Datasets
Models
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| a | b/arm_model/model.ipynb | ||
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| 1 | { |
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| 2 | "cells": [ |
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| 3 | { |
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| 4 | "cell_type": "markdown", |
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| 5 | "metadata": { |
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| 6 | "ein.tags": "worksheet-0", |
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| 7 | "slideshow": { |
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| 8 | "slide_type": "-" |
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| 9 | } |
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| 10 | }, |
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| 11 | "source": [ |
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| 12 | "# Simplified Arm Mode" |
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| 13 | ] |
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| 14 | }, |
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| 15 | { |
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| 16 | "cell_type": "markdown", |
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| 17 | "metadata": { |
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| 18 | "ein.tags": "worksheet-0", |
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| 19 | "slideshow": { |
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| 20 | "slide_type": "-" |
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| 21 | } |
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| 22 | }, |
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| 23 | "source": [ |
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| 24 | "## Introduction" |
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| 25 | ] |
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| 26 | }, |
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| 27 | { |
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| 28 | "cell_type": "markdown", |
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| 29 | "metadata": { |
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| 30 | "ein.tags": "worksheet-0", |
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| 31 | "slideshow": { |
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| 32 | "slide_type": "-" |
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| 33 | } |
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| 34 | }, |
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| 35 | "source": [ |
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| 36 | "This notebook presents the analytical derivations of the equations of motion for\n", |
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| 37 | "three degrees of freedom and nine muscles arm model, some of them being\n", |
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| 38 | "bi-articular, appropriately constructed to demonstrate both kinematic and\n", |
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| 39 | "dynamic redundancy (e.g. $d < n < m$). The model is inspired from [1] with some\n", |
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| 40 | "minor modifications and improvements." |
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| 41 | ] |
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| 42 | }, |
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| 43 | { |
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| 44 | "cell_type": "markdown", |
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| 45 | "metadata": { |
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| 46 | "ein.tags": "worksheet-0", |
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| 47 | "slideshow": { |
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| 48 | "slide_type": "-" |
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| 49 | } |
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| 50 | }, |
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| 51 | "source": [ |
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| 52 | "## Model Constants" |
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| 53 | ] |
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| 54 | }, |
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| 55 | { |
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| 56 | "cell_type": "markdown", |
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| 57 | "metadata": { |
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| 58 | "ein.tags": "worksheet-0", |
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| 59 | "slideshow": { |
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| 60 | "slide_type": "-" |
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| 61 | } |
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| 62 | }, |
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| 63 | "source": [ |
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| 64 | "Abbreviations:\n", |
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| 65 | "\n", |
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| 66 | "- DoFs: Degrees of Freedom\n", |
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| 67 | "- EoMs: Equations of Motion\n", |
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| 68 | "- KE: Kinetic Energy\n", |
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| 69 | "- PE: Potential Energy\n", |
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| 70 | "- CoM: center of mass\n", |
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| 71 | "\n", |
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| 72 | "The following constants are used in the model:\n", |
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| 73 | "\n", |
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| 74 | "- $m$ mass of a segment\n", |
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| 75 | "- $I_{z_i}$ inertia around $z$-axis\n", |
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| 76 | "- $L_i$ length of a segment\n", |
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| 77 | "- $L_{c_i}$ length of the CoM as defined in local frame of a body\n", |
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| 78 | "- $a_i$ muscle origin point as defined in the local frame of a body\n", |
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| 79 | "- $b_i$ muscle insertion point as defined in the local frame of a body\n", |
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| 80 | "- $g$ gravity\n", |
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| 81 | "- $q_i$ are the generalized coordinates\n", |
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| 82 | "- $u_i$ are the generalized speeds\n", |
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| 83 | "- $\\tau$ are the generalized forces\n", |
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| 84 | "\n", |
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| 85 | "Please note that there are some differences from [1]: 1) $L_{g_i} \\rightarrow\n", |
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| 86 | "L_{c_i}$, 2) $a_i$ is always the muscle origin, 3) $b_i$ is always the muscle\n", |
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| 87 | "insertion and 4) we don't use double indexing for the bi-articular muscles." |
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| 88 | ] |
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| 89 | }, |
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| 90 | { |
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| 91 | "cell_type": "code", |
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| 92 | "execution_count": 1, |
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| 93 | "metadata": { |
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| 94 | "autoscroll": false, |
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| 95 | "ein.hycell": false, |
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| 96 | "ein.tags": "worksheet-0", |
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| 97 | "slideshow": { |
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| 98 | "slide_type": "-" |
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| 99 | } |
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| 100 | }, |
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| 101 | "outputs": [ |
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| 102 | { |
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| 103 | "name": "stdout", |
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| 104 | "output_type": "stream", |
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| 105 | "text": [ |
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| 106 | "The autoreload extension is already loaded. To reload it, use:\n", |
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| 107 | " %reload_ext autoreload\n" |
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| 108 | ] |
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| 109 | } |
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| 110 | ], |
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| 111 | "source": [ |
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| 112 | "# notebook general configuration\n", |
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| 113 | "\n", |
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| 114 | "%load_ext autoreload\n", |
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| 115 | "%autoreload 2\n", |
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| 116 | "\n", |
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| 117 | "# imports and utilities\n", |
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| 118 | "import sympy as sp\n", |
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| 119 | "from IPython.display import display, Image\n", |
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| 120 | "sp.interactive.printing.init_printing()\n", |
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| 121 | "\n", |
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| 122 | "import logging\n", |
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| 123 | "logging.basicConfig(level=logging.INFO)\n", |
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| 124 | "\n", |
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| 125 | "# plot\n", |
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| 126 | "%matplotlib inline\n", |
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| 127 | "from matplotlib.pyplot import *\n", |
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| 128 | "rcParams['figure.figsize'] = (10.0, 6.0)\n", |
