# Loads and Free Body Diagrams

Understanding what loads are and how they are transferred from each component of the robot down to the ground will go a long way to increasing your understanding of how to design structural and mechanical systems.  Here is a quick primer on loads and visualizing them via free body diagrams.

Newton’s 1st Law

An object in motion stays in motion in a straight line, unless acted upon by unbalanced force. A push or pull will cause object to speed up, slow down, or change direction.

Basically, objects just keep on doing whatever they are doing unless they are acted upon by an unbalanced force.

• Ketchup stays in the bottom (at rest) until you bang (outside force) on the end of the bottom.
• A headrest in a car prevents whiplash injuries during a rear-end collision ( your head goes forward and then jerks backward).
• Animation 1 – ladder truck
• Animation 2 – no seatbelt

Free-body Diagram: Single Body

Free-body diagrams are used to show the relative magnitude and direction of all forces acting on an object.

This diagram above shows four forces acting upon an object. There aren’t always four forces, For example, there could be one, two, or three forces.  If a block is at rest on a table top. Here is the diagram of the forces acting on the block.

In this diagram above, there are normal and gravitational forces on the block. Below a block is free-falling in a vacuum. Neglecting air resistance, below is the free-body diagram showing the forces involved.

In this diagram above, gravity is the only force acting on the block. Below a block is free-falling from a tree to the ground at constant velocity. Considering air resistance, below is the free body diagram for this situation.

In this diagram above, gravity pulls down on the block while air resistance pushes up on the block as it falls through air. Below a rightward force is applied to a block in order to move it across a desk. Considering frictional forces and neglecting air resistance, below is the free-body diagram.

In this diagram above, the applied force arrow points to the right. Notice how friction force points in the opposite direction. Finally, there is still gravity and normal forces involved.  Below a block is descending with a constant velocity. Considering air resistance, below is the free-body diagram.

In this diagram above, gravity pulls down on the block, while air resistance pushes up as the block falls. Below a block is dragged across loosely packed snow with a rightward acceleration. below is the free-body diagram.

The rightward force arrow points to the right. Friction slows the blocks progress and pulls in the opposite direction. Normal forces still apply as does gravitational force since we are on planet Earth. Below is a block moving upwards toward its peak after having been launched into the air. Neglecting air resistance, below is the free-body diagram.

In this diagram above, the force of gravity is the only force described. Below a block rolls down hill.

In this diagram above, the lock is coasting down the hill, there is still the dragging friction of the road (left pointing arrow) as well as gravity and normal forces. Now let’s take a look at what happens when unbalanced forces do not become completely balanced (or cancelled) by other individual forces. An unbalanced forces exists when the vertical and horizontal forces do not cancel each other out. Below, notice the upward force of 1200 Neutons (N) is more than gravity (800 N). The net force is 400 N up.

Below, notice that while the normal force and gravitation forces are balanced (each are 50 N) the force of friction results in unbalanced force on the horizontal axis. The net force is 20 N left.

Another way to look at balances and unbalanced forces.

Balanced

Unbalanced

Free-body Diagram:2 dimension examples

Free-body Diagram:3 dimension examples

A load case is a combination of different types of loads with safety factors applied to them. A structure is checked for strength and serviceability against all the load cases it is likely to experience during its lifetime.

Typical load cases for design for strength (ultimate load cases; ULS) are:

A typical load case for design for serviceability (characteristic load cases; SLS) is: