# General equation of a roulette

Currently I am trying to derive the equations x and y shown in the attached picture. I am struggling to find the horizontal and vertical components of lines u and v with angle phi and phi one. Could someone suggest a hint please?

• Law of gearing in mechanical design, general involutes ... Jan 10, 2021 at 19:16
• I meant more of a mathematical hint thanks anyhow Jan 10, 2021 at 19:26
• If you go through the theory of gears without slipping there are considerations of equal arc lengths, so that $s=R_1 \theta_1=R_2 \theta_2$ etc. Jan 10, 2021 at 19:29