Abstract
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.
Highlights
This paper presents methods for modelling and designing an ideal path trajectory between straight and bend track path segments for racing greyhounds
To develop a numerical technique for the clothoid which incorporates greyhound kinematics variables, we looked into the characteristics of the mathematical model of the clothoid curve
This paper presents a numerical method for generating racing greyhound clothoid transitions for track path designs along with an equation for modelling any kind of clothoid curves
Summary
Greyhound angular displacement rate constant stride length, s (m) change per stride, d (deg/stride). A G2 curvature continuity as found in the clothoid transitions where the rate of change of the jerk is not smooth would induce all the racing greyhounds following the lure to follow one unique transition into the bend to keep instantaneous jerk to the minimum. This is because the window of jerk initiation is much longer in composite curve transitions because of the gradual development of jerk and on average it is four transition segments or four greyhound strides compared to just one stride in the clothoid transitions
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