Load & Stability Analysis
Punch Force Modelling & Design Philosophy
A boxing punch does not apply a constant force over time. Instead, the force-time history is highly transient, with a short-duration peak lasting only a few milliseconds. Designing directly from the absolute instantaneous peak would be excessively conservative for many structural and actuation components. For BoxBunny, the adopted load philosophy therefore distinguishes between:
- a characteristic training load, representing a strong but realistic punch during normal gym use, and
- a structural design load, representing a conservative upper-bound event that the robot structure must survive without failure.
Based on literature reviews of punching biomechanics, the following values were adopted:
Fdesign = 1.5 × Fchar = 2.7 kN
The characteristic value of 1.8 kN was selected as a strong but realistic punch for the target user group. The structural design load of 2.7 kN was obtained by applying a factor of 1.5 to account for impact amplification, user variability, modelling simplifications, and manufacturing tolerances.
This distinction maps onto:
- Ultimate Limit State (ULS): structural integrity under rare, hard punches.
- Serviceability Limit State (SLS): repeated-use performance, wear, and normal training behaviour.
For the base subsystem, the critical case is the ULS structural design load, because the base must not tip or fail under a worst-credible strike.
Phase 1 Fair Implementation: Body Placement
During the first fair-stage implementation, the robot was mounted on a 1220 mm × 580 mm wooden board. At that stage, the most important engineering question was where along the 1220 mm board length the main robot body should be positioned. This was treated as an overturning problem. When the robot is struck from the front, the most likely tipping mode is forward rotation about the front edge of the support region.
The forward punch creates an overturning moment:
Opposing this is the restoring moment from the weight of the robot:
where W is the total system weight and xCG is the horizontal distance from the front pivot edge to the centre of gravity.
Shifting the robot body further rearward increases xCG, which increases restoring moment and improves anti-tipping behaviour. However, shifting it too far rearward would reduce practical front clearance or complicate the layout. The fair-stage calculation therefore acted as a placement study, balancing restoring moment, user footwork space, and assembly practicality.
This early analysis established a principle that remained valid throughout later iterations: the base layout should be defined by overturning mechanics and user-space constraints, not by symmetry or convenience. It directly influenced the later decision to adopt a smaller-front / wider-rear welded trapezoidal base.
Stability Analysis of the Final Base
For the later welded-base design, the same stability logic was retained in a more formalised form. When a punch impacts the robot's upper body, two potential failure modes arise at the base: sliding (where the horizontal punch force exceeds static floor friction) and tipping (where the overturning moment exceeds the restoring moment).
Tipping was selected as the governing failure mode because floor friction is highly variable (e.g., rubber mats, concrete, interlocking foam). A robot that is inherently stable against tipping through geometry and mass distribution alone will remain safe on any floor surface without relying on favourable friction.
The key design requirement is that the restoring moment must exceed the overturning moment by a sufficient margin:
This expresses the requirement that the restoring moment exceed the overturning moment with a factor of safety of at least 1.5.
This factor of safety is consistent with the broader load-analysis philosophy adopted for BoxBunny: punching is impulsive, user-dependent, and not perfectly repeatable, so a conservative but practical design margin is appropriate. Floor friction was recognised as beneficial but treated only as a secondary effect. The base was required to remain upright through geometry and mass distribution alone.
Factor of Safety Justification
The moderate factor of safety of 1.5 was explicitly selected to account for the following physical uncertainties:
| Uncertainty Source | Effect |
|---|---|
| Punch intensity variation | Users range from beginners (~200 N) to experienced boxers (~1.5 kN) |
| Strike height variation | Head strikes produce larger overturning lever arms than torso strikes |
| Impact direction | Off-axis punches (hooks, angled straights) introduce unpredictable lateral components |
| Modelling simplifications | CG location estimated from CAD; actual mass distribution differs slightly after wiring and assembly |
| Fabrication tolerances | Weld distortion, material variation, and assembly alignment affect actual pivot geometry |
Requirement Traceability
This overturning analysis verifies compliance with system-level requirement RM-1 (Structural Stability): the robot must remain upright under worst-credible punching loads without relying on external anchoring. The analysis is also coupled to RM-3 (Portability): adding ballast to increase the restoring moment directly increases the robot's transport mass. The trapezoidal base geometry optimises this trade-off by biasing the self-weight rearward rather than increasing total mass.
