GoKawiilSmooth Move: Taming Trajectories with Polynomials
This article is all about movement. Of a vehicle, or a robot, or something like a 3D printer.
A 3D printer is really just a specialized robot with a hot glue gun which it can move in multiple directions while squirting out molten plastic.
Position, Velocity, Acceleration …
Our robot, or print head, has a position in space and also a velocity which is how fast it is moving and an acceleration which is how rapidly that velocity is changing.
Velocity is just the derivative of position: how fast is our position changing. Acceleration is the derivative of velocity: how rapidly our velocity is increasing or decreasing.
These are all vectors in that they have both magnitude and direction but for (many) 3D printers and machines each axis is a separate mechanism, so this article is for now going to talk about them as if they were scalars, eg: just a positive or negative number.
… Jerk?
Jerk is the derivative of acceleration, which might seem like a pretty abstract thing to be worried about.
But imagine a mass in a box under constant acceleration. Springs inside the box are pushing the mass to cause it to accelerate too. But if we change the size or direction of the acceleration, the mass is going to slide around until it reaches a new equilibrium.
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