Introduction to ROBOTIC concepts,Statics

Introduction to ROBOTIC Mechanical Engineering Theory, Statics
Want to optimize your Robot parameters mathematically? Want to verify that an expensive motor you are about to purchase has enough torque? This is a math tutorial for robot chassis construction. This tutorial is useful if you would like to mathematically either prove your robot will work, or optimize it so that it would work better. Better yet, I have one of those degree thingies in Mechanical Engineering so this tutorial should be extra useful . . .

My approach will be talking about the most common calculation uses of mechanical forces for robots. I will offer specific application examples, the theory, equations, and some pretty graphs to help you understand.


Theory: Statics
Statics is concerned about how a mechanical system would act if everything is perfectly motionless and rigid. It is the most fundamental of all calculations, and mathematically is no more complicated then highschool algebra. All you need to understand is how to build an equation from the mechanical parts you use.

Remember in elementary you learned (or should have learned) that for every force there is an equal & opposite force? For example, if I were to stand straight, then push you forcefully, I would end up forcefully pushing myself back at an equal amount. If you push a wall, the wall is pushing you back. Why is this important? Easy. If an object weighs 10 pounds, your actuator needs to be able to lift at least 10 pounds. This sounds numbingly simple, right?

Now suppose you add in friction of joints, efficiency rates, multiple actuators, & unevenly distributed weight across an oddly shaped object. Obviously the problem can balloon to something quite complex. This is what I will talk about, all directly relating to robotics & in simplified form.

Friction
Calculating friction is often a black art. There are many situations which are hard to factor in such as surface tension, humidity, etc. But there are several sure ways to find a reasonable value to help you build your robot. The first thing you should look at is what is called the coefficient of friction. This is a dimensionless property which can be looked up for any two materials. What does this number mean? Well suppose you are standing on ice with rubber shoes and you want to calculate the pushing force required to slide across the ice.

force of friction = weight * u.rubber-ice

Just multiple the force being applied perpendicular to the contacting materials (your weight) and multiply that by the coefficient of friction of ice against rubber. This would be the force required to counter friction to slide across the ice.

Understanding friction is also useful when designing robot pincers. If the friction is miscalculated, your robot victims would be able to escape! Now we cant have that . . . So here is how you do it. A robot pincer squeezes from both sides. So this is your force. The typical human however wants to fall down out of your robot pincers by gravity.

Now all you need to do is squeeze hard enough so that the force of friction is greater than the force of gravity.

force_squeeze * u.pincer-human_neck > human_weight

You probably won't find a reliable coefficient of friction for robot pincers rubbing up against a human neck, but using higher friction pincer material will help.

Actually, finding the coefficient of friction can be a little more complicated. There are actually two coeffiecients. It turns out that friction is related to the rubbing velocity of the materials. Ever notice how it is easier to push a heavy object across the ground after it is already moving?

The static coefficient of friction is when the materials are stationary.
The kinetic coefficient of friction is when the materials are already in motion against each other. What makes it a black art is that there is never any exact clear boundary between the two values.

Here is a quick coefficient of friction lookup reference of some common materials you may use:

Material 1 Aluminum Aluminum Plexiglass Plexiglass Polystyrene Polystyrene Polythene Rubber Rubber Rubber Rubber Teflon Teflon Wood Wood Wood Wood Wood Wood

Material 2 Aluminum Steel Plexiglass Steel Polystyrene Steel Steel Asphalt (dry) Asphalt (wet) Concrete (dry) Concrete (wet) Steel Teflon Wood (clean) Wood (wet) Metals (clean) Metals (wet) Brick Concrete

Static 1.05 - 1.35 0.61 0.8 0.4 - 0.5 0.5 0.3 - 0.35 0.2 0.5 - 0.8 0.25 - 0.75 0.6 - 0.85 0.45 - 0.75 0.04 0.04 0.25 - 0.5 0.2 0.2 - 0.6 0.2 0.6 0.62

Kinetic 1.4 0.47 - - - - - - - - - - - - - - - - -