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| 129 | "\n", |
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| 130 | "# utility for displaying intermediate results\n", |
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| 131 | "enable_display = True\n", |
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| 132 | "def disp(*statement):\n", |
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| 133 | " if (enable_display):\n", |
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| 134 | " display(*statement)" |
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| 135 | ] |
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| 136 | }, |
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| 137 | { |
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| 138 | "cell_type": "code", |
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| 139 | "execution_count": 2, |
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| 140 | "metadata": { |
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| 141 | "autoscroll": false, |
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| 142 | "ein.hycell": false, |
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| 143 | "ein.tags": "worksheet-0", |
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| 144 | "slideshow": { |
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| 145 | "slide_type": "-" |
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| 146 | } |
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| 147 | }, |
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| 148 | "outputs": [ |
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| 149 | { |
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| 150 | "data": { |
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| 151 | "image/png": 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\n", |
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| 152 | "text/latex": [ |
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| 153 | "$$\\left \\{ Iz_{1} : 0.0141, \\quad Iz_{2} : 0.012, \\quad Iz_{3} : 0.001, \\quad L_{1} : 0.31, \\quad L_{2} : 0.27, \\quad L_{3} : 0.15, \\quad Lc_{1} : 0.165, \\quad Lc_{2} : 0.135, \\quad Lc_{3} : 0.075, \\quad a_{1} : 0.055, \\quad a_{2} : 0.055, \\quad a_{3} : 0.22, \\quad a_{4} : 0.24, \\quad a_{5} : 0.04, \\quad a_{6} : 0.04, \\quad a_{7} : 0.22, \\quad a_{8} : 0.06, \\quad a_{9} : 0.26, \\quad b_{1} : 0.08, \\quad b_{2} : 0.11, \\quad b_{3} : 0.03, \\quad b_{4} : 0.03, \\quad b_{5} : 0.045, \\quad b_{6} : 0.045, \\quad b_{7} : 0.048, \\quad b_{8} : 0.05, \\quad b_{9} : 0.03, \\quad g : 9.81, \\quad m_{1} : 1.93, \\quad m_{2} : 1.32, \\quad m_{3} : 0.35\\right \\}$$" |
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| 154 | ], |
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| 155 | "text/plain": [ |
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| 156 | "{Iz₁: 0.0141, Iz₂: 0.012, Iz₃: 0.001, L₁: 0.31, L₂: 0.27, L₃: 0.15, Lc₁: 0.165\n", |
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| 157 | ", Lc₂: 0.135, Lc₃: 0.075, a₁: 0.055, a₂: 0.055, a₃: 0.22, a₄: 0.24, a₅: 0.04, \n", |
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| 158 | "a₆: 0.04, a₇: 0.22, a₈: 0.06, a₉: 0.26, b₁: 0.08, b₂: 0.11, b₃: 0.03, b₄: 0.03\n", |
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| 159 | ", b₅: 0.045, b₆: 0.045, b₇: 0.048, b₈: 0.05, b₉: 0.03, g: 9.81, m₁: 1.93, m₂: \n", |
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| 160 | "1.32, m₃: 0.35}" |
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| 161 | ] |
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| 162 | }, |
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| 163 | "metadata": {}, |
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| 164 | "output_type": "display_data" |
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| 165 | } |
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| 166 | ], |
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| 167 | "source": [ |
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| 168 | "# construct model\n", |
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| 169 | "from model import ArmModel\n", |
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| 170 | "model = ArmModel(use_gravity=1, use_coordinate_limits=0, use_viscosity=0)\n", |
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| 171 | "\n", |
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| 172 | "disp(model.constants)" |
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| 173 | ] |
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| 174 | }, |
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| 175 | { |
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| 176 | "cell_type": "markdown", |
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| 177 | "metadata": { |
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| 178 | "ein.tags": "worksheet-0", |
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| 179 | "slideshow": { |
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| 180 | "slide_type": "-" |
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| 181 | } |
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| 182 | }, |
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| 183 | "source": [ |
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| 184 | "## Dynamics" |
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| 185 | ] |
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| 186 | }, |
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| 187 | { |
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| 188 | "cell_type": "markdown", |
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| 189 | "metadata": { |
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| 190 | "ein.tags": "worksheet-0", |
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| 191 | "slideshow": { |
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| 192 | "slide_type": "-" |
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| 193 | } |
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| 194 | }, |
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| 195 | "source": [ |
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| 196 | "The simplified arm model has three DoFs and nine muscles, some of them being\n", |
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| 197 | "bi-articular. The analytical expressions of the EoMs form is given by\n", |
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| 198 | "\n", |
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| 199 | "\n", |
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| 200 | "\\begin{equation}\\label{equ:eom-standard-form}\n", |
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| 201 | " M(q) \\ddot{q} + C(q, \\dot{q})\\dot{q} + \\tau_g(q) = \\tau\n", |
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| 202 | "\\end{equation}\n", |
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| 203 | "\n", |
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| 204 | "\n", |
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| 205 | "where $M \\in \\Re^{n \\times n}$ represents the inertia mass matrix, $n$ the DoFs\n", |
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| 206 | "of the model, $q, \\dot{q}, \\ddot{q} \\in \\Re^{n}$ the generalized coordinates and\n", |
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| 207 | "their derivatives, $C \\in \\Re^{n \\times n}$ the Coriolis and centrifugal matrix,\n", |
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| 208 | "$\\tau_g \\in \\Re^{n}$ the gravity contribution and $\\tau$ the specified\n", |
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| 209 | "generalized forces.\n", |
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| 210 | "\n", |
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| 211 | "As the model is an open kinematic chain a simple procedure to derive the EoMs\n", |
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| 212 | "can be followed. Assuming that the spatial velocity (translational, rotational)\n", |
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| 213 | "of each body segment is given by $u_b = [v, \\omega]^T \\in \\Re^{6 \\times 1}$, the\n", |
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| 214 | "KE of the system in body local coordinates is defined as\n", |
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| 215 | "\n", |
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| 216 | "\n", |
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| 217 | "\\begin{equation}\\label{equ:spatial-ke}\n", |
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| 218 | " K = \\frac{1}{2} \\sum\\limits_{i=1}^{n_b} (m_i v_i^2 + I_i \\omega_i^2) =\n", |
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| 219 | " \\frac{1}{2} \\sum\\limits_{i=1}^{n_b} u_i^T M_i u_i\n", |
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| 220 | "\\end{equation}\n", |
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| 221 | " \n", |
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| 222 | "\n", |
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| 223 | "where $M_i = diag(m_i, m_i, m_i, [I_i]_{3 \\times 3}) \\in \\Re^{6 \\times 6}$\n", |
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| 224 | "denotes the spatial inertia mass matrix, $m_i$ the mass and $I_i \\in \\Re^{3\n", |
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| 225 | "\\times 3}$ the inertia matrix of body $i$. The spatial quantities are related\n", |
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| 226 | "to the generalized coordinates by the body Jacobian $u_b = J_b \\dot{q}, \\; J_b\n", |
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| 227 | "\\in \\Re^{6 \\times n}$. The total KE is coordinate invariant, thus it can be\n", |
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| 228 | "expressed in different coordinate system\n", |
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| 229 | " \n", |
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| 230 | "\n", |
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| 231 | "\\begin{equation}\\label{equ:ke-transformation}\n", |
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| 232 | " K = \\frac{1}{2} \\sum\\limits_{i=1}^{n_b} q^T J_i^T M_i J_i q\n", |
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| 233 | "\\end{equation}\n", |
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| 234 | "\n", |
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| 235 | "\n", |
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| 236 | "Following the above definition, the inertia mass matrix of the system can be\n", |
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| 237 | "written as\n", |
||
| 238 | "\n", |
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| 239 | " \n", |
