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  1. \documentclass[]{article}
  2.  
  3. %opening
  4. \title{}
  5. \author{}
  6.  
  7. \begin{document}
  8.    
  9.     \maketitle
  10.    
  11.     \begin{abstract}
  12.     \end{abstract}
  13.    
  14.     $T_{0}^1(q_1)=\left[\begin{array}{cccc} 0 & 0 & -1.0 & 0\\ 1.0 & 0 & 0 & 150.0\\ 0 & -1.0 & 0 & 475.0\\ 0 & 0 & 0 & 1.0 \end{array}\right]
  15.    
  16.  
  17. $T_{1}^2(q_2)=\left[\begin{array}{cccc} 0.5 & -0.866 & 0 & 300.0\\ 0.866 & 0.5 & 0 & 519.6\\ 0 & 0 & 1.0 & 0\\ 0 & 0 & 0 & 1.0 \end{array}\right]
  18.  
  19.  
  20. $T_{2}^3(q_3)=\left[\begin{array}{cccc} 0.2588 & 0 & -0.9659 & 31.06\\ 0.9659 & 0 & 0.2588 & 115.9\\ 0 & -1.0 & 0 & 0\\ 0 & 0 & 0 & 1.0 \end{array}\right]
  21.  
  22.  
  23. $T_{3}^4(q_4)=\left[\begin{array}{cccc} 0.5 & 0 & 0.866 & 0\\ 0.866 & 0 & -0.5 & 0\\ 0 & 1.0 & 0 & 720.0\\ 0 & 0 & 0 & 1.0 \end{array}\right]
  24.  
  25.  
  26. $T_{4}^5(q_5)=\left[\begin{array}{cccc} 0.7071 & 0 & 0.7071 & 0\\ -0.7071 & 0 & 0.7071 & 0\\ 0 & -1.0 & 0 & 0\\ 0 & 0 & 0 & 1.0 \end{array}\right]
  27.  
  28.  
  29.  
  30. $T_{5}^6(q_6)=\left[\begin{array}{cccc} 0 & 1.0 & 0 & 0\\ -1.0 & 0 & 0 & 0\\ 0 & 0 & 1.0 & 150.0\\ 0 & 0 & 0 & 1.0 \end{array}\right]
  31.  
  32.  
  33. \begin{footnotesize}
  34.  
  35. $T_{0}^6(q)=\left[\begin{array}{cccc} S_{6}(C_{4}S_{1}-C_{23}C_{1}S_{4})+C_{6}(C_{5}(S_{1}S_{4}+C_{23}C_{1}C_{4})-S_{23}C_{1}S_{5})&C_{6}(C_{4}S_{1}-C_{23}C_{1}S_{4})-S_{6}(C_{5}(S_{1}S_{4}+C_{23}C_{1}C_{4})-S_{23}C_{1}S_{5})&-S_{5}(S_{1}S_{4}+C_{23}C_{1}C_{4})-S_{23}C_{1}C_{5}&30C_{1}(4C_{23}+20C_{2}+5)-150S_{5}(S_{1}S_{4}+C_{23}C_{1}C_{4})-720S_{23}C_{1}-150S_{23}C_{1}C_{5}\\
  36. -S_{6}(C_{1}C_{4}+C_{23}S_{1}S_{4})-C_{6}(C_{5}(C_{1}S_{4}-C_{23}C_{4}S_{1})+S_{23}S_{1}S_{5})&S_{6}(C_{5}(C_{1}S_{4}-C_{23}C_{4}S_{1})+S_{23}S_{1}S_{5})-C_{6}(C_{1}C_{4}+C_{23}S_{1}S_{4})&S_{5}(C_{1}S_{4}-C_{23}C_{4}S_{1})-S_{23}C_{5}S_{1}&150S_{5}(C_{1}S_{4}-C_{23}C_{4}S_{1})+30S_{1}(4C_{23}+20C_{2}+5)-720S_{23}S_{1}-150S_{23}C_{5}S_{1}\\
  37. S_{23}S_{4}S_{6}-C_{6}(C_{23}S_{5}+S_{23}C_{4}C_{5})&S_{6}(C_{23}S_{5}+S_{23}C_{4}C_{5})+S_{23}C_{6}S_{4}&S_{23}C_{4}S_{5}-C_{23}C_{5}&150S_{23}C_{4}S_{5}-120S_{23}-600S_{2}-150C_{23}C_{5}-720C_{23}+475\\
  38. 0&0&0&1 \end{array}\right]
  39.  
  40. \end{footnotesize}
  41.  
  42.  
  43. $T_{0}^6(q)=\left[\begin{array}{cccc} -0.5 & 0.6124 & 0.6124 & 91.86\\ -0.6124 & 0.25 & -0.75 & -256.5\\ -0.6124 & -0.75 & 0.25 & 417.1\\ 0 & 0 & 0 & 1.0 \end{array}\right]
  44.  
  45.  
  46.  
  47. \section{}
  48.  
  49. \end{document}
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