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Rigid Body Statics

Fundamentals: Are you ready to explore the world of rigid bodies?

In this chapter, we will dive into the fascinating world of rigid body mechanics and explore:

  • The invisible forces that act on objects and set them in motion or slow them down.
  • The secret of cutting free, which allows us to isolate the most important forces acting on an object.
  • The magical free body diagrams, which show us how forces and moments act on an object.
  • The rigid body and its six degrees of freedom, which give it its mobility.
  • The 6 axioms of rigid body statics, which are the foundation for everything we know about objects at rest.

Are you ready to uncover these secrets?

Then buckle up and let's go on an exciting journey into the world of rigid body mechanics!

It's going to be exciting!

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Table of Contents

3. Degrees of Freedom

More Than Just Room to Move

Hey, have you ever wondered how many ways you can move your body? Infinite? Nope! In Technical Mechanics, there's a term for that: Degrees of Freedom.

What Are Degrees of Freedom?

In rigid body statics, degrees of freedom describe the number of independent movements that a rigid body or system can perform without bending or breaking. In other words: How many ways can the body move in the plane or in space without changing its shape?

The more degrees of freedom a system has, the more flexible it is.

Types of Degrees of Freedom:
  • Translation: Movement in a straight line, on an axis of a local coordinate system
  • Rotation: Rotational movement around an axis of a local coordinate system
Number of Degrees of Freedom:

The number of degrees of freedom depends on the type of system and the constraints that restrict it.

Let's consider a rigid body that can move freely, i.e. without any constraints:

In 3D space it has a whopping 6 degrees of freedom:

  • 3 Translations: Linear movements along the x, y, and z coordinate axes
  • 3 Rotations: Rotational movements around the x, y, and z coordinate axes

In the 2D plane it's a bit less spectacular, but still cool:

  • 2 Translations: Linear movements along the x and y coordinate axes
  • 1 Rotation: Rotational movement around the z coordinate axis

3D or 2D, it doesn't matter: Depending on how you're "held", you have fewer degrees of freedom. A block in a vice, for example, has none at all – it's pretty unfree!

So what are you waiting for? Try out your degrees of freedom and dance, hop and twirl your way through the world!

Fun Fact:

Did you know that Archimedes already thought about degrees of freedom over 2000 years ago? The clever Greek was a real fan of rigid bodies and even constructed bridges and ships with them. Crazy, right?

Okay, enough chit-chat – let's go! Move your body and enjoy your degrees of freedom!