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| 240 | "\\begin{equation}\\label{equ:mass-matrix}\n", |
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| 241 | " M(q) = \\sum\\limits_{i=1}^{n_b} J_i^T M_i J_i\n", |
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| 242 | "\\end{equation}\n", |
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| 243 | " \n", |
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| 244 | "\n", |
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| 245 | "Furthermore, the Coriolis and centrifugal forces $C(q, \\dot{q}) \\dot{q}$ can be\n", |
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| 246 | "determined directly from the inertia mass matrix\n", |
||
| 247 | "\n", |
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| 248 | "\n", |
||
| 249 | "\\begin{equation}\\label{equ:coriolis-matrix}\n", |
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| 250 | " C_{ij}(q, \\dot{q}) = \\sum\\limits_{k=1}^{n} \\Gamma_{ijk} \\; \\dot{q}_k, \\; i, j\n", |
||
| 251 | " \\in [1, \\dots n], \\;\n", |
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| 252 | " \\Gamma_{ijk} = \\frac{1}{2} (\n", |
||
| 253 | " \\frac{\\partial M_{ij}(q)}{\\partial q_k} +\n", |
||
| 254 | " \\frac{\\partial M_{ik}(q)}{\\partial q_j} -\n", |
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| 255 | " \\frac{\\partial M_{kj}(q)}{\\partial q_i})\n", |
||
| 256 | "\\end{equation}\n", |
||
| 257 | "\n", |
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| 258 | "\n", |
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| 259 | "where the functions $\\Gamma_{ijk}$ are called the Christoffel symbols. The\n", |
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| 260 | "gravity contribution can be determined from the PE function\n", |
||
| 261 | " \n", |
||
| 262 | "\n", |
||
| 263 | "\\begin{equation}\\label{equ:gravity-pe}\n", |
||
| 264 | " \\begin{gathered}\n", |
||
| 265 | " g(q) = \\frac{\\partial V(q)}{\\partial q}, \\; V(q) = \\sum\\limits_{i=1}^{n_b} m_i g h_i(q)\n", |
||
| 266 | " \\end{gathered}\n", |
||
| 267 | "\\end{equation}\n", |
||
| 268 | "\n", |
||
| 269 | "\n", |
||
| 270 | "where $h_i(q)$ denotes the vertical displacement of body $i$ with respect to the\n", |
||
| 271 | "ground. In this derivation we chose to collect all forces that act on the system\n", |
||
| 272 | "in the term $f(q, \\dot{q})$." |
||
| 273 | ] |
||
| 274 | }, |
||
| 275 | { |
||
| 276 | "cell_type": "code", |
||
| 277 | "execution_count": 3, |
||
| 278 | "metadata": { |
||
| 279 | "autoscroll": false, |
||
| 280 | "ein.hycell": false, |
||
| 281 | "ein.tags": "worksheet-0", |
||
| 282 | "slideshow": { |
||
| 283 | "slide_type": "-" |
||
| 284 | } |
||
| 285 | }, |
||
| 286 | "outputs": [ |
||
| 287 | { |
||
| 288 | "data": { |
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| 289 | "image/png": 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\n", |
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| 290 | "text/latex": [ |
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| 291 | "$$\\left [ \\left[\\begin{matrix}Lc_{1} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )}\\\\Lc_{1} \\sin{\\left (\\theta_{1}{\\left (t \\right )} \\right )}\\\\0\\\\0\\\\0\\\\\\theta_{1}{\\left (t \\right )}\\end{matrix}\\right], \\quad \\left[\\begin{matrix}L_{1} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + Lc_{2} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )}\\\\L_{1} \\sin{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + Lc_{2} \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )}\\\\0\\\\0\\\\0\\\\\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )}\\end{matrix}\\right], \\quad \\left[\\begin{matrix}L_{1} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + L_{2} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} + Lc_{3} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )}\\\\L_{1} \\sin{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + L_{2} \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} + Lc_{3} \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )}\\\\0\\\\0\\\\0\\\\\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )}\\end{matrix}\\right]\\right ]$$" |
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| 292 | ], |
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| 293 | "text/plain": [ |
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| 294 | "⎡⎡Lc₁⋅cos(θ₁(t))⎤ ⎡L₁⋅cos(θ₁(t)) + Lc₂⋅cos(θ₁(t) + θ₂(t))⎤ ⎡L₁⋅cos(θ₁(t)) + \n", |
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| 295 | "⎢⎢ ⎥ ⎢ ⎥ ⎢ \n", |
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| 296 | "⎢⎢Lc₁⋅sin(θ₁(t))⎥ ⎢L₁⋅sin(θ₁(t)) + Lc₂⋅sin(θ₁(t) + θ₂(t))⎥ ⎢L₁⋅sin(θ₁(t)) + \n", |
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| 297 | "⎢⎢ ⎥ ⎢ ⎥ ⎢ \n", |
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| 298 | "⎢⎢ 0 ⎥ ⎢ 0 ⎥ ⎢ \n", |
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| 299 | "⎢⎢ ⎥, ⎢ ⎥, ⎢ \n", |
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| 300 | "⎢⎢ 0 ⎥ ⎢ 0 ⎥ ⎢ \n", |
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| 301 | "⎢⎢ ⎥ ⎢ ⎥ ⎢ \n", |
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| 302 | "⎢⎢ 0 ⎥ ⎢ 0 ⎥ ⎢ \n", |
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| 303 | "⎢⎢ ⎥ ⎢ ⎥ ⎢ \n", |
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| 304 | "⎣⎣ θ₁(t) ⎦ ⎣ θ₁(t) + θ₂(t) ⎦ ⎣ \n", |
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| 305 | "\n", |
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| 306 | "L₂⋅cos(θ₁(t) + θ₂(t)) + Lc₃⋅cos(θ₁(t) + θ₂(t) + θ₃(t))⎤⎤\n", |
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| 307 | " ⎥⎥\n", |
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| 308 | "L₂⋅sin(θ₁(t) + θ₂(t)) + Lc₃⋅sin(θ₁(t) + θ₂(t) + θ₃(t))⎥⎥\n", |
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| 309 | " ⎥⎥\n", |
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| 310 | " 0 ⎥⎥\n", |
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| 311 | " ⎥⎥\n", |
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| 312 | " 0 ⎥⎥\n", |
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| 313 | " ⎥⎥\n", |
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| 314 | " 0 ⎥⎥\n", |
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| 315 | " ⎥⎥\n", |
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| 316 | " θ₁(t) + θ₂(t) + θ₃(t) ⎦⎦" |
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| 317 | ] |
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| 318 | }, |
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| 319 | "metadata": {}, |
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| 320 | "output_type": "display_data" |
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| 321 | }, |
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| 322 | { |
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| 323 | "data": { |
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| 324 | "image/png": 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\n", 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| 325 | "text/latex": [ |
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| 326 | "$$\\left [ \\left[\\begin{matrix}- Lc_{1} \\sin{\\left (\\theta_{1}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{1}{\\left (t \\right )}\\\\Lc_{1} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{1}{\\left (t \\right )}\\\\0\\\\0\\\\0\\\\\\frac{d}{d t} \\theta_{1}{\\left (t \\right )}\\end{matrix}\\right], \\quad \\left[\\begin{matrix}- L_{1} \\sin{\\left (\\theta_{1}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{1}{\\left (t \\right )} - Lc_{2} \\left(\\frac{d}{d t} \\theta_{1}{\\left (t \\right )} + \\frac{d}{d t} \\theta_{2}{\\left (t \\right )}\\right) \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )}\\\\L_{1} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{1}{\\left (t \\right )} + Lc_{2} \\left(\\frac{d}{d t} \\theta_{1}{\\left (t \\right )} + \\frac{d}{d t} \\theta_{2}{\\left (t \\right )}\\right) \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )}\\\\0\\\\0\\\\0\\\\\\frac{d}{d t} \\theta_{1}{\\left (t \\right )} + \\frac{d}{d t} \\theta_{2}{\\left (t \\right )}\\end{matrix}\\right], \\quad \\left[\\begin{matrix}- L_{1} \\sin{\\left (\\theta_{1}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{1}{\\left (t \\right )} - L_{2} \\left(\\frac{d}{d t} \\theta_{1}{\\left (t \\right )} + \\frac{d}{d t} \\theta_{2}{\\left (t \\right )}\\right) \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} - Lc_{3} \\left(\\frac{d}{d t} \\theta_{1}{\\left (t \\right )} + \\frac{d}{d t} \\theta_{2}{\\left (t \\right )} + \\frac{d}{d t} \\theta_{3}{\\left (t \\right )}\\right) \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )}\\\\L_{1} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{1}{\\left (t \\right )} + L_{2} \\left(\\frac{d}{d t} \\theta_{1}{\\left (t \\right )} + \\frac{d}{d t} \\theta_{2}{\\left (t \\right )}\\right) \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} + Lc_{3} \\left(\\frac{d}{d t} \\theta_{1}{\\left (t \\right )} + \\frac{d}{d t} \\theta_{2}{\\left (t \\right )} + \\frac{d}{d t} \\theta_{3}{\\left (t \\right )}\\right) \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )}\\\\0\\\\0\\\\0\\\\\\frac{d}{d t} \\theta_{1}{\\left (t \\right )} + \\frac{d}{d t} \\theta_{2}{\\left (t \\right )} + \\frac{d}{d t} \\theta_{3}{\\left (t \\right )}\\end{matrix}\\right]\\right ]$$" |
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| 327 | ], |
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| 328 | "text/plain": [ |
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| 329 | "⎡⎡ d ⎤ ⎡ d ⎛d d \n", |
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| 330 | "⎢⎢-Lc₁⋅sin(θ₁(t))⋅──(θ₁(t))⎥ ⎢- L₁⋅sin(θ₁(t))⋅──(θ₁(t)) - Lc₂⋅⎜──(θ₁(t)) + ──\n", |
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| 331 | "⎢⎢ dt ⎥ ⎢ dt ⎝dt dt\n", |
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| 332 | "⎢⎢ ⎥ ⎢ \n", |
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| 333 | "⎢⎢ d ⎥ ⎢ d ⎛d d \n", |
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| 334 | "⎢⎢Lc₁⋅cos(θ₁(t))⋅──(θ₁(t)) ⎥ ⎢ L₁⋅cos(θ₁(t))⋅──(θ₁(t)) + Lc₂⋅⎜──(θ₁(t)) + ──(\n", |
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| 335 | "⎢⎢ dt ⎥ ⎢ dt ⎝dt dt \n", |
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| 336 | "⎢⎢ ⎥ ⎢ \n", |
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| 337 | "⎢⎢ 0 ⎥, ⎢ 0 \n", |
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| 338 | "⎢⎢ ⎥ ⎢ \n", |
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| 339 | "⎢⎢ 0 ⎥ ⎢ 0 \n", |
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| 340 | "⎢⎢ ⎥ ⎢ \n", |
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| 341 | "⎢⎢ 0 ⎥ ⎢ 0 \n", |
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| 342 | "⎢⎢ ⎥ ⎢ \n", |
