1, y1 = 0.0, 0.0\n", "x2, y2 = 1.0, 1.0 \n", "x3, y3 = 1.1, 1.0\n", "x4, y4 = 2.1, 0.0\n", "\n", "hfig, hax = plt.subplots(1,1, figsize=(8,3))\n", "hax.plot((x1,x2), (y1,y2), 'b-', (x1,x2), (y1,y2), 'ro', linewidth=3, markersize=12)\n", "hax.add_patch(matplotlib.patches.FancyArrowPatch(posA=(x1+np.sqrt(2)/3, y1),\n", " posB=(x2/3, y2/3),\\\n", " arrowstyle='->,head_length=10,head_width=5', connectionstyle='arc3,rad=0.3'))\n", "plt.text(1/2, 1/5, '$\\\\theta_1$', fontsize=24)\n", "hax.plot((x3,x4), (y3,y4), 'b-', (x3,x4), (y3,y4), 'ro', linewidth=3, markersize=12)\n", "hax.add_patch(matplotlib.patches.FancyArrowPatch(posA=(x4+np.sqrt(2)/3, y4),\n", " posB=(x4-1/3, y4+1/3),\\\n", " arrowstyle='->,head_length=10,head_width=5', connectionstyle='arc3,rad=0.3'))\n", "hax.xaxis.set_ticks((x1,x2,x3,x4))\n", "hax.yaxis.set_ticks((y1,y2,y3,y4))\n", "hax.xaxis.set_ticklabels(('x1','x2','x3','x4'), fontsize=20)\n", "hax.yaxis.set_ticklabels(('$y_1,\\,y_4′,′y_2,\\,y_3$'), fontsize=20)\n", "plt.text(x4+.2,y4+.3,'$\\\\theta_2$', fontsize=24)\n", "hax.add_patch(matplotlib.patches.FancyArrowPatch(posA=(x2-1/3, y2-1/3),\n", " posB=(x3+1/3, y3-1/3),\\\n", " arrowstyle='->,head_length=10,head_width=5', connectionstyle='arc3,rad=0.3'))\n", "plt.text(x1+.8,y1+.35,'$\\\\theta_J=\\\\theta_2-\\\\theta_1$', fontsize=24)\n", "hax.set_xlim(min([x1,x2,x3,x4])-0.1, max([x1,x2,x3,x4])+0.5)\n", "hax.set_ylim(min([y1,y2,y3,y4])-0.1, max([y1,y2,y3,y4])+0.1)\n", "hax.grid(xdata=(0,1), ydata=(0,1))\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": { "id": "DPEfJdRMkGzq" }, "source": [ "The joint angle shown above is simply the difference between the adjacent segment angles:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 67 }, "id": "0zcls8TbkHY4", "outputId": "c96b5cd2-d3b1-4173-8c01-0336d28dad7c" }, "outputs": [ { "data": { "text/latex": [ "$\\theta_1=\\;′+str(ang1)+′^o$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\theta_2=\\;′+str(ang2)+′^o$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\theta_J=\\;′+str(ang2−ang1)+′^o$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x1, y1, x2, y2 = 0, 0, 1, 1 \n", "x3, y3, x4, y4 = 1.1, 1, 2.1, 0\n", "ang1 = np.arctan2(y2-y1, x2-x1)*180/np.pi\n", "ang2 = np.arctan2(y3-y4, x3-x4)*180/np.pi\n", "\n", "#print('Angle 1:', ang1, '\\nAngle 2:', ang2, '\\nJoint angle:', ang2-ang1)\n", "display(Latex('$\\\\theta_1=\\;′+str(ang1)+′^o$'))\n", "display(Latex('$\\\\theta_2=\\;′+str(ang2)+′^o$'))\n", "display(Latex('$\\\\theta_J=\\;′+str(ang2−ang1)+′^o$'))" ] }, { "cell_type": "markdown", "metadata": { "id": "ET0AYfIzkMX_" }, "source": [ "The following convention is commonly used to describe the knee and ankle joint angles at the sagittal plane (figure from Winter 2005):\n", "\n", "
Joint angle convention
Figure. Convention for the sagital joint angles of the lower limb (from Winter, 2009).
" ] }, { "cell_type": "markdown", "metadata": { "id": "vZOIrIH6kO58" }, "source": [ "## Angle between two 3D vectors\n", "\n", "In certain cases, we have access to the 3D coordinates of markers but we just care for the angle between segments in the plane defined by these segments (but if there is considerable movement in different planes, this simple 2D angle might give unexpected results). \n", "Consider that `p1` and `p2` are the 3D coordinates of markers placed on segment 1 and `p2` and `p3` are the 3D coordinates of the markers on segment 2. \n", "\n", "To determine the 2D angle between the segments, one can use the definition of the dot product:\n", "\n", "\n", "$$ \\mathbf{a} \\cdot \\mathbf{b} = ||\\mathbf{a}||\\:||\\mathbf{b}||\\:cos(\\theta)\\;\\;\\; \\Rightarrow \\;\\;\\; angle = arccos\\left(\\frac{dot(p2-p1,\\;p3-p2)}{norm(p2-p1)*norm(p3-p2)\\;\\;\\;\\;\\;} \\right) $$\n", "\n", "\n", "Or using the definition of the cross product:\n", "\n", "\n", "$$ \\mathbf{a} \\times \\mathbf{b} = ||\\mathbf{a}||\\:||\\mathbf{b}||\\:sin(\\theta) \\;\\; \\Rightarrow \\;\\; angle = arcsin\\left(\\frac{cross(p2-p1,\\;p3-p2)}{norm(p2-p1)*norm(p3-p2)\\;\\;\\;\\;\\;} \\right) $$\n", "\n", "\n", "But because `arctan2` has a better numerical accuracy, combine the dot and cross products, and in Python notation:\n", "```python\n", "angle = np.arctan2(np.linalg.norm(np.cross(p1-p2, p4-p3)), np.dot(p1-p2, p4-p3))\n", "```\n", "See [this notebook](http://nbviewer.ipython.org/github/demotu/BMC/blob/master/notebooks/ScalarVector.ipynb) for a review on the mathematical functions cross product and scalar product." ] }, { "cell_type": "markdown", "metadata": { "id": "4Ic0Cl3rkjpH" }, "source": [ "We can use the formula above for the angle between two 3D vectors to calculate the joint angle even with the 2D vectors we calculated before:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 34 }, "id": "ISMWh6i0klHq", "outputId": "9508d7db-5113-4344-ed0f-0fb99943488f" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Joint angle: 90.0\n" ] } ], "source": [ "p1, p2 = np.array([0, 0]), np.array([1, 1]) # segment 1\n", "p3, p4 = np.array([1.1, 1]), np.array([2.1, 0]) # segment 2\n", "\n", "angle = np.arctan2(np.linalg.norm(np.cross(p1-p2, p4-p3)), np.dot(p1-p2, p4-p3))*180/np.pi\n", "\n", "print('Joint angle:', '{0:.1f}'.format(angle))" ] }, { "cell_type": "markdown", "metadata": { "id": "l5dkxdTbkma_" }, "source": [ "As expected, the same result. \n", "\n", "In Numpy, if the third components of vectors are zero, we don't even need to type them; Numpy takes care of adding zero as the third component for the cross product." ] }, { "cell_type": "markdown", "metadata": { "id": "5FGBwWBvkp7z" }, "source": [ "## Angular position, velocity, and acceleration\n", "\n", "The angular position is a vector, its direction is given by the perpendicular axis to the plane where the angular position is described, and the motion if it occurs it's said to occur around this axis." ] }, { "cell_type": "markdown", "metadata": { "id": "3rcNt5Ymkuz3" }, "source": [ "Angular velocity is the rate (with respect to time) of change of the angular position:\n", "\n", "\n", "$$ \\mathbf{\\omega}(t) = \\frac{\\mathbf{\\theta}(t_2)-\\mathbf{\\theta}(t_1)}{t_2-t_1} = \\frac{\\Delta \\mathbf{\\theta}}{\\Delta t}$$\n", "\n", "\n", "\n", "$$ \\mathbf{\\omega}(t) = \\frac{d\\mathbf{\\theta}(t)}{dt} $$\n", "" ] }, { "cell_type": "markdown", "metadata": { "id": "uqJN5TWNk0xZ" }, "source": [ "Angular acceleration is the rate (with respect to time) of change of the angular velocity, which can also be given by the second-order rate of change of the angular position:\n", "\n", "\n", "$$ \\mathbf{\\alpha}(t) = \\frac{\\mathbf{\\omega}(t_2)-\\mathbf{\\omega}(t_1)}{t_2-t_1} = \\frac{\\Delta \\mathbf{\\omega}}{\\Delta t}$$\n", "\n", "\n", "Likewise, angular acceleration is the first-order derivative of the angular velocity or the second-order derivative of the angular position vector: \n", "\n", "\n", "$$ \\mathbf{\\alpha}(t) = \\frac{d\\mathbf{\\omega}(t)}{dt} = \\frac{d^2\\mathbf{\\theta}(t)}{dt^2} $$\n", "\n", "\n", "The direction of the angular velocity and acceleration vectors is the same as the angular position (perpendicular to the plane of rotation) and the sense is given by the right-hand rule." ] }, { "cell_type": "markdown", "metadata": { "id": "ol0tvt7Yk31i" }, "source": [ "### The antiderivative\n", "\n", "As the angular acceleration is the derivative of the angular velocity which is the derivative of angular position, the inverse mathematical operation is the [antiderivative](http://en.wikipedia.org/wiki/Antiderivative) (or integral):\n", "\n", "\n", "$$ \\mathbf{\\theta}(t) = \\mathbf{\\theta}_0 + \\int \\mathbf{\\omega}(t) dt $$\n", "\n", "$$ \\mathbf{\\omega}(t) = \\mathbf{\\omega}_0 + \\int \\mathbf{\\alpha}(t) dt $$\n", "" ] }, { "cell_type": "markdown", "metadata": { "id": "BZys4xBhk8-Z" }, "source": [ "## Relationship between linear and angular kinematics\n", "\n", "Consider a particle rotating around a point at a fixed distance `r` (circular motion), as the particle moves along the circle, it travels an arc of length `s`. \n", "The angular position of the particle is:\n", "\n", "\n", "$$ \\theta = \\frac{s}{r} $$\n", "\n", "\n", "Which is in fact similar to the definition of the angular measure radian:\n", "\n", "
Figure. An arc of a circle with the same length as the radius of that circle corresponds to an angle of 1 radian (image from Wikipedia).
" ] }, { "cell_type": "markdown", "metadata": { "id": "l9BWl2kLlGkd" }, "source": [ "Then, the distance travelled by the particle is the arc length:\n", "\n", "\n", "$$ s = r\\theta $$\n", "\n", "\n", "As the radius is constant, the relation between linear and angular velocity and acceleration is straightfoward:\n", "\n", "\n", "$$ v = \\frac{ds}{dt} = r\\frac{d\\theta}{dt} = r\\omega $$\n", "\n", "$$ a = \\frac{dv}{dt} = r\\frac{d\\omega}{dt} = r\\alpha $$\n", "" ] }, { "cell_type": "markdown", "metadata": { "id": "T9Q-JU9blLJS" }, "source": [ "## Further reading\n", "\n", "- Read pages 718-742 of the 15th chapter of the [Ruina and Rudra's book] (http://ruina.tam.cornell.edu/Book/index.html) about circular motion of particle. " ] }, { "cell_type": "markdown", "metadata": { "id": "VQOn2E5FlaPo" }, "source": [ "## Video lectures on the Internet\n", "\n", "- Khan Academy: [Uniform Circular Motion Introduction](https://www.khanacademy.org/science/ap-physics-1/ap-centripetal-force-and-gravitation)\n", "- [Angular Motion and Torque](https://www.youtube.com/watch?v=jNc2SflUl9U)\n", "- [Rotational Motion Physics, Basic Introduction, Angular Velocity & Tangential Acceleration](https://www.youtube.com/watch?v=WQ9AH2S8B6Y) " ] }, { "cell_type": "markdown", "metadata": { "id": "qn_mn7izlmHv" }, "source": [ "## Problems\n", "\n", "1. A gymnast performs giant circles around the horizontal bar (with the official dimensions for Artistic Gymnastics) at a constant rate of one circle every 2 s and consider that his center of mass is 1 m distant from the bar. At the lowest point (exactly beneath the bigh bar), the gymnast releases the bar, moves forward, and lands standing on the ground. \n", " a) Calculate the angular and lineat velocity of the gymnast's center of mass at the point of release. \n", " b) Calculate the horizontal distance travelled by the gymnast's center of mass. \n", "\n", "2. With the data from Table A1 of Winter (2009) and the convention for the sagital joint angles of the lower limb: \n", " a. Calculate and plot the angles of the foot, leg, and thigh segments. \n", " b. Calculate and plot the angles of the ankle, knee, and hip joint. \n", " c. Calculate and plot the velocities and accelerations for the angles calculated in B. \n", " d. Compare the ankle angle using the two different conventions described by Winter (2009), that is, defining the foot segment with the MT5 or the TOE marker. \n", " e. Knowing that a stride period corresponds to the data between frames 1 and 70 (two subsequents toe-off by the right foot), can you suggest a possible candidate for automatic determination of a stride? Hint: look at the vertical displacement and acceleration of the heel marker. \n", " \n", " [Clik here for the data from Table A.1 (Winter, 2009)](./../data/WinterTableA1.txt) from [Winter's book student site](http://bcs.wiley.com/he-bcs/Books?action=index&bcsId=5453&itemId=0470398183). \n", " \n", " Example: load data and plot the markers' positions:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 370 }, "id": "BBFKdpVllr_q", "outputId": "5d80eaa3-0f4e-45ad-bfe4-54b914d5d9b0" }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "filename = './../data/WinterTableA1.txt'\n", "data = np.loadtxt(filename, skiprows=2, unpack=False)\n", "markers = ['RIB CAGE', 'HIP', 'KNEE', 'FIBULA', 'ANKLE', 'HEEL', 'MT5', 'TOE']\n", "\n", "fig = plt.figure(figsize=(10, 6))\n", "\n", "ax = plt.subplot2grid((2,2),(0, 0))\n", "ax.plot(data[: ,1], data[:, 2::2])\n", "ax.set_xlabel('Time [s]', fontsize=14)\n", "ax.set_ylabel('Horizontal [cm]', fontsize=14)\n", "\n", "ax = plt.subplot2grid((2, 2),(0, 1))\n", "ax.plot(data[: ,1], data[:, 3::2])\n", "ax.set_xlabel('Time [s]', fontsize=14)\n", "ax.set_ylabel('Vertical [cm]', fontsize=14)\n", "\n", "ax = plt.subplot2grid((2, 2), (1, 0), colspan=2)\n", "ax.plot(data[:, 2::2], data[:, 3::2])\n", "ax.set_xlabel('Horizontal [cm]', fontsize=14)\n", "ax.set_ylabel('Vertical [cm]', fontsize=14)\n", "plt.suptitle('Table A.1 (Winter, 2009): female, 22 yrs, 55.7 kg, 156 cm, ' \\\n", " 'fast cadence (115 steps/min)', y=1.02, fontsize=14)\n", "ax.legend(markers, loc=\"upper right\", title='Markers')\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": { "id": "zKR_iv2vlvCS" }, "source": [ "## References\n", "\n", "- Winter DA (2009) [Biomechanics and motor control of human movement](http://books.google.com.br/books?id=_bFHL08IWfwC). 4th edition. Hoboken, EUA: Wiley." ] } ], "metadata": { "colab": { "name": "TESTE_ANGULAR_KINEMATICS.ipynb", "provenance": [] }, "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": "3.9.13" } }, "nbformat": 4, "nbformat_minor": 4 }