Implications for the Welded Base-Feet Design
The transition from the wooden board to the welded trapezoidal steel base can be understood directly through the load analysis:
- The analysis showed that the base should provide stronger restoring leverage behind the centre of mass. This is why the final base became wider at the rear and narrower at the front.
- It reinforced the importance of keeping the assembly's mass as low as practical to support a favourable low vertical mass concentration.
- It clarified that the mounted plate and welded frame must be treated as part of the structural load path. Punch loads applied high on the robot must ultimately flow through the structure and into the floor without excessive compliance.
Detailed Stability Check: Phase 1 (Fair)
The objective of this analysis is to verify that the robot remains stable and does not tip over when subjected to a representative backward‑directed lateral punch force during operation (tipping backwards about the rear base edge).
Assumptions:
- The applied punch force acts horizontally and is modelled in the backward direction.
- The force is applied at the upper punching interface (worst-case lever arm).
- The robot behaves as a rigid body during loading.
- Ground contact is idealised as a single pivot edge at the rear of the base.
- Friction effects are neglected in the primary stability check.
- Total mass (m): 53 kg
- Weight (W): 53 × 9.81 = 519.93 N
- Design punch force (F): 2700 N
- Height of force application (h): 1100 mm (1.1 m)
- CoG offset (b): For the 1220 mm board, the CoG projection lay 492 mm from the front. Thus, the rear-edge CoG offset b = 1220 - 492 = 728 mm (0.728 m).
To ensure the robot remains stable without tipping over, the required horizontal distance between the CoG and the rear pivot edge (bmin) is determined from moment equilibrium and the target factor of safety (FoS ≥ 1.5):
To convert this into a minimum board footprint length (Lmin) for a rear-edge pivot, we use the CAD-measured CoG position from the front edge (xCoG,front = 0.492 m):
Lmin = 0.492 + (1.5 × 1.1 / 519.93) × Fback ≈ 0.492 + 0.00317 × Fback
If the measured backward-directed operational load is approximately 229 N, then Lmin ≈ 1.22 m, which precisely matched the 1220 mm Fair-stage board length used.
To determine the maximum allowable backward-directed load at the target FoS (1.5):
This static continuous limit of 229 N initially appears low compared to the 1.35 kN operational dynamic load. However, a static model assumes a continuous push. In reality, a boxing punch is fundamentally a short-duration impulse (lasting ~15 milliseconds). A 1.35 kN peak force applied over 15 ms transfers less kinetic energy than a 229 N continuous force applied over a tenth of a second. Because the punch dissipates long before it can physically accelerate the robot's CoG past the tipping pivot, this geometry successfully prevented tip-over during Fair operation.
Detailed Stability Check: Phase 2 (Final)
The objective of the Phase 2 (Final) stability analysis is to confirm that the final base design and final assembled mass distribution provide sufficient resistance to tip‑over under the final design loading envelope.
The same moment‑equilibrium approach used in Phase 1 is retained for Phase 2. For the critical loading direction considered (backward tipping), the final robot is assumed to pivot about the rear base edge. Stability is assessed by comparing the overturning moment from a backward-directed lateral load applied at height against the restoring moment due to the robot weight acting through the CoG offset.
Overturning Moment Calculation:
For Phase 2, the backward-directed force magnitude used for tipping assessment reflects the 1.35 kN operational dynamic punch. As proven in Phase 1, the dynamic impulse of this strike is comfortably absorbed by the base. With the final mass increasing to ~105 kg, the equivalent continuous static tipping threshold is massively increased, meaning it remains safely immune to the 1.35 kN impulse.
Restoring Moment Calculation:
Factor of Safety:
The Phase 2 base design (with an increased system mass estimated at ~105 kg) significantly increases the restoring moment margin through a wider support polygon and a lower CoG compared to the Fair-stage prototype. The final build acceptance criterion remains FoS ≥ 1.5 under the defined operational load case.
Compared with the Fair-stage prototype, the final welded base provides vastly improved stability due to increased structural stiffness, more controlled mass placement, and a significantly more robust support polygon.
Remaining Analytical Gaps
- Continuous updating of the final centre of mass as more hardware is installed.
- Verification of the tipping calculation using the exact support polygon of the final welded base-feet assembly.
- Confirmation that the tip-and-roll transport mode does not compromise stability during handling.
- Comparison of the analytical tipping model against experimental behaviour for full-system confirmation.