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+sin⁡t)r(1−cos⁡t))=r(ti―+j―+q―(t)), t∈R
  2. Unit Vectors: p―(t)=(−cos⁡t−sin⁡t),q―(t)=(sin⁡t−cos⁡t)
  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
    Generated: 31 Dec 1969, 20:59:59
    151 of 151 images
    Base Path: /usr/local/
    Glob Path: Images/Cycloid*.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 >
Messages:
0 secs.