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| 343 | "⎢⎢ d ⎥ ⎢ d d \n", |
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| 344 | "⎢⎢ ──(θ₁(t)) ⎥ ⎢ ──(θ₁(t)) + ──(θ₂(t))\n", |
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| 345 | "⎣⎣ dt ⎦ ⎣ dt dt \n", |
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| 346 | "\n", |
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| 347 | " ⎞ ⎤ ⎡ d ⎛d d \n", |
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| 348 | "(θ₂(t))⎟⋅sin(θ₁(t) + θ₂(t))⎥ ⎢- L₁⋅sin(θ₁(t))⋅──(θ₁(t)) - L₂⋅⎜──(θ₁(t)) + ──(\n", |
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| 349 | " ⎠ ⎥ ⎢ dt ⎝dt dt \n", |
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| 350 | " ⎥ ⎢ \n", |
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| 351 | " ⎞ ⎥ ⎢ d ⎛d d \n", |
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| 352 | "θ₂(t))⎟⋅cos(θ₁(t) + θ₂(t)) ⎥ ⎢ L₁⋅cos(θ₁(t))⋅──(θ₁(t)) + L₂⋅⎜──(θ₁(t)) + ──(θ\n", |
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| 353 | " ⎠ ⎥ ⎢ dt ⎝dt dt \n", |
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| 354 | " ⎥ ⎢ \n", |
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| 355 | " ⎥, ⎢ \n", |
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| 356 | " ⎥ ⎢ \n", |
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| 357 | " ⎥ ⎢ \n", |
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| 358 | " ⎥ ⎢ \n", |
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| 359 | " ⎥ ⎢ \n", |
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| 360 | " ⎥ ⎢ \n", |
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| 361 | " ⎥ ⎢ \n", |
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| 362 | " ⎥ ⎢ \n", |
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| 363 | " ⎦ ⎣ \n", |
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| 364 | "\n", |
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| 365 | " ⎞ ⎛d d d ⎞ \n", |
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| 366 | "θ₂(t))⎟⋅sin(θ₁(t) + θ₂(t)) - Lc₃⋅⎜──(θ₁(t)) + ──(θ₂(t)) + ──(θ₃(t))⎟⋅sin(θ₁(t)\n", |
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| 367 | " ⎠ ⎝dt dt dt ⎠ \n", |
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| 368 | " \n", |
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| 369 | " ⎞ ⎛d d d ⎞ \n", |
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| 370 | "₂(t))⎟⋅cos(θ₁(t) + θ₂(t)) + Lc₃⋅⎜──(θ₁(t)) + ──(θ₂(t)) + ──(θ₃(t))⎟⋅cos(θ₁(t) \n", |
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| 371 | " ⎠ ⎝dt dt dt ⎠ \n", |
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| 372 | " \n", |
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| 373 | " 0 \n", |
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| 374 | " \n", |
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| 375 | " 0 \n", |
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| 376 | " \n", |
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| 377 | " 0 \n", |
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| 378 | " \n", |
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| 379 | " d d d \n", |
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| 380 | " ──(θ₁(t)) + ──(θ₂(t)) + ──(θ₃(t)) \n", |
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| 381 | " dt dt dt \n", |
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| 382 | "\n", |
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| 383 | " ⎤⎤\n", |
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| 384 | " + θ₂(t) + θ₃(t))⎥⎥\n", |
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| 385 | " ⎥⎥\n", |
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| 386 | " ⎥⎥\n", |
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| 387 | " ⎥⎥\n", |
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| 388 | "+ θ₂(t) + θ₃(t)) ⎥⎥\n", |
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| 389 | " ⎥⎥\n", |
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| 390 | " ⎥⎥\n", |
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| 391 | " ⎥⎥\n", |
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| 392 | " ⎥⎥\n", |
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| 393 | " ⎥⎥\n", |
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| 394 | " ⎥⎥\n", |
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| 395 | " ⎥⎥\n", |
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| 396 | " ⎥⎥\n", |
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| 397 | " ⎥⎥\n", |
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| 398 | " ⎥⎥\n", |
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| 399 | " ⎦⎦" |
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| 400 | ] |
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| 401 | }, |
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| 402 | "metadata": {}, |
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| 403 | "output_type": "display_data" |
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| 404 | }, |
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| 405 | { |
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| 406 | "data": { |
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\n", |
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| 408 | "text/latex": [ |
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| 409 | "$$\\left [ \\left[\\begin{matrix}- Lc_{1} \\sin{\\left (\\theta_{1}{\\left (t \\right )} \\right )} & 0 & 0\\\\Lc_{1} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\\\1 & 0 & 0\\end{matrix}\\right], \\quad \\left[\\begin{matrix}- L_{1} \\sin{\\left (\\theta_{1}{\\left (t \\right )} \\right )} - Lc_{2} \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} & - Lc_{2} \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} & 0\\\\L_{1} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + Lc_{2} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} & Lc_{2} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\\\1 & 1 & 0\\end{matrix}\\right], \\quad \\left[\\begin{matrix}- L_{1} \\sin{\\left (\\theta_{1}{\\left (t \\right )} \\right )} - L_{2} \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} - Lc_{3} \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} & - L_{2} \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} - Lc_{3} \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} & - Lc_{3} \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )}\\\\L_{1} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + L_{2} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} + Lc_{3} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} & L_{2} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} + Lc_{3} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} & Lc_{3} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )}\\\\0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\\\1 & 1 & 1\\end{matrix}\\right]\\right ]$$" |
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| 410 | ], |
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| 411 | "text/plain": [ |
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| 412 | "⎡⎡-Lc₁⋅sin(θ₁(t)) 0 0⎤ ⎡-L₁⋅sin(θ₁(t)) - Lc₂⋅sin(θ₁(t) + θ₂(t)) -Lc₂⋅sin(θ\n", |
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| 413 | "⎢⎢ ⎥ ⎢ \n", |
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| 414 | "⎢⎢Lc₁⋅cos(θ₁(t)) 0 0⎥ ⎢L₁⋅cos(θ₁(t)) + Lc₂⋅cos(θ₁(t) + θ₂(t)) Lc₂⋅cos(θ₁\n", |
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| 415 | "⎢⎢ ⎥ ⎢ \n", |
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| 416 | "⎢⎢ 0 0 0⎥ ⎢ 0 \n", |
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| 417 | "⎢⎢ ⎥, ⎢ \n", |
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| 418 | "⎢⎢ 0 0 0⎥ ⎢ 0 \n", |
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| 419 | "⎢⎢ ⎥ ⎢ \n", |
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| 420 | "⎢⎢ 0 0 0⎥ ⎢ 0 \n", |
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| 421 | "⎢⎢ ⎥ ⎢ \n", |
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| 422 | "⎣⎣ 1 0 0⎦ ⎣ 1 \n", |
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| 423 | "\n", |
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| 424 | "₁(t) + θ₂(t)) 0⎤ ⎡-L₁⋅sin(θ₁(t)) - L₂⋅sin(θ₁(t) + θ₂(t)) - Lc₃⋅sin(θ₁(t) + θ\n", |
||
| 425 | " ⎥ ⎢ \n", |
||
| 426 | "(t) + θ₂(t)) 0⎥ ⎢L₁⋅cos(θ₁(t)) + L₂⋅cos(θ₁(t) + θ₂(t)) + Lc₃⋅cos(θ₁(t) + θ₂\n", |
||
| 427 | " ⎥ ⎢ \n", |
||
| 428 | " 0 0⎥ ⎢ 0 \n", |
||
| 429 | " ⎥, ⎢ \n", |
||
| 430 | " 0 0⎥ ⎢ 0 \n", |
||
| 431 | " ⎥ ⎢ \n", |
||
| 432 | " 0 0⎥ ⎢ 0 \n", |
||
| 433 | " ⎥ ⎢ \n", |
||
| 434 | " 1 0⎦ ⎣ 1 \n", |
||
| 435 | "\n", |
||
| 436 | "₂(t) + θ₃(t)) -L₂⋅sin(θ₁(t) + θ₂(t)) - Lc₃⋅sin(θ₁(t) + θ₂(t) + θ₃(t)) -Lc₃⋅s\n", |
||
| 437 | " \n", |
||
| 438 | "(t) + θ₃(t)) L₂⋅cos(θ₁(t) + θ₂(t)) + Lc₃⋅cos(θ₁(t) + θ₂(t) + θ₃(t)) Lc₃⋅co\n", |
||
| 439 | " \n", |
||
| 440 | " 0 \n", |
||
| 441 | " \n", |
||
| 442 | " 0 \n", |
||
| 443 | " \n", |
||
| 444 | " 0 \n", |
||
| 445 | " \n", |
||
| 446 | " 1 \n", |
||
| 447 | "\n", |
||
| 448 | "in(θ₁(t) + θ₂(t) + θ₃(t))⎤⎤\n", |
||
| 449 | " ⎥⎥\n", |
||
| 450 | "s(θ₁(t) + θ₂(t) + θ₃(t)) ⎥⎥\n", |
||
| 451 | " ⎥⎥\n", |
||
| 452 | " 0 ⎥⎥\n", |
||
| 453 | " ⎥⎥\n", |
||
| 454 | " 0 ⎥⎥\n", |
||
| 455 | " ⎥⎥\n", |
||
| 456 | " 0 ⎥⎥\n", |
||
| 457 | " ⎥⎥\n", |
||
| 458 | " 1 ⎦⎦" |
||
| 459 | ] |
||
| 460 | }, |
||
| 461 | "metadata": {}, |
||
| 462 | "output_type": "display_data" |
||
| 463 | } |
||
| 464 | ], |
||
| 465 | "source": [ |
||
| 466 | "# define the spatial coordinates for the CoM in terms of Lcs' and q's\n", |
||
| 467 | "disp(model.xc[1:])\n", |
||
| 468 | "# define CoM spatial velocities\n", |
||
| 469 | "disp(model.vc[1:])\n", |
||
| 470 | "#define CoM Jacobian\n", |
||
| 471 | "disp(model.Jc[1:])" |
||
| 472 | ] |
||
| 473 | }, |
||
| 474 | { |
||
| 475 | "cell_type": "code", |
||
| 476 | "execution_count": 4, |
||
| 477 | "metadata": { |
||
| 478 | "autoscroll": false, |
||
| 479 | "ein.hycell": false, |
||
| 480 | "ein.tags": "worksheet-0", |
||
| 481 | "slideshow": { |
||
| 482 | "slide_type": "-" |
||
| 483 | } |
||
| 484 | }, |
||
| 485 | "outputs": [ |
||
| 486 | { |
||
| 487 | "data": { |
||
| 488 | "text/plain": [ |
||
| 489 | "'M_{1,1} = '" |
||
| 490 | ] |
||
| 491 | }, |
||
| 492 | "metadata": {}, |
||
| 493 | "output_type": "display_data" |
||
| 494 | }, |
||
| 495 | { |
||
| 496 | "data": { |
||
| 497 | "image/png": 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Mxu1DPWprEGkVhaOn3BeswNqat2Hojr7UswtQF2jup7BL8wNBXyLg7TN9QTxlkN5yn7cCZ8x6Gwb1/R9hiq4s0AB/vwAAAABJRU5ErkJggg==\n", |
||
| 498 | "text/latex": [ |
||
| 499 | "$$Iz_{1} + Iz_{2} + Iz_{3} + L_{1}^{2} m_{2} + L_{1}^{2} m_{3} + 2 L_{1} L_{2} m_{3} \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + 2 L_{1} Lc_{2} m_{2} \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + 2 L_{1} Lc_{3} m_{3} \\cos{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} + L_{2}^{2} m_{3} + 2 L_{2} Lc_{3} m_{3} \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + Lc_{1}^{2} m_{1} + Lc_{2}^{2} m_{2} + Lc_{3}^{2} m_{3}$$" |
