Statics and Stability

Tipping Stability

For the system to avoid tipping, the center of mass (COM) must remain within the supporting polygon. When the arm is fully extended, components like segment 3 and the hand assembly can extend beyond this polygon, increasing the risk of tipping.

Pivot Point for Analysis

The analysis uses the edge of the base as the pivot point because tipping occurs around this edge. The structure rotates about this point when tipping happens.

Torque Contributions

Overturning (Tipping) Moment

Components outside the support polygon exert an overturning moment that promotes tipping. This moment is calculated by:

\[M_{overturning} = \sum (F_{gravity} \cdot d)\]

where d is the horizontal distance from the pivot edge to the component’s COM.

Restoring Moment

Components within the support polygon (e.g., the base, segment 1 and segment 2) provide a restoring moment that resists tipping. The restoring moment is given by:

\[M_{restoring} = \sum (F_{gravity} \cdot d)\]

where d denotes the horizontal distance from the pivot edge to these stable components’ COM.

Comparison of Moments

• If \(M_{restoring} > M_{overturning},\) the system remains stable.
• If \(M_{overturning} > M_{restoring},\) the system will tip.