This paper presents methods for modelling and designing an ideal path trajectory between straight and bend track path segments for racing greyhounds. To do this, we numerically generate clothoid and algebraic curve segments for racing quadrupeds using a sequential vector transformation method as well as using a helper equation for approaching ideal clothoid segments that would respect greyhound kinematic parameters and boundary conditions of the track. Further, we look into the limitations of using a clothoid curve for racing dog track path design and propose a smooth composite curve for track transition design which roughly maintains G3 curvature continuity for smooth jerk to overcome limitations of a clothoid transition. Finally, we show results from race data modelling and past injury data, which provide a strong indication of clothoid curve segments improving the dynamics and safety of racing greyhounds while reducing injuries.