Trochoid
= Trochoid
{wiki}
The trajectory of a point at fixed distance $a$ from the centre of a circle of radius $r$ rolling along a line. In coordinates aligned with that line it has a linear centre displacement plus sinusoidal components. The case $a=r$ is a <cycloid>; $a<r$ gives a shortened trajectory and $a>r$ gives loops. An inclined rolling line rotates this geometry relative to horizontal and vertical coordinates.