Center of Gravity — Build Stability Guide

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Why CoG Matters for Override

Three game mechanics specifically punish high or off-center CoG. If you ignore CoG, you'll find out the hard way at competition.

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The most common Override-killer. A team builds a strong manipulator and a good drivetrain, then loses matches because their robot tips when an opponent pushes them on a toggle, or rocks when their arm extends past the chassis edge. CoG decisions are made in CAD/build week; the consequences appear in match week.

Three Override mechanics that punish bad CoG

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Toggle

Pushing

Toggles are 2.05" wide and you're shoving them. Opposing alliance might shove back. High CoG = robot tips during the push. Low CoG = you win the contest.

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King

of Hill

Endgame: 20-second contest at 18″ midfield height. Robots bump for control. High CoG = you get knocked off; low + wide = you stay.

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Arm

Extension

When you reach to score on a goal, the arm sticks out past the wheelbase. CoG shifts toward the arm. If it shifts past the wheel edge — you tip.

What this guide covers

Section 1 — The Physics: Why robots tip, what the "stability margin" is, and the simple formula that predicts whether your robot will fall over.
Section 2 — Component Placement: Where to put every heavy V5 component (brain, battery, pneumatic tanks, motors). Tier-1 placement rules with real masses.
Section 3 — CoG Calculator: Interactive 3D tool. Plug in component positions, get center of gravity, tipping margin, and stability rating.
Section 4 — Override + Notebook: Override-specific applications and how to document CoG analysis on slide 47 (Electronics & Wiring) and slide 38 (Manipulator CAD).

What you should know by end of Phase A

Why placing the battery low matters more than placing the brain low.
What tipping margin means and how to calculate it for your robot.
Where to put pneumatic tanks (if you use pneumatics) for best stability.
Why robots with high arms need wider wheelbases.
How to estimate CoG without a CAD model — just a scale and a tape measure.

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The Physics

Center of gravity, tipping margin, and the math that predicts when your robot will fall over.

What "Center of Gravity" Means

Center of gravity (CoG) is the average position of all the mass on your robot — the point where you could (theoretically) balance the whole robot on a single fingertip. Every component contributes to the CoG location proportional to its mass and how far it is from a reference point.

For a V5RC robot, CoG has three coordinates that matter:

X (left/right): Should be on the centerline. Off-center = robot pulls to one side and tips on tight turns.
Y (front/back): Should be near the wheelbase center. Front-heavy = wheelies under acceleration; back-heavy = front lifts when arm extends.
Z (height): Lower is better. High CoG = tippy. Low CoG = stable. This is the most important axis.

The Tipping Formula

A robot tips over when its CoG passes outside the line between the support wheels. The simple version:

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Tipping condition: tan(tip angle) = (½ × wheelbase width) ÷ (CoG height above ground)

Stability margin: the angle (in degrees) the robot can tilt before tipping. Larger = more stable.

What this means in practice:

Wheelbase Width	CoG Height	Stability Angle	Rating
17"	3"	71°	Excellent — almost can't tip
17"	5"	60°	Very stable
17"	8"	47°	OK for normal driving
17"	10"	40°	Marginal — careful with arm extension
17"	13"	33°	Tippy — won't survive contact
17"	17"	27°	Unstable — will tip from a bump

Override target: stability angle ≥ 50° for normal driving + 40° minimum with arm fully extended. That means CoG height should stay below ~7″ during normal operation, and below ~10″ even with the arm extended.

Why CoG Height Matters Most

The wheelbase width is mostly fixed (~17″ for an 18″ robot leaving room for wheels and bumpers). The dynamic variable you can actually control is CoG height. And small height changes have big effects:

Lowering CoG by 1″ at a 5″ height (going from 5″ to 4″) increases your stability angle by about 5°.
Raising CoG by 1″ from 8″ to 9″ loses you about 3° of stability.
Doubling CoG height from 4″ to 8″ cuts your stability angle nearly in half.

Two Forces That Move CoG

Static CoG

The CoG when the robot is sitting still in starting configuration. Determined by where you mount each component. Fixed when you build, hard to change without rebuilding.

Dynamic CoG

The CoG during a match, which moves as mechanisms move:

Arm extends: CoG shifts toward the arm and up. A 0.5 lb claw at the end of a 12″ arm shifts a 17 lb robot's CoG by about 0.4″ in the direction of the arm.
Robot lifts game pieces: CoG rises by approximately (piece_mass × piece_height_above_chassis) ÷ total_mass.
Pneumatic tank discharges: tank mass drops by ~30% as air is used; mostly negligible for CoG but matters for repeated calculations.
Driver pushes opponent: reaction forces try to tip you backward. Need stability margin to absorb the push without tipping.

