SmtC: Show me the Code
Ole Peter Smith
Instituto de Matemática e Estatística
Universidade Federal de Goiás
http://www.olesmith.com.br

Rolloids
O conhecimento adquirimos com os livros e os mestres.
A sabedoria aprendemos com o povo e os humildes.
Cora Coralina
< Quadratic | Cycloid | Trochoids >

Cycloid: Rolling Circle on Line

  1. Parametrization, rC: r(t)=(r(t+sint)r(1cost))=r(ti+j+q(t)), tR
  2. Unit Vectors: p(t)=(costsint),q(t)=(sintcost)
  3. Properties:
  4. The Evolute of a Cycloid is again a Cycloid
  5. Cycloid:
    2_Palestras/2021/02_Curves/03_Rolloids/01_Cycloid/Images/Cycloid-000.svg
  6. TikZ:
    TiKZ Listing: Cycloid.tikz.tex. PDF   PNG   SVG   ZIP*  
    %Uses \tikzmath{\r=2;}
    
    
    %\R{\t}
    \newcommand{\R}[2]
    {
       \Q{#1}{Q}
       
       \coordinate (#2) at ($#1*(i)+(j)+(Q)$);
       \coordinate (#2) at ($\r*(#2)$);
    }
    
    %Rolling center
    %\RC{\t}
    \newcommand{\RC}[2]
    {
       \coordinate (#2) at (\r*#1,\r);
    }
    
    
    
    %\dR{\t}
    \newcommand{\dR}[2]
    {
       \P{#1}{P}
       
       \coordinate (#2) at ($(i)+(P)$);
       \coordinate (#2) at ($\r*(#2)$);
    }
    
    
    %\V{\t}{\varname}
    \newcommand{\V}[2]
    {
       \tikzmath{#2=1+cos(deg(#1));}
       \tikzmath{#2=\r*sqrt(2*#2);}
    }
    
    
    %Velocity Normal
    %\dN{\t}{\coordname}
    \newcommand{\dRN}[2]
    {
       \Q{#1}{Q}
       
       \coordinate (#2) at ($(j)+(Q)$);
       \coordinate (#2) at ($\r*(#2)$);
    }
    
    
    
    %\ddR{\t}{\coordname}
    \newcommand{\ddR}[2]
    {
       \Q{#1}{Q}
       
       \coordinate (#2) at ($-(Q)$);
       \coordinate (#2) at ($\r*(#2)$);
    }
    
    
    %\V{\t}{\varname}
    \newcommand{\Det}[2]
    {
       \tikzmath{#2=(cos(deg(#1))+1);}
       \tikzmath{#2=-\r*\r*#2;}
    }
    
    %\Evolute{\t}{\coordname}
    \newcommand{\Evolute}[2]
    {
       \Q{#1}{Q}
       
       \tikzmath{\cost=cos(deg(#1));}
       %\tikzmath{\sint=sin(deg(#1));}
       
       %%\tikzmath{\rphi=1+\cost;}
       %%\tikzmath{\rphi=-\rphi/(\cost+1);}
       
       \coordinate (#2) at ($#1*(i)-(j)-(Q)$);
       \coordinate (#2) at ($\r*(#2)$);
    }
    
< Quadratic | Cycloid | Trochoids >
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