||
| 500 | ], |
||
| 501 | "text/plain": [ |
||
| 502 | " 2 2 \n", |
||
| 503 | "Iz₁ + Iz₂ + Iz₃ + L₁ ⋅m₂ + L₁ ⋅m₃ + 2⋅L₁⋅L₂⋅m₃⋅cos(θ₂(t)) + 2⋅L₁⋅Lc₂⋅m₂⋅cos(θ₂\n", |
||
| 504 | "\n", |
||
| 505 | " 2 2\n", |
||
| 506 | "(t)) + 2⋅L₁⋅Lc₃⋅m₃⋅cos(θ₂(t) + θ₃(t)) + L₂ ⋅m₃ + 2⋅L₂⋅Lc₃⋅m₃⋅cos(θ₃(t)) + Lc₁ \n", |
||
| 507 | "\n", |
||
| 508 | " 2 2 \n", |
||
| 509 | "⋅m₁ + Lc₂ ⋅m₂ + Lc₃ ⋅m₃" |
||
| 510 | ] |
||
| 511 | }, |
||
| 512 | "metadata": {}, |
||
| 513 | "output_type": "display_data" |
||
| 514 | }, |
||
| 515 | { |
||
| 516 | "data": { |
||
| 517 | "text/plain": [ |
||
| 518 | "'M_{1,2} = '" |
||
| 519 | ] |
||
| 520 | }, |
||
| 521 | "metadata": {}, |
||
| 522 | "output_type": "display_data" |
||
| 523 | }, |
||
| 524 | { |
||
| 525 | "data": { |
||
| 526 | "image/png": "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\n", |
||
| 527 | "text/latex": [ |
||
| 528 | "$$Iz_{2} + Iz_{3} + L_{1} L_{2} m_{3} \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + L_{1} Lc_{2} m_{2} \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + L_{1} Lc_{3} m_{3} \\cos{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} + L_{2}^{2} m_{3} + 2 L_{2} Lc_{3} m_{3} \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + Lc_{2}^{2} m_{2} + Lc_{3}^{2} m_{3}$$" |
||
| 529 | ], |
||
| 530 | "text/plain": [ |
||
| 531 | " \n", |
||
| 532 | "Iz₂ + Iz₃ + L₁⋅L₂⋅m₃⋅cos(θ₂(t)) + L₁⋅Lc₂⋅m₂⋅cos(θ₂(t)) + L₁⋅Lc₃⋅m₃⋅cos(θ₂(t) +\n", |
||
| 533 | "\n", |
||
| 534 | " 2 2 2 \n", |
||
| 535 | " θ₃(t)) + L₂ ⋅m₃ + 2⋅L₂⋅Lc₃⋅m₃⋅cos(θ₃(t)) + Lc₂ ⋅m₂ + Lc₃ ⋅m₃" |
||
| 536 | ] |
||
| 537 | }, |
||
| 538 | "metadata": {}, |
||
| 539 | "output_type": "display_data" |
||
| 540 | }, |
||
| 541 | { |
||
| 542 | "data": { |
||
| 543 | "text/plain": [ |
||
| 544 | "'M_{1,3} = '" |
||
| 545 | ] |
||
| 546 | }, |
||
| 547 | "metadata": {}, |
||
| 548 | "output_type": "display_data" |
||
| 549 | }, |
||
| 550 | { |
||
| 551 | "data": { |
||
| 552 | "image/png": "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\n", |
||
| 553 | "text/latex": [ |
||
| 554 | "$$Iz_{3} + L_{1} Lc_{3} m_{3} \\cos{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} + L_{2} Lc_{3} m_{3} \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + Lc_{3}^{2} m_{3}$$" |
||
| 555 | ], |
||
| 556 | "text/plain": [ |
||
| 557 | " 2 \n", |
||
| 558 | "Iz₃ + L₁⋅Lc₃⋅m₃⋅cos(θ₂(t) + θ₃(t)) + L₂⋅Lc₃⋅m₃⋅cos(θ₃(t)) + Lc₃ ⋅m₃" |
||
| 559 | ] |
||
| 560 | }, |
||
| 561 | "metadata": {}, |
||
| 562 | "output_type": "display_data" |
||
| 563 | }, |
||
| 564 | { |
||
| 565 | "data": { |
||
| 566 | "text/plain": [ |
||
| 567 | "'M_{2,1} = '" |
||
| 568 | ] |
||
| 569 | }, |
||
| 570 | "metadata": {}, |
||
| 571 | "output_type": "display_data" |
||
| 572 | }, |
||
| 573 | { |
||
| 574 | "data": { |
||
| 575 | "image/png": "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\n", |
||
| 576 | "text/latex": [ |
||
| 577 | "$$Iz_{2} + Iz_{3} + L_{1} L_{2} m_{3} \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + L_{1} Lc_{2} m_{2} \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + L_{1} Lc_{3} m_{3} \\cos{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} + L_{2}^{2} m_{3} + 2 L_{2} Lc_{3} m_{3} \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + Lc_{2}^{2} m_{2} + Lc_{3}^{2} m_{3}$$" |
||
| 578 | ], |
||
| 579 | "text/plain": [ |
||
| 580 | " \n", |
||
| 581 | "Iz₂ + Iz₃ + L₁⋅L₂⋅m₃⋅cos(θ₂(t)) + L₁⋅Lc₂⋅m₂⋅cos(θ₂(t)) + L₁⋅Lc₃⋅m₃⋅cos(θ₂(t) +\n", |
||
| 582 | "\n", |
||
| 583 | " 2 2 2 \n", |
||
| 584 | " θ₃(t)) + L₂ ⋅m₃ + 2⋅L₂⋅Lc₃⋅m₃⋅cos(θ₃(t)) + Lc₂ ⋅m₂ + Lc₃ ⋅m₃" |
||
| 585 | ] |
||
| 586 | }, |
||
| 587 | "metadata": {}, |
||
| 588 | "output_type": "display_data" |
||
| 589 | }, |
||
| 590 | { |
||
| 591 | "data": { |
||
| 592 | "text/plain": [ |
||
| 593 | "'M_{2,2} = '" |
||
| 594 | ] |
||
| 595 | }, |
||
| 596 | "metadata": {}, |
||
| 597 | "output_type": "display_data" |
||
| 598 | }, |
||
| 599 | { |
||
| 600 | "data": { |
||
| 601 | "image/png": "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\n", |
||
| 602 | "text/latex": [ |
||
| 603 | "$$Iz_{2} + Iz_{3} + L_{2}^{2} m_{3} + 2 L_{2} Lc_{3} m_{3} \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + Lc_{2}^{2} m_{2} + Lc_{3}^{2} m_{3}$$" |
||
| 604 | ], |
||
| 605 | "text/plain": [ |
||
| 606 | " 2 2 2 \n", |
||
| 607 | "Iz₂ + Iz₃ + L₂ ⋅m₃ + 2⋅L₂⋅Lc₃⋅m₃⋅cos(θ₃(t)) + Lc₂ ⋅m₂ + Lc₃ ⋅m₃" |
||
| 608 | ] |
||
| 609 | }, |
||
| 610 | "metadata": {}, |
||
| 611 | "output_type": "display_data" |
||
| 612 | }, |
||
| 613 | { |
||
| 614 | "data": { |
||
| 615 | "text/plain": [ |
||
| 616 | "'M_{2,3} = '" |
||
| 617 | ] |
||
| 618 | }, |
||
| 619 | "metadata": {}, |
||
| 620 | "output_type": "display_data" |
||
| 621 | }, |
||
| 622 | { |
||
| 623 | "data": { |
||
| 624 | "image/png": "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\n", |
||
| 625 | "text/latex": [ |
||
| 626 | "$$Iz_{3} + L_{2} Lc_{3} m_{3} \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + Lc_{3}^{2} m_{3}$$" |
||
| 627 | ], |
||
| 628 | "text/plain": [ |
||
| 629 | " 2 \n", |
||
| 630 | "Iz₃ + L₂⋅Lc₃⋅m₃⋅cos(θ₃(t)) + Lc₃ ⋅m₃" |
||
| 631 | ] |
||
| 632 | }, |
||
| 633 | "metadata": {}, |
||
| 634 | "output_type": "display_data" |
||
| 635 | }, |
||
| 636 | { |
||
| 637 | "data": { |
||
| 638 | "text/plain": [ |
||
| 639 | "'M_{3,1} = '" |
||
| 640 | ] |
||
| 641 | }, |
||
| 642 | "metadata": {}, |
||
| 643 | "output_type": "display_data" |
||
| 644 | }, |
||
| 645 | { |
||
| 646 | "data": { |
||
| 647 | "image/png": "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\n", |
||
| 648 | "text/latex": [ |
||
| 649 | "$$Iz_{3} + L_{1} Lc_{3} m_{3} \\cos{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} + L_{2} Lc_{3} m_{3} \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + Lc_{3}^{2} m_{3}$$" |
||
| 650 | ], |
||
| 651 | "text/plain": [ |
||
| 652 | " 2 \n", |
||
| 653 | "Iz₃ + L₁⋅Lc₃⋅m₃⋅cos(θ₂(t) + θ₃(t)) + L₂⋅Lc₃⋅m₃⋅cos(θ₃(t)) + Lc₃ ⋅m₃" |
||
| 654 | ] |
||
| 655 | }, |
||
| 656 | "metadata": {}, |
||
| 657 | "output_type": "display_data" |
||
| 658 | }, |
||
| 659 | { |
||
| 660 | "data": { |
||
| 661 | "text/plain": [ |
||
| 662 | "'M_{3,2} = '" |
||
| 663 | ] |
||
| 664 | }, |
||
| 665 | "metadata": {}, |
||
| 666 | "output_type": "display_data" |
||
| 667 | }, |
||
| 668 | { |
||
| 669 | "data": { |
||
| 670 | "image/png": "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\n", |
||
| 671 | "text/latex": [ |
||
| 672 | "$$Iz_{3} + L_{2} Lc_{3} m_{3} \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + Lc_{3}^{2} m_{3}$$" |
||
| 673 | ], |
||
| 674 | "text/plain": [ |
||
| 675 | " 2 \n", |
||
| 676 | "Iz₃ + L₂⋅Lc₃⋅m₃⋅cos(θ₃(t)) + Lc₃ ⋅m₃" |
||
| 677 | ] |
||
| 678 | }, |
||
| 679 | "metadata": {}, |
||
| 680 | "output_type": "display_data" |
||
| 681 | }, |
||
| 682 | { |
||
| 683 | "data": { |
||
| 684 | "text/plain": [ |
||
| 685 | "'M_{3,3} = '" |
||
| 686 | ] |
||
| 687 | }, |
||
| 688 | "metadata": {}, |
||
| 689 | "output_type": "display_data" |
||
| 690 | }, |
||
| 691 | { |
||
| 692 | "data": { |
||
| 693 | "image/png": "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\n", |
||
| 694 | "text/latex": [ |
||
| 695 | "$$Iz_{3} + Lc_{3}^{2} m_{3}$$" |
||
| 696 | ], |
||
| 697 | "text/plain": [ |
||
| 698 | " 2 \n", |
||
| 699 | "Iz₃ + Lc₃ ⋅m₃" |
||
| 700 | ] |
||
| 701 | }, |
||
| 702 | "metadata": {}, |
||
| 703 | "output_type": "display_data" |
||
| 704 | } |
||
| 705 | ], |
||
| 706 | "source": [ |
||
| 707 | "# generate the inertial mass matrix\n", |
||
| 708 | "M = model.M\n", |
||
| 709 | "for i in range(0, M.shape[0]):\n", |
||
| 710 | " for j in range(0, M.shape[1]):\n", |
||
| 711 | " disp('M_{' + str(i + 1) + ',' + str(j + 1) + '} = ', M[i, j])" |
||
| 712 | ] |
||
| 713 | }, |
||
| 714 | { |
||
| 715 | "cell_type": "code", |
||
| 716 | "execution_count": 5, |
||
| 717 | "metadata": { |
||
| 718 | "autoscroll": false, |
||
| 719 | "ein.hycell": false, |
||
| 720 | "ein.tags": "worksheet-0", |
||
| 721 | "slideshow": { |
||
| 722 | "slide_type": "-" |
||
| 723 | } |
||
| 724 | }, |
||
| 725 | "outputs": [ |
||
| 726 | { |
||
| 727 | "data": { |
||
| 728 | "text/plain": [ |
||
| 729 | "'f_1 = '" |
||
| 730 | ] |
||
| 731 | }, |
||
| 732 | "metadata": {}, |
||
| 733 | "output_type": "display_data" |
||
| 734 | }, |
||
| 735 | { |
||
| 736 | "data": { |
||
| 737 | "image/png": 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\n", 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| 738 | "text/latex": [ |
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| 739 | "$$Lc_{1} g m_{1} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + g m_{2} \\left(L_{1} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + Lc_{2} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )}\\right) + g m_{3} \\left(L_{1} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + L_{2} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} + Lc_{3} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )}\\right) - 2 L_{1} L_{2} m_{3} \\sin{\\left (\\theta_{2}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{1}{\\left (t \\right )} \\frac{d}{d t} \\theta_{2}{\\left (t \\right )} + L_{1} L_{2} m_{3} \\sin{\\left (\\theta_{2}{\\left (t \\right )} \\right )} \\left(\\frac{d}{d t} \\theta_{2}{\\left (t \\right )}\\right)^{2} + 2 L_{1} Lc_{2} m_{2} \\sin{\\left (\\theta_{2}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{1}{\\left (t \\right )} \\frac{d}{d t} \\theta_{2}{\\left (t \\right )} + L_{1} Lc_{2} m_{2} \\sin{\\left (\\theta_{2}{\\left (t \\right )} \\right )} \\left(\\frac{d}{d t} \\theta_{2}{\\left (t \\right )}\\right)^{2} + 2 L_{1} Lc_{3} m_{3} \\sin{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{1}{\\left (t \\right )} \\frac{d}{d t} \\theta_{2}{\\left (t \\right )} + 2 L_{1} Lc_{3} m_{3} \\sin{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{1}{\\left (t \\right )} \\frac{d}{d t} \\theta_{3}{\\left (t \\right )} + L_{1} Lc_{3} m_{3} \\sin{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} \\left(\\frac{d}{d t} \\theta_{2}{\\left (t \\right )}\\right)^{2} + 2 L_{1} Lc_{3} m_{3} \\sin{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{2}{\\left (t \\right )} \\frac{d}{d t} \\theta_{3}{\\left (t \\right )} + L_{1} Lc_{3} m_{3} \\sin{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} \\left(\\frac{d}{d t} \\theta_{3}{\\left (t \\right )}\\right)^{2} + 2 L_{2} Lc_{3} m_{3} \\sin{\\left (\\theta_{3}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{1}{\\left (t \\right )} \\frac{d}{d t} \\theta_{3}{\\left (t \\right )} + 2 L_{2} Lc_{3} m_{3} \\sin{\\left (\\theta_{3}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{2}{\\left (t \\right )} \\frac{d}{d t} \\theta_{3}{\\left (t \\right )} + L_{2} Lc_{3} m_{3} \\sin{\\left (\\theta_{3}{\\left (t \\right )} \\right )} \\left(\\frac{d}{d t} \\theta_{3}{\\left (t \\right )}\\right)^{2}$$" |
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| 740 | ], |
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| 741 | "text/plain": [ |
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| 742 | " \n", |
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| 743 | " \n", |
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| 744 | "Lc₁⋅g⋅m₁⋅cos(θ₁(t)) + g⋅m₂⋅(L₁⋅cos(θ₁(t)) + Lc₂⋅cos(θ₁(t) + θ₂(t))) + g⋅m₃⋅(L₁\n", |
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| 745 | " \n", |
||
| 746 | "\n", |
||
| 747 | " \n", |
||
| 748 | " \n", |
||
| 749 | "⋅cos(θ₁(t)) + L₂⋅cos(θ₁(t) + θ₂(t)) + Lc₃⋅cos(θ₁(t) + θ₂(t) + θ₃(t))) - 2⋅L₁⋅L\n", |
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| 750 | " \n", |
||
| 751 | "\n", |
||
| 752 | " 2 \n", |
||
| 753 | " d d ⎛d ⎞ \n", |
||
| 754 | "₂⋅m₃⋅sin(θ₂(t))⋅──(θ₁(t))⋅──(θ₂(t)) + L₁⋅L₂⋅m₃⋅sin(θ₂(t))⋅⎜──(θ₂(t))⎟ + 2⋅L₁⋅\n", |
||
| 755 | " dt dt ⎝dt ⎠ \n", |
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| 756 | "\n", |
||
| 757 | " 2 \n", |
||
| 758 | " d d ⎛d ⎞ \n", |
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| 759 | "Lc₂⋅m₂⋅sin(θ₂(t))⋅──(θ₁(t))⋅──(θ₂(t)) + L₁⋅Lc₂⋅m₂⋅sin(θ₂(t))⋅⎜──(θ₂(t))⎟ + 2⋅\n", |
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| 760 | " dt dt ⎝dt ⎠ \n", |
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| 761 | "\n", |
||
| 762 | " \n", |
||
| 763 | " d d \n", |
||
| 764 | "L₁⋅Lc₃⋅m₃⋅sin(θ₂(t) + θ₃(t))⋅──(θ₁(t))⋅──(θ₂(t)) + 2⋅L₁⋅Lc₃⋅m₃⋅sin(θ₂(t) + θ₃(\n", |
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| 765 | " dt dt \n", |
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| 766 | "\n", |
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| 767 | " 2 \n", |
||
| 768 | " d d ⎛d ⎞ \n", |
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| 769 | "t))⋅──(θ₁(t))⋅──(θ₃(t)) + L₁⋅Lc₃⋅m₃⋅sin(θ₂(t) + θ₃(t))⋅⎜──(θ₂(t))⎟ + 2⋅L₁⋅Lc₃\n", |
||
| 770 | " dt dt ⎝dt ⎠ \n", |
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| 771 | "\n", |
||
| 772 | " \n", |
||
| 773 | " d d ⎛d \n", |
||
| 774 | "⋅m₃⋅sin(θ₂(t) + θ₃(t))⋅──(θ₂(t))⋅──(θ₃(t)) + L₁⋅Lc₃⋅m₃⋅sin(θ₂(t) + θ₃(t))⋅⎜──(\n", |
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| 775 | " dt dt ⎝dt \n", |
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| 776 | "\n", |
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| 777 | " 2 \n", |
||
| 778 | " ⎞ d d \n", |
||
| 779 | "θ₃(t))⎟ + 2⋅L₂⋅Lc₃⋅m₃⋅sin(θ₃(t))⋅──(θ₁(t))⋅──(θ₃(t)) + 2⋅L₂⋅Lc₃⋅m₃⋅sin(θ₃(t))\n", |
||
| 780 | " ⎠ dt dt \n", |
||
| 781 | "\n", |
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| 782 | " 2\n", |
||
| 783 | " d d ⎛d ⎞ \n", |
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| 784 | "⋅──(θ₂(t))⋅──(θ₃(t)) + L₂⋅Lc₃⋅m₃⋅sin(θ₃(t))⋅⎜──(θ₃(t))⎟ \n", |
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| 785 | " dt dt ⎝dt ⎠ " |
||
| 786 | ] |
||
| 787 | }, |
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| 788 | "metadata": {}, |
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| 789 | "output_type": "display_data" |
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| 790 | }, |
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| 791 | { |
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| 792 | "data": { |
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| 793 | "text/plain": [ |
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| 794 | "'f_2 = '" |
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| 795 | ] |
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| 796 | }, |
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| 797 | "metadata": {}, |
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| 798 | "output_type": "display_data" |
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| 799 | }, |
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| 800 | { |
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| 801 | "data": { |
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| 802 | "image/png": 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\n", |
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| 803 | "text/latex": [ |
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| 804 | "$$- L_{2} Lc_{3} m_{3} \\left(\\frac{d}{d t} \\theta_{1}{\\left (t \\right )} + \\frac{d}{d t} \\theta_{2}{\\left (t \\right )} + \\frac{d}{d t} \\theta_{3}{\\left (t \\right )}\\right) \\sin{\\left (\\theta_{3}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{3}{\\left (t \\right )} - L_{2} Lc_{3} m_{3} \\sin{\\left (\\theta_{3}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{2}{\\left (t \\right )} \\frac{d}{d t} \\theta_{3}{\\left (t \\right )} + Lc_{2} g m_{2} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} + g m_{3} \\left(L_{2} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} + Lc_{3} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )}\\right) + \\left(L_{1} \\left(L_{2} m_{3} \\sin{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + Lc_{2} m_{2} \\sin{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + Lc_{3} m_{3} \\sin{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )}\\right) \\frac{d}{d t} \\theta_{1}{\\left (t \\right )} - L_{2} Lc_{3} m_{3} \\sin{\\left (\\theta_{3}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{3}{\\left (t \\right )}\\right) \\frac{d}{d t} \\theta_{1}{\\left (t \\right )}$$" |
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| 805 | ], |
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| 806 | "text/plain": [ |
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| 807 | " ⎛d d d ⎞ d \n", |
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| 808 | "- L₂⋅Lc₃⋅m₃⋅⎜──(θ₁(t)) + ──(θ₂(t)) + ──(θ₃(t))⎟⋅sin(θ₃(t))⋅──(θ₃(t)) - L₂⋅Lc₃⋅\n", |
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| 809 | " ⎝dt dt dt ⎠ dt \n", |
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| 810 | "\n", |
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| 811 | " d d \n", |
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| 812 | "m₃⋅sin(θ₃(t))⋅──(θ₂(t))⋅──(θ₃(t)) + Lc₂⋅g⋅m₂⋅cos(θ₁(t) + θ₂(t)) + g⋅m₃⋅(L₂⋅cos\n", |
||
| 813 | " dt dt \n", |
||
| 814 | "\n", |
||
| 815 | " ⎛ \n", |
||
| 816 | "(θ₁(t) + θ₂(t)) + Lc₃⋅cos(θ₁(t) + θ₂(t) + θ₃(t))) + ⎜L₁⋅(L₂⋅m₃⋅sin(θ₂(t)) + Lc\n", |
||
| 817 | " ⎝ \n", |
||
| 818 | "\n", |
||
| 819 | " d \n", |
||
| 820 | "₂⋅m₂⋅sin(θ₂(t)) + Lc₃⋅m₃⋅sin(θ₂(t) + θ₃(t)))⋅──(θ₁(t)) - L₂⋅Lc₃⋅m₃⋅sin(θ₃(t))⋅\n", |
||
| 821 | " dt \n", |
||
| 822 | "\n", |
||
| 823 | "d ⎞ d \n", |
||
| 824 | "──(θ₃(t))⎟⋅──(θ₁(t))\n", |
||
| 825 | "dt ⎠ dt " |
||
| 826 | ] |
||
| 827 | }, |
||
| 828 | "metadata": {}, |
||
| 829 | "output_type": "display_data" |
||
| 830 | }, |
||
| 831 | { |
||
| 832 | "data": { |
||
| 833 | "text/plain": [ |
||
| 834 | "'f_3 = '" |
||
| 835 | ] |
||
| 836 | }, |
||
| 837 | "metadata": {}, |
||
| 838 | "output_type": "display_data" |
||
| 839 | }, |
||
| 840 | { |
||
| 841 | "data": { |
||
| 842 | "image/png": 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\n", |
||
| 843 | "text/latex": [ |
||
| 844 | "$$Lc_{3} g m_{3} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} + Lc_{3} m_{3} \\left(L_{1} \\sin{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} \\left(\\frac{d}{d t} \\theta_{1}{\\left (t \\right )}\\right)^{2} + L_{2} \\sin{\\left (\\theta_{3}{\\left (t \\right )} \\right )} \\left(\\frac{d}{d t} \\theta_{1}{\\left (t \\right )}\\right)^{2} + 2 L_{2} \\sin{\\left (\\theta_{3}{\\left (t \\right )} \\right )} \\frac{d}{d t} \\theta_{1}{\\left (t \\right )} \\frac{d}{d t} \\theta_{2}{\\left (t \\right )} + L_{2} \\sin{\\left (\\theta_{3}{\\left (t \\right )} \\right )} \\left(\\frac{d}{d t} \\theta_{2}{\\left (t \\right )}\\right)^{2}\\right)$$" |
||
| 845 | ], |
||
| 846 | "text/plain": [ |
||
| 847 | " ⎛ \n", |
||
| 848 | " ⎜ ⎛d \n", |
||
| 849 | "Lc₃⋅g⋅m₃⋅cos(θ₁(t) + θ₂(t) + θ₃(t)) + Lc₃⋅m₃⋅⎜L₁⋅sin(θ₂(t) + θ₃(t))⋅⎜──(θ₁(t))\n", |
||
| 850 | " ⎝ ⎝dt \n", |
||
| 851 | "\n", |
||
| 852 | " 2 2 \n", |
||
| 853 | "⎞ ⎛d ⎞ d d \n", |
||
| 854 | "⎟ + L₂⋅sin(θ₃(t))⋅⎜──(θ₁(t))⎟ + 2⋅L₂⋅sin(θ₃(t))⋅──(θ₁(t))⋅──(θ₂(t)) + L₂⋅sin\n", |
||
| 855 | "⎠ ⎝dt ⎠ dt dt \n", |
||
| 856 | "\n", |
||
| 857 | " 2⎞\n", |
||
| 858 | " ⎛d ⎞ ⎟\n", |
||
| 859 | "(θ₃(t))⋅⎜──(θ₂(t))⎟ ⎟\n", |
||
| 860 | " ⎝dt ⎠ ⎠" |
||
| 861 | ] |
||
| 862 | }, |
||
| 863 | "metadata": {}, |
||
| 864 | "output_type": "display_data" |
||
| 865 | } |
||
| 866 | ], |
||
| 867 | "source": [ |
||
| 868 | "# total forces from Coriolis, centrafugal and gravity\n", |
||
| 869 | "f = model.f\n", |
||
| 870 | "for i in range(0, f.shape[0]):\n", |
||
| 871 | " disp('f_' + str(i + 1) + ' = ', f[i])" |
||
| 872 | ] |
||
| 873 | }, |
||
| 874 | { |
||
| 875 | "cell_type": "markdown", |
||
| 876 | "metadata": { |
||
| 877 | "ein.tags": "worksheet-0", |
||
| 878 | "slideshow": { |
||
| 879 | "slide_type": "-" |
||
| 880 | } |
||
| 881 | }, |
||
| 882 | "source": [ |
||
| 883 | "## Muscle Moment Arm" |
||
| 884 | ] |
||
| 885 | }, |
||
| 886 | { |
||
| 887 | "cell_type": "markdown", |
||
| 888 | "metadata": { |
||
| 889 | "ein.tags": "worksheet-0", |
||
| 890 | "slideshow": { |
||
| 891 | "slide_type": "-" |
||
| 892 | } |
||
| 893 | }, |
||
| 894 | "source": [ |
||
| 895 | "The muscle forces $f_m$ are transformed into joint space generalized forces\n", |
||
| 896 | "($\\tau$) by the moment arm matrix ($\\tau = -R^T f_m$). For a n-lateral polygon\n", |
||
| 897 | "it can be shown that the derivative of the side length with respect to the\n", |
||
| 898 | "opposite angle is the moment arm component. As a consequence, when expressing\n", |
||
| 899 | "the muscle length as a function of the generalized coordinates of the model, the\n", |
||
| 900 | "moment arm matrix is evaluated by $R = \\frac{\\partial l_{mt}}{\\partial q}$. The\n", |
||
| 901 | "analytical expressions of the EoMs following our convention are provided below\n", |
||
| 902 | "\n", |
||
| 903 | "\\begin{equation}\\label{equ:eom-notation}\n", |
||
| 904 | " \\begin{gathered}\n", |
||
| 905 | " M(q) \\ddot{q} + f(q, \\dot{q}) = \\tau \\\\\n", |
||
| 906 | " \\tau = -R^T(q) f_m\n", |
||
| 907 | " \\end{gathered}\n", |
||
| 908 | "\\end{equation}" |
||
| 909 | ] |
||
| 910 | }, |
||
| 911 | { |
||
| 912 | "cell_type": "code", |
||
| 913 | "execution_count": 6, |
||
| 914 | "metadata": { |
||
| 915 | "autoscroll": false, |
||
| 916 | "ein.hycell": false, |
||
| 917 | "ein.tags": "worksheet-0", |
||
| 918 | "slideshow": { |
||
| 919 | "slide_type": "-" |
||
| 920 | } |
||
| 921 | }, |
||
| 922 | "outputs": [ |
||
| 923 | { |
||
| 924 | "data": { |
||
| 925 | "text/plain": [ |
||
| 926 | "'l_m = '" |
||
| 927 | ] |
||
| 928 | }, |
||
| 929 | "metadata": {}, |
||
| 930 | "output_type": "display_data" |
||
| 931 | }, |
||
| 932 | { |
||
