# Modeling piston/crank with position loop equation, excel plot

 P: 799 It's pretty difficult to follow your steps, so I cannot comment in detail on your work. I think we need not use so many variables (please excuse me if I misunderstand something). Two coordinates are enough: $$\phi$$ (angle between AC and AB) and x. The only geometric condition relating the coordinates is: $$b^2=a^2+x^2-2axcos\phi$$ Plug a=3 and b=5 in, then solve for x (x>0 as the origin is at A): $$x=\sqrt{9cos^2\phi +16}+3cos\phi$$ Thus: $$\dot{x}=-(\frac{9sin\phi cos\phi}{\sqrt{9cos^2\phi +16}}+3sin\phi)\dot{\phi}$$ From here, we can find the constant angular velocity of AC in the range $$0<\phi <\pi$$ and $$\dot{x}<180 in/s$$. Then the rest is simple. The graph I obtained looks akin to yours.