Genetic Cubic n{C/A} Ratios For Elementary Robotics Design

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What This post Is About

This post provides a toolbox of genetic Cubic coefficient ratios n{C/A} and n{C} ratios in Header Graph 1 applied to a depressed Cubic y=Ax³ — Cx+0 in black with Roots, Tp’s and in green the Sum Of gradients = — 3C at all possible 3 real roots (between Tp(y)’s) as presented in my recent post; Designing Polynomials Using Sum of Gradients at the Roots.

Knowing/deciding Coefficient C, the Sum of Gradients at any 3 real root combinations can be a useful design tool for Robot accelerations etc.

Robotics Design for Kinematics and Trajectory Planning

With elementary Robotics Design it is presumably simpler to start with a Depressed Cubic y=Ax³ — Cx+D so that fundamental start and end points and overall dimension windows can be established. For example for a specified Tp(x) it is easy to apply ‘Big Dipper’ y= — 2x³+0 function in red, to calculate Tp(y) and vis versa. It is also important to understand Cubic Polynomial architecture for design of co-functions for efficient robotic movements and control such as arms, elbow and wrist movements etc.