Can you describe what a robot is in mathematical terms?

Answer 1

A robot is a multi-rotational axis mechanism. To solve robotic positioning and velocity problems, you must convert the coordinate system of each of the individual motors into a common coordinate system, in order to determine the relative motion required of each axis to generate the desired tool-path or position.

This requires Matrices and Linear Algebra - the simultaneous solution of n-equations with n-unknowns.

Have fun.

By the way, this is the same kind of math used for Finite Element Analysis of Loads and Deflections (stress and strain) or Heat Transfer.

Answer 2

All models are inaccurate, some models are useful.

Mathematics is used to model. A perfect model would require a second universe that was a photocopy of the current one within which your object of interest resided.

There are infinitely many approximate predictive models that can be used to describe the structure, form, behavior, and control of the robot. They are all useful, but not perfect. The real world is messy and complex, so the elegant models break down.

Finite elements can describe solid structure
Fluid Dynamics can describe pneumatics, hydraulics and fluid flow.
Z-transforms and state-space models can describe the fundamental nature of the robot behavior model, and convolution with time-based phenomena can describe the interactions of the robot with time-dependent phenomena.

Even with those you have an approximation. There are defects in metal, breakdowns of fluid models (like cavitation), and imprecisions in state description and environment description so the z-transform models also break down.

You, me, or anyone can describe some of what a robot might be light in mathematical terms, but not all of what a robot actually ends up like.

Answer 3

Think about it as you would if you were going to make a 3-d model in a computer program. Define what a solid body is (prism) and what a joint is (limit on movement of a body). Define standard physics, and then describe the various inputs the robot receives and how it processes them and how it responds to them. To actually do all the work for that would be astronomical, but I'm hoping you're going for high-level here.

Cheers!

Answer 4

oh my gosh. ok i dont have an answer for this yet this one time this guy i comprehend made this mathematical formula to what number females contained in the international were his soul associates. it became extraordinary. haha i in simple terms concept you may discover that humorous:)

Answer 5

It is the same as any machine. It would be in binary math. In other words: plus or minus, one or zero, on or off, etc.