| 933 | "data": { |
||
| 934 | "image/png": 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\n", |
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| 935 | "text/latex": [ |
||
| 936 | "$$\\left[\\begin{matrix}\\sqrt{a_{1}^{2} + 2 a_{1} b_{1} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + b_{1}^{2}}\\\\\\sqrt{a_{2}^{2} - 2 a_{2} b_{2} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + b_{2}^{2}}\\\\\\sqrt{b_{3}^{2} + b_{3} \\left(2 L_{1} - 2 a_{3}\\right) \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + \\left(L_{1} - a_{3}\\right)^{2}}\\\\\\sqrt{b_{4}^{2} - b_{4} \\left(2 L_{1} - 2 a_{4}\\right) \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + \\left(L_{1} - a_{4}\\right)^{2}}\\\\\\sqrt{L_{1}^{2} + 2 L_{1} a_{5} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + 2 L_{1} b_{5} \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + a_{5}^{2} + 2 a_{5} b_{5} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} + b_{5}^{2}}\\\\\\sqrt{L_{1}^{2} - 2 L_{1} a_{6} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} - 2 L_{1} b_{6} \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + a_{6}^{2} + 2 a_{6} b_{6} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} + b_{6}^{2}}\\\\\\sqrt{b_{7}^{2} + b_{7} \\left(2 L_{2} - 2 a_{7}\\right) \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + \\left(L_{2} - a_{7}\\right)^{2}}\\\\\\sqrt{b_{8}^{2} - b_{8} \\left(2 L_{2} - 2 a_{8}\\right) \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + \\left(L_{2} - a_{8}\\right)^{2}}\\\\\\sqrt{L_{2}^{2} + 2 L_{2} b_{9} \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + L_{2} \\left(2 L_{1} - 2 a_{9}\\right) \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + b_{9}^{2} + b_{9} \\left(2 L_{1} - 2 a_{9}\\right) \\cos{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} + \\left(L_{1} - a_{9}\\right)^{2}}\\end{matrix}\\right]$$" |
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| 937 | ], |
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| 938 | "text/plain": [ |
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| 939 | "⎡ ________________________________ \n", |
||
| 940 | "⎢ ╱ 2 2 \n", |
||
| 941 | "⎢ ╲╱ a₁ + 2⋅a₁⋅b₁⋅cos(θ₁(t)) + b₁ \n", |
||
| 942 | "⎢ \n", |
||
| 943 | "⎢ ________________________________ \n", |
||
| 944 | "⎢ ╱ 2 2 \n", |
||
| 945 | "⎢ ╲╱ a₂ - 2⋅a₂⋅b₂⋅cos(θ₁(t)) + b₂ \n", |
||
| 946 | "⎢ \n", |
||
| 947 | "⎢ __________________________________________\n", |
||
| 948 | "⎢ ╱ 2 \n", |
||
| 949 | "⎢ ╲╱ b₃ + b₃⋅(2⋅L₁ - 2⋅a₃)⋅cos(θ₂(t)) + (L₁ -\n", |
||
| 950 | "⎢ \n", |
||
| 951 | "⎢ __________________________________________\n", |
||
| 952 | "⎢ ╱ 2 \n", |
||
| 953 | "⎢ ╲╱ b₄ - b₄⋅(2⋅L₁ - 2⋅a₄)⋅cos(θ₂(t)) + (L₁ -\n", |
||
| 954 | "⎢ \n", |
||
| 955 | "⎢ ______________________________________________________________\n", |
||
| 956 | "⎢ ╱ 2 2 \n", |
||
| 957 | "⎢ ╲╱ L₁ + 2⋅L₁⋅a₅⋅cos(θ₁(t)) + 2⋅L₁⋅b₅⋅cos(θ₂(t)) + a₅ + 2⋅a₅⋅b₅\n", |
||
| 958 | "⎢ \n", |
||
| 959 | "⎢ ______________________________________________________________\n", |
||
| 960 | "⎢ ╱ 2 2 \n", |
||
| 961 | "⎢ ╲╱ L₁ - 2⋅L₁⋅a₆⋅cos(θ₁(t)) - 2⋅L₁⋅b₆⋅cos(θ₂(t)) + a₆ + 2⋅a₆⋅b₆\n", |
||
| 962 | "⎢ \n", |
||
| 963 | "⎢ __________________________________________\n", |
||
| 964 | "⎢ ╱ 2 \n", |
||
| 965 | "⎢ ╲╱ b₇ + b₇⋅(2⋅L₂ - 2⋅a₇)⋅cos(θ₃(t)) + (L₂ -\n", |
||
| 966 | "⎢ \n", |
||
| 967 | "⎢ __________________________________________\n", |
||
| 968 | "⎢ ╱ 2 \n", |
||
| 969 | "⎢ ╲╱ b₈ - b₈⋅(2⋅L₂ - 2⋅a₈)⋅cos(θ₃(t)) + (L₂ -\n", |
||
| 970 | "⎢ \n", |
||
| 971 | "⎢ __________________________________________________________________________\n", |
||
| 972 | "⎢ ╱ 2 2 \n", |
||
| 973 | "⎣╲╱ L₂ + 2⋅L₂⋅b₉⋅cos(θ₃(t)) + L₂⋅(2⋅L₁ - 2⋅a₉)⋅cos(θ₂(t)) + b₉ + b₉⋅(2⋅L₁ -\n", |
||
| 974 | "\n", |
||
| 975 | " ⎤\n", |
||
| 976 | " ⎥\n", |
||
| 977 | " ⎥\n", |
||
| 978 | " ⎥\n", |
||
| 979 | " ⎥\n", |
||
| 980 | " ⎥\n", |
||
| 981 | " ⎥\n", |
||
| 982 | " ⎥\n", |
||
| 983 | "______ ⎥\n", |
||
| 984 | " 2 ⎥\n", |
||
| 985 | " a₃) ⎥\n", |
||
| 986 | " ⎥\n", |
||
| 987 | "______ ⎥\n", |
||
| 988 | " 2 ⎥\n", |
||
| 989 | " a₄) ⎥\n", |
||
| 990 | " ⎥\n", |
||
| 991 | "__________________________ ⎥\n", |
||
| 992 | " 2 ⎥\n", |
||
| 993 | "⋅cos(θ₁(t) + θ₂(t)) + b₅ ⎥\n", |
||
| 994 | " ⎥\n", |
||
| 995 | "__________________________ ⎥\n", |
||
| 996 | " 2 ⎥\n", |
||
| 997 | "⋅cos(θ₁(t) + θ₂(t)) + b₆ ⎥\n", |
||
| 998 | " ⎥\n", |
||
| 999 | "______ ⎥\n", |
||
| 1000 | " 2 ⎥\n", |
||
| 1001 | " a₇) ⎥\n", |
||
| 1002 | " ⎥\n", |
||
| 1003 | "______ ⎥\n", |
||
| 1004 | " 2 ⎥\n", |
||
| 1005 | " a₈) ⎥\n", |
||
| 1006 | " ⎥\n", |
||
| 1007 | "_______________________________________⎥\n", |
||
| 1008 | " 2 ⎥\n", |
||
| 1009 | " 2⋅a₉)⋅cos(θ₂(t) + θ₃(t)) + (L₁ - a₉) ⎦" |
||
| 1010 | ] |
||
| 1011 | }, |
||
| 1012 | "metadata": {}, |
||
| 1013 | "output_type": "display_data" |
||
| 1014 | }, |
||
| 1015 | { |
||
| 1016 | "data": { |
||
| 1017 | "text/plain": [ |
||
| 1018 | "'R = '" |
||
| 1019 | ] |
||
| 1020 | }, |
||
| 1021 | "metadata": {}, |
||
| 1022 | "output_type": "display_data" |
||
| 1023 | }, |
||
| 1024 | { |
||
| 1025 | "data": { |
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| 1026 | "image/png": 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\n", |
||
| 1027 | "text/latex": [ |
||
| 1028 | "$$\\left[\\begin{matrix}- \\frac{a_{1} b_{1} \\sin{\\left (\\theta_{1}{\\left (t \\right )} \\right )}}{\\sqrt{a_{1}^{2} + 2 a_{1} b_{1} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + b_{1}^{2}}} & 0 & 0\\\\\\frac{a_{2} b_{2} \\sin{\\left (\\theta_{1}{\\left (t \\right )} \\right )}}{\\sqrt{a_{2}^{2} - 2 a_{2} b_{2} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + b_{2}^{2}}} & 0 & 0\\\\0 & - \\frac{b_{3} \\left(2 L_{1} - 2 a_{3}\\right) \\sin{\\left (\\theta_{2}{\\left (t \\right )} \\right )}}{2 \\sqrt{b_{3}^{2} + b_{3} \\left(2 L_{1} - 2 a_{3}\\right) \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + \\left(L_{1} - a_{3}\\right)^{2}}} & 0\\\\0 & \\frac{b_{4} \\left(2 L_{1} - 2 a_{4}\\right) \\sin{\\left (\\theta_{2}{\\left (t \\right )} \\right )}}{2 \\sqrt{b_{4}^{2} - b_{4} \\left(2 L_{1} - 2 a_{4}\\right) \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + \\left(L_{1} - a_{4}\\right)^{2}}} & 0\\\\- \\frac{a_{5} \\left(L_{1} \\sin{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + b_{5} \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )}\\right)}{\\sqrt{L_{1}^{2} + 2 L_{1} a_{5} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + 2 L_{1} b_{5} \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + a_{5}^{2} + 2 a_{5} b_{5} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} + b_{5}^{2}}} & - \\frac{b_{5} \\left(L_{1} \\sin{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + a_{5} \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )}\\right)}{\\sqrt{L_{1}^{2} + 2 L_{1} a_{5} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} + 2 L_{1} b_{5} \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + a_{5}^{2} + 2 a_{5} b_{5} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} + b_{5}^{2}}} & 0\\\\\\frac{a_{6} \\left(L_{1} \\sin{\\left (\\theta_{1}{\\left (t \\right )} \\right )} - b_{6} \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )}\\right)}{\\sqrt{L_{1}^{2} - 2 L_{1} a_{6} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} - 2 L_{1} b_{6} \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + a_{6}^{2} + 2 a_{6} b_{6} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} + b_{6}^{2}}} & \\frac{b_{6} \\left(L_{1} \\sin{\\left (\\theta_{2}{\\left (t \\right )} \\right )} - a_{6} \\sin{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )}\\right)}{\\sqrt{L_{1}^{2} - 2 L_{1} a_{6} \\cos{\\left (\\theta_{1}{\\left (t \\right )} \\right )} - 2 L_{1} b_{6} \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + a_{6}^{2} + 2 a_{6} b_{6} \\cos{\\left (\\theta_{1}{\\left (t \\right )} + \\theta_{2}{\\left (t \\right )} \\right )} + b_{6}^{2}}} & 0\\\\0 & 0 & - \\frac{b_{7} \\left(2 L_{2} - 2 a_{7}\\right) \\sin{\\left (\\theta_{3}{\\left (t \\right )} \\right )}}{2 \\sqrt{b_{7}^{2} + b_{7} \\left(2 L_{2} - 2 a_{7}\\right) \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + \\left(L_{2} - a_{7}\\right)^{2}}}\\\\0 & 0 & \\frac{b_{8} \\left(2 L_{2} - 2 a_{8}\\right) \\sin{\\left (\\theta_{3}{\\left (t \\right )} \\right )}}{2 \\sqrt{b_{8}^{2} - b_{8} \\left(2 L_{2} - 2 a_{8}\\right) \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + \\left(L_{2} - a_{8}\\right)^{2}}}\\\\0 & \\frac{- \\frac{L_{2}}{2} \\left(2 L_{1} - 2 a_{9}\\right) \\sin{\\left (\\theta_{2}{\\left (t \\right )} \\right )} - \\frac{b_{9}}{2} \\left(2 L_{1} - 2 a_{9}\\right) \\sin{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )}}{\\sqrt{L_{2}^{2} + 2 L_{2} b_{9} \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + L_{2} \\left(2 L_{1} - 2 a_{9}\\right) \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + b_{9}^{2} + b_{9} \\left(2 L_{1} - 2 a_{9}\\right) \\cos{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} + \\left(L_{1} - a_{9}\\right)^{2}}} & \\frac{- L_{2} b_{9} \\sin{\\left (\\theta_{3}{\\left (t \\right )} \\right )} - \\frac{b_{9}}{2} \\left(2 L_{1} - 2 a_{9}\\right) \\sin{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )}}{\\sqrt{L_{2}^{2} + 2 L_{2} b_{9} \\cos{\\left (\\theta_{3}{\\left (t \\right )} \\right )} + L_{2} \\left(2 L_{1} - 2 a_{9}\\right) \\cos{\\left (\\theta_{2}{\\left (t \\right )} \\right )} + b_{9}^{2} + b_{9} \\left(2 L_{1} - 2 a_{9}\\right) \\cos{\\left (\\theta_{2}{\\left (t \\right )} + \\theta_{3}{\\left (t \\right )} \\right )} + \\left(L_{1} - a_{9}\\right)^{2}}}\\end{matrix}\\right]$$" |
||
| 1029 | ], |
||
| 1030 | "text/plain": [ |
||
| 1031 | "⎡ -a₁⋅b₁⋅sin(θ₁(t)) \n", |
||
| 1032 | "⎢ ─────────────────────────────────── \n", |
||
| 1033 | "⎢ ________________________________ \n", |
||
| 1034 | "⎢ ╱ 2 2 \n", |
||
| 1035 | "⎢ ╲╱ a₁ + 2⋅a₁⋅b₁⋅cos(θ₁(t)) + b₁ \n", |
||
| 1036 | "⎢ \n", |
||
| 1037 | "⎢ a₂⋅b₂⋅sin(θ₁(t)) \n", |
||
| 1038 | "⎢ ─────────────────────────────────── \n", |
||
| 1039 | "⎢ ________________________________ \n", |
||
| 1040 | "⎢ ╱ 2 2 \n", |
||
| 1041 | "⎢ ╲╱ a₂ - 2⋅a₂⋅b₂⋅cos(θ₁(t)) + b₂ \n", |
||
| 1042 | "⎢ \n", |
||
| 1043 | "⎢ \n", |
||
| 1044 | "⎢ 0 \n", |
||
| 1045 | "⎢ \n", |
||
| 1046 | "⎢ \n", |
||
| 1047 | "⎢ \n", |
||
| 1048 | "⎢ \n", |
||
| 1049 | "⎢ \n", |
||
| 1050 | "⎢ 0 \n", |
||
| 1051 | "⎢ \n", |
||
| 1052 | "⎢ \n", |
||
| 1053 | "⎢ \n", |
||
| 1054 | "⎢ \n", |
||
| 1055 | "⎢ -a₅⋅(L₁⋅sin(θ₁(t)) + b₅⋅sin(θ₁(t) + θ₂(t))) \n", |
||
| 1056 | "⎢─────────────────────────────────────────────────────────────────────────────\n", |
||
| 1057 | "⎢ __________________________________________________________________________\n", |
||
| 1058 | "⎢ ╱ 2 2 \n", |
||
| 1059 | "⎢╲╱ L₁ + 2⋅L₁⋅a₅⋅cos(θ₁(t)) + 2⋅L₁⋅b₅⋅cos(θ₂(t)) + a₅ + 2⋅a₅⋅b₅⋅cos(θ₁(t) +\n", |
||
| 1060 | "⎢ \n", |
||
