Mass, Center of Mass, and Stability

Where mass is located can matter as much as how much mass the robot has.

A battery mounted low and centered affects the robot differently from the same battery mounted high on a moving arm.

Center of mass

The center of mass is the point where the system's mass can be treated as concentrated for many motion and stability problems.

For a simple two-mass line:

m1 ---- x1 -------- x2 ---- m2

the combined center depends on both mass and position.

You do not need a perfect analytical model for every robot. You do need to notice when a design moves large mass far from the support area.

Tipping is a geometry problem

A robot remains statically stable when the vertical projection of its center of mass stays inside its support polygon.

For a four-wheel robot, imagine the polygon formed by the wheel contact points.

As an arm extends, the center of mass can move toward an edge.

top view

o----------------o
|       ● COM    |
|                |
o----------------o

If the projected center moves outside the support area, gravity creates a tipping moment instead of restoring the robot.

Dynamic effects

Acceleration changes the practical stability margin.

A tall robot can remain stable while parked and tip during:

• hard acceleration;
• sudden braking;
• fast turning;
• arm motion;
• collision.

That is why a "worked fine on the stand" test is not enough.

Tradeoff example

You want a sensor mast 1.5 meters high.

Option A uses a heavy rigid structure. Option B uses a lighter structure with more flex.

The decision involves:

• sensor stability;
• center of mass;
• vibration;
• structural stiffness;
• motor load;
• protection from impact.

No single variable wins automatically.

Stability review

Take your mechanism design from Unit 2 or invent a mobile robot with one moving mechanism.

Sketch two configurations:

1. mechanism retracted;
2. mechanism extended.

Mark the estimated center-of-mass shift and identify the most dangerous motion condition.

Then propose one design change:

• move a heavy component;
• widen support;
• reduce moving mass;
• limit acceleration;
• change the mechanism geometry.

Explain what tradeoff the change creates.