| 1061 | "⎢ a₆⋅(L₁⋅sin(θ₁(t)) - b₆⋅sin(θ₁(t) + θ₂(t))) \n", |
||
| 1062 | "⎢─────────────────────────────────────────────────────────────────────────────\n", |
||
| 1063 | "⎢ __________________________________________________________________________\n", |
||
| 1064 | "⎢ ╱ 2 2 \n", |
||
| 1065 | "⎢╲╱ L₁ - 2⋅L₁⋅a₆⋅cos(θ₁(t)) - 2⋅L₁⋅b₆⋅cos(θ₂(t)) + a₆ + 2⋅a₆⋅b₆⋅cos(θ₁(t) +\n", |
||
| 1066 | "⎢ \n", |
||
| 1067 | "⎢ \n", |
||
| 1068 | "⎢ 0 \n", |
||
| 1069 | "⎢ \n", |
||
| 1070 | "⎢ \n", |
||
| 1071 | "⎢ \n", |
||
| 1072 | "⎢ \n", |
||
| 1073 | "⎢ \n", |
||
| 1074 | "⎢ 0 \n", |
||
| 1075 | "⎢ \n", |
||
| 1076 | "⎢ \n", |
||
| 1077 | "⎢ \n", |
||
| 1078 | "⎢ \n", |
||
| 1079 | "⎢ \n", |
||
| 1080 | "⎢ \n", |
||
| 1081 | "⎢ \n", |
||
| 1082 | "⎢ 0 \n", |
||
| 1083 | "⎢ \n", |
||
| 1084 | "⎢ \n", |
||
| 1085 | "⎣ \n", |
||
| 1086 | "\n", |
||
| 1087 | " \n", |
||
| 1088 | " 0 \n", |
||
| 1089 | " \n", |
||
| 1090 | " \n", |
||
| 1091 | " \n", |
||
| 1092 | " \n", |
||
| 1093 | " \n", |
||
| 1094 | " 0 \n", |
||
| 1095 | " \n", |
||
| 1096 | " \n", |
||
| 1097 | " \n", |
||
| 1098 | " \n", |
||
| 1099 | " -b₃⋅(2⋅L₁ - 2⋅a₃)⋅s\n", |
||
| 1100 | " ───────────────────────────────\n", |
||
| 1101 | " __________________________\n", |
||
| 1102 | " ╱ 2 \n", |
||
| 1103 | " 2⋅╲╱ b₃ + b₃⋅(2⋅L₁ - 2⋅a₃)⋅co\n", |
||
| 1104 | " \n", |
||
| 1105 | " b₄⋅(2⋅L₁ - 2⋅a₄)⋅s\n", |
||
| 1106 | " ───────────────────────────────\n", |
||
| 1107 | " __________________________\n", |
||
| 1108 | " ╱ 2 \n", |
||
| 1109 | " 2⋅╲╱ b₄ - b₄⋅(2⋅L₁ - 2⋅a₄)⋅co\n", |
||
| 1110 | " \n", |
||
| 1111 | " -b₅⋅(L₁⋅sin(θ₂(t)) + a₅⋅si\n", |
||
| 1112 | "────────────── ──────────────────────────────────────────────────\n", |
||
| 1113 | "______________ _______________________________________________\n", |
||
| 1114 | " 2 ╱ 2 \n", |
||
| 1115 | " θ₂(t)) + b₅ ╲╱ L₁ + 2⋅L₁⋅a₅⋅cos(θ₁(t)) + 2⋅L₁⋅b₅⋅cos(θ₂(t)) \n", |
||
| 1116 | " \n", |
||
| 1117 | " b₆⋅(L₁⋅sin(θ₂(t)) - a₆⋅si\n", |
||
| 1118 | "────────────── ──────────────────────────────────────────────────\n", |
||
| 1119 | "______________ _______________________________________________\n", |
||
| 1120 | " 2 ╱ 2 \n", |
||
| 1121 | " θ₂(t)) + b₆ ╲╱ L₁ - 2⋅L₁⋅a₆⋅cos(θ₁(t)) - 2⋅L₁⋅b₆⋅cos(θ₂(t)) \n", |
||
| 1122 | " \n", |
||
| 1123 | " \n", |
||
| 1124 | " 0 \n", |
||
| 1125 | " \n", |
||
| 1126 | " \n", |
||
| 1127 | " \n", |
||
| 1128 | " \n", |
||
| 1129 | " \n", |
||
| 1130 | " 0 \n", |
||
| 1131 | " \n", |
||
| 1132 | " \n", |
||
| 1133 | " \n", |
||
| 1134 | " \n", |
||
| 1135 | " L₂⋅(2⋅L₁ - 2⋅a₉)⋅sin(θ₂(t)) b₉⋅(2⋅\n", |
||
| 1136 | " - ─────────────────────────── - ──────\n", |
||
| 1137 | " 2 \n", |
||
| 1138 | " ──────────────────────────────────────────────────────────────\n", |
||
| 1139 | " ___________________________________________________________\n", |
||
| 1140 | " ╱ 2 \n", |
||
| 1141 | " ╲╱ L₂ + 2⋅L₂⋅b₉⋅cos(θ₃(t)) + L₂⋅(2⋅L₁ - 2⋅a₉)⋅cos(θ₂(t)) + b\n", |
||
| 1142 | "\n", |
||
| 1143 | " \n", |
||
| 1144 | " \n", |
||
| 1145 | " \n", |
||
| 1146 | " \n", |
||
| 1147 | " \n", |
||
| 1148 | " \n", |
||
| 1149 | " \n", |
||
| 1150 | " \n", |
||
| 1151 | " \n", |
||
| 1152 | " \n", |
||
| 1153 | " \n", |
||
| 1154 | " \n", |
||
| 1155 | "in(θ₂(t)) \n", |
||
| 1156 | "────────────────────── \n", |
||
| 1157 | "______________________ \n", |
||
| 1158 | " 2 \n", |
||
| 1159 | "s(θ₂(t)) + (L₁ - a₃) \n", |
||
| 1160 | " \n", |
||
| 1161 | "in(θ₂(t)) \n", |
||
| 1162 | "────────────────────── \n", |
||
| 1163 | "______________________ \n", |
||
| 1164 | " 2 \n", |
||
| 1165 | "s(θ₂(t)) + (L₁ - a₄) \n", |
||
| 1166 | " \n", |
||
| 1167 | "n(θ₁(t) + θ₂(t))) \n", |
||
| 1168 | "───────────────────────────────────────── \n", |
||
| 1169 | "_________________________________________ \n", |
||
| 1170 | " 2 2 \n", |
||
| 1171 | "+ a₅ + 2⋅a₅⋅b₅⋅cos(θ₁(t) + θ₂(t)) + b₅ \n", |
||
| 1172 | " \n", |
||
| 1173 | "n(θ₁(t) + θ₂(t))) \n", |
||
| 1174 | "───────────────────────────────────────── \n", |
||
| 1175 | "_________________________________________ \n", |
||
| 1176 | " 2 2 \n", |
||
| 1177 | "+ a₆ + 2⋅a₆⋅b₆⋅cos(θ₁(t) + θ₂(t)) + b₆ \n", |
||
| 1178 | " \n", |
||
| 1179 | " \n", |
||
| 1180 | " \n", |
||
| 1181 | " \n", |
||
| 1182 | " \n", |
||
| 1183 | " \n", |
||
| 1184 | " \n", |
||
| 1185 | " \n", |
||
| 1186 | " \n", |
||
| 1187 | " \n", |
||
| 1188 | " \n", |
||
| 1189 | " \n", |
||
| 1190 | " \n", |
||
| 1191 | "L₁ - 2⋅a₉)⋅sin(θ₂(t) + θ₃(t)) \n", |
||
| 1192 | "───────────────────────────── \n", |
||
| 1193 | " 2 \n", |
||
| 1194 | "────────────────────────────────────────────────────── ──────────────────────\n", |
||
| 1195 | "______________________________________________________ ___________________\n", |
||
| 1196 | " 2 2 ╱ 2 \n", |
||
| 1197 | "₉ + b₉⋅(2⋅L₁ - 2⋅a₉)⋅cos(θ₂(t) + θ₃(t)) + (L₁ - a₉) ╲╱ L₂ + 2⋅L₂⋅b₉⋅cos(\n", |
||
| 1198 | "\n", |
||
| 1199 | " \n", |
||
| 1200 | " 0 \n", |
||
| 1201 | " \n", |
||
| 1202 | " \n", |
||
| 1203 | " \n", |
||
| 1204 | " \n", |
||
| 1205 | " \n", |
||
| 1206 | " 0 \n", |
||
| 1207 | " \n", |
||
| 1208 | " \n", |
||
| 1209 | " \n", |
||
| 1210 | " \n", |
||
| 1211 | " \n", |
||
| 1212 | " 0 \n", |
||
| 1213 | " \n", |
||
| 1214 | " \n", |
||
| 1215 | " \n", |
||
| 1216 | " \n", |
||
| 1217 | " \n", |
||
| 1218 | " 0 \n", |
||
| 1219 | " \n", |
||
| 1220 | " \n", |
||
| 1221 | " \n", |
||
| 1222 | " \n", |
||
| 1223 | " \n", |
||
| 1224 | " 0 \n", |
||
| 1225 | " \n", |
||
| 1226 | " \n", |
||
| 1227 | " \n", |
||
| 1228 | " \n", |
||
| 1229 | " \n", |
||
| 1230 | " 0 \n", |
||
| 1231 | " \n", |
||
| 1232 | " \n", |
||
| 1233 | " \n", |
||
| 1234 | " \n", |
||
| 1235 | " -b₇⋅(2⋅L₂ - 2⋅a₇)⋅sin(θ₃(t)) \n", |
||
| 1236 | " ───────────────────────────────────────────────────── \n", |
||
| 1237 | " ________________________________________________ \n", |
||
| 1238 | " ╱ 2 2 \n", |
||
| 1239 | " 2⋅╲╱ b₇ + b₇⋅(2⋅L₂ - 2⋅a₇)⋅cos(θ₃(t)) + (L₂ - a₇) \n", |
||
| 1240 | " \n", |
||
| 1241 | " b₈⋅(2⋅L₂ - 2⋅a₈)⋅sin(θ₃(t)) \n", |
||
| 1242 | " ───────────────────────────────────────────────────── \n", |
||
| 1243 | " ________________________________________________ \n", |
||
| 1244 | " ╱ 2 2 \n", |
||
| 1245 | " 2⋅╲╱ b₈ - b₈⋅(2⋅L₂ - 2⋅a₈)⋅cos(θ₃(t)) + (L₂ - a₈) \n", |
||
| 1246 | " \n", |
||
| 1247 | " b₉⋅(2⋅L₁ - 2⋅a₉)⋅sin(θ₂(t) + θ₃(t)) \n", |
||
| 1248 | " -L₂⋅b₉⋅sin(θ₃(t)) - ─────────────────────────────────── \n", |
||
| 1249 | " 2 \n", |
||
| 1250 | "──────────────────────────────────────────────────────────────────────────────\n", |
||
| 1251 | "______________________________________________________________________________\n", |
||
| 1252 | " 2 \n", |
||
| 1253 | "θ₃(t)) + L₂⋅(2⋅L₁ - 2⋅a₉)⋅cos(θ₂(t)) + b₉ + b₉⋅(2⋅L₁ - 2⋅a₉)⋅cos(θ₂(t) + θ₃(t\n", |
||
| 1254 | "\n", |
||
| 1255 | " ⎤\n", |
||
| 1256 | " ⎥\n", |
||
| 1257 | " ⎥\n", |
||
| 1258 | " ⎥\n", |
||
| 1259 | " ⎥\n", |
||
| 1260 | " ⎥\n", |
||
| 1261 | " ⎥\n", |
||
| 1262 | " ⎥\n", |
||
| 1263 | " ⎥\n", |
||
| 1264 | " ⎥\n", |
||
| 1265 | " ⎥\n", |
||
| 1266 | " ⎥\n", |
||
| 1267 | " ⎥\n", |
||
| 1268 | " ⎥\n", |
||
| 1269 | " ⎥\n", |
||
| 1270 | " ⎥\n", |
||
| 1271 | " ⎥\n", |
||
| 1272 | " ⎥\n", |
||
| 1273 | " ⎥\n", |
||
| 1274 | " ⎥\n", |
||
| 1275 | " ⎥\n", |
||
| 1276 | " ⎥\n", |
||
| 1277 | " ⎥\n", |
||
| 1278 | " ⎥\n", |
||
| 1279 | " ⎥\n", |
||
| 1280 | " ⎥\n", |
||
| 1281 | " ⎥\n", |
||
| 1282 | " ⎥\n", |
||
| 1283 | " ⎥\n", |
||
| 1284 | " ⎥\n", |
||
| 1285 | " ⎥\n", |
||
| 1286 | " ⎥\n", |
||
| 1287 | " ⎥\n", |
||
| 1288 | " ⎥\n", |
||
| 1289 | " ⎥\n", |
||
| 1290 | " ⎥\n", |
||
| 1291 | " ⎥\n", |
||
| 1292 | " ⎥\n", |
||
| 1293 | " ⎥\n", |
||
| 1294 | " ⎥\n", |
||
| 1295 | " ⎥\n", |
||
| 1296 | " ⎥\n", |
||
| 1297 | " ⎥\n", |
||
| 1298 | " ⎥\n", |
||
| 1299 | " ⎥\n", |
||
| 1300 | " ⎥\n", |
||
| 1301 | " ⎥\n", |
||
| 1302 | " ⎥\n", |
||
| 1303 | " ⎥\n", |
||
| 1304 | " ⎥\n", |
||
| 1305 | " ⎥\n", |
||
| 1306 | "────────────────⎥\n", |
||
| 1307 | "________________⎥\n", |
||
| 1308 | " 2 ⎥\n", |
||
| 1309 | ")) + (L₁ - a₉) ⎦" |
||
| 1310 | ] |
||
| 1311 | }, |
||
| 1312 | "metadata": {}, |
||
| 1313 | "output_type": "display_data" |
||
| 1314 | } |
||
| 1315 | ], |
||
| 1316 | "source": [ |
||
| 1317 | "# assert that moment arm is correctly evaluated\n", |
||
| 1318 | "# model.test_muscle_geometry() # slow\n", |
||
| 1319 | "# muscle length\n", |
||
| 1320 | "disp('l_m = ', model.lm)\n", |
||
| 1321 | "# moment arm\n", |
||
| 1322 | "disp('R = ', model.R)" |
||
| 1323 | ] |
||
| 1324 | }, |
||
| 1325 | { |
||
| 1326 | "cell_type": "code", |
||
| 1327 | "execution_count": 7, |
||
| 1328 | "metadata": { |
||
| 1329 | "autoscroll": false, |
||
| 1330 | "ein.hycell": false, |
||
| 1331 | "ein.tags": "worksheet-0", |
||
| 1332 | "slideshow": { |
||
| 1333 | "slide_type": "-" |
||
| 1334 | } |
||
| 1335 | }, |
||
| 1336 | "outputs": [ |
||
| 1337 | { |
||
| 1338 | "data": { |
||
| 1339 | "image/png": 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\n", |
||
| 1340 | "text/plain": [ |
||
| 1341 | "<Figure size 720x720 with 1 Axes>" |
||
| 1342 | ] |
||
| 1343 | }, |
||
| 1344 | "metadata": { |
||
| 1345 | "needs_background": "light" |
||
| 1346 | }, |
||
| 1347 | "output_type": "display_data" |
||
| 1348 | } |
||
| 1349 | ], |
||
| 1350 | "source": [ |
||
| 1351 | "# draw model\n", |
||
| 1352 | "fig, ax = subplots(1, 1, figsize=(10, 10), frameon=False)\n", |
||
| 1353 | "model.draw_model([60, 70, 50], True, ax, 1, False)\n", |
||
| 1354 | "fig.tight_layout()\n", |
||
| 1355 | "fig.savefig('results/arm_model.pdf', dpi=600, format='pdf',\n", |
||
| 1356 | " transparent=True, pad_inches=0, bbox_inches='tight')" |
||
| 1357 | ] |
||
| 1358 | }, |
||
| 1359 | { |
||
| 1360 | "cell_type": "markdown", |
||
| 1361 | "metadata": { |
||
| 1362 | "ein.tags": "worksheet-0", |
||
| 1363 | "slideshow": { |
||
| 1364 | "slide_type": "-" |
||
| 1365 | } |
||
| 1366 | }, |
||
| 1367 | "source": [ |
||
| 1368 | "[1] K. Tahara, Z. W. Luo, and S. Arimoto, “On Control Mechanism of Human-Like\n", |
||
| 1369 | "Reaching Movements with Musculo-Skeletal Redundancy,” in International\n", |
||
| 1370 | "Conference on Intelligent Robots and Systems, 2006, pp. 1402–1409." |
||
| 1371 | ] |
||
| 1372 | } |
||
| 1373 | ], |
||
| 1374 | "metadata": { |
||
| 1375 | "kernelspec": { |
||
| 1376 | "display_name": "Python 2", |
||
| 1377 | "language": "python", |
||
| 1378 | "name": "python2" |
||
| 1379 | }, |
||
| 1380 | "language_info": { |
||
| 1381 | "codemirror_mode": { |
||
| 1382 | "name": "ipython", |
||
| 1383 | "version": 2 |
||
| 1384 | }, |
||
| 1385 | "file_extension": ".py", |
||
| 1386 | "mimetype": "text/x-python", |
||
| 1387 | "name": "python", |
||
| 1388 | "nbconvert_exporter": "python", |
||
| 1389 | "pygments_lexer": "ipython2", |
||
| 1390 | "version": "2.7.15" |
||
| 1391 | }, |
||
| 1392 | "name": "model.ipynb" |
||
| 1393 | }, |
||
| 1394 | "nbformat": 4, |
||
| 1395 | "nbformat_minor": 2 |
||
| 1396 | } |