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Design rule: calculate static CoG first. Then calculate dynamic CoG with arm fully extended + game piece in the manipulator. The worst-case dynamic CoG is the number that matters — that's when you're most likely to tip.

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Component Placement Guide

Every heavy component on a V5RC robot, with mass and recommended placement. Place by mass — the heaviest things get the most thought.

Component Masses (Reference Table)

Component	Mass	Notes
V5 Battery (276-4811)	~354 g (0.78 lb)	Single largest discrete component on most robots
V5 Brain (276-4810)	~285 g (0.63 lb)	Second-heaviest single component
V5 Smart Motor 11W (276-4840)	155 g (0.34 lb)	Per motor; multiply by motor count
V5 Half-Motor 5.5W (276-7065)	~115 g (0.25 lb)	Per motor; lighter than 11W
Pneumatic Reservoir (single tank)	~120 g (0.26 lb)	Add ~30 g for full air pressure
Pneumatic Reservoir (dual stacked)	~250 g (0.55 lb)	Common configuration for arm-heavy bots
Pneumatic Solenoid + Mounting	~50 g (0.11 lb)	Per solenoid (most teams use 2-4)
5″ Standoff Spike (each)	~5 g (0.01 lb)	Negligible individually; can add up across structure
4″ Omni Wheel	~85 g (0.19 lb)	Per wheel; 4 wheels = 340 g total
2.75″ Omni Wheel	~50 g (0.11 lb)	Per wheel; 4 wheels = 200 g total
5×35 c-channel (per inch)	~7.5 g/in (0.017 lb/in)	The chassis structure adds up fast

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Typical Override robot total mass: 5-7 kg (11-15 lb), depending on configuration. Battery + brain alone account for ~640 g (10-12% of total). The structure (c-channel, plates, fasteners) is usually the largest mass category at ~50% of total.

Placement Tier 1 — The Heavy Hitters

354gV5 Battery

V5 Battery

Place: LOW + CENTER Within 2″ of ground

The single biggest CoG-affecting component. Mount as low as possible — ideally directly on the bottom plate of the chassis between the drivetrain motors. Should be removable without tools (you swap it between matches). Avoid mounting above 4″ — every inch the battery goes up costs ~0.4″ of CoG height because of how heavy it is.

285gV5 Brain

V5 Brain

Place: LOW + ACCESSIBLE Within 4″ of ground

Second-heaviest component. Mount low but with the touchscreen accessible from above (you tap it for downloads, autonomous selection, diagnostics). Keep the cables clear — Smart Cable strain on a buried Brain is a common failure. Avoid mounting on the arm or anywhere that moves during a match.

~250gPneumatic Tanks (×2 stacked)

Pneumatic Reservoir(s)

Place: LOW + SYMMETRIC Behind battery preferred

If you use pneumatics, stacked dual tanks are common. Mount low, behind the battery if possible (rear-of-chassis area). Symmetrical L/R placement matters — putting both tanks on one side creates left-right CoG imbalance and the robot pulls to one side. Keep tanks AWAY from the arm side because as the arm extends, dynamic CoG shifts toward the arm and you don't want extra mass there.

Placement Tier 2 — Per-Motor Decisions

155g×4 Drive Motors

Drivetrain Motors (4 × 11W = 620 g total)

Place: LOW + SYMMETRIC In line with wheels

Drivetrain motors are unavoidable mass low on the robot — that's actually a feature, since they keep CoG low. Mount in pairs (left/right) at the same height. Don't mount one drive motor higher than another for "packaging convenience" — it creates left/right CoG imbalance. Outer-edge mounting is preferred for cooling and access.

155g×1 Arm Motor (or ×2)

Arm Motor(s)

Place: NEAR ARM PIVOT As low as the arm allows

Mount arm motor(s) AT or BELOW the arm pivot, never above. A motor mounted high on the arm itself adds dynamic CoG that swings as the arm moves — terrible for stability. Use chain or gear drive from a low motor position to lift the arm. The Spartan Hero Bot V1.5 uses two arm motors mirrored at the pivot point — that's the pattern.

155g×1 Manipulator Motor

Manipulator/Intake Motor

Place: AT MANIPULATOR BASE Not on the moving end

If your manipulator is at the end of an arm, the manipulator motor should be at the arm BASE (the pivot side), with chain/gear drive to the manipulator. Putting the motor at the manipulator end massively increases the moment arm and hurts stability when the arm is extended.

115g×2 Half-Motors

5.5W Half-Motors (drivetrain)

Place: LOW + SYMMETRIC

If using half-motors on the drivetrain (e.g., the 4×Blue + 2×5.5W = 55W config), mount them low with the drive motors. Their lower mass (115 g vs 155 g) means slightly less CoG impact, but they still need to be paired left/right.

Placement Anti-Patterns (What NOT to Do)

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Battery on top of brain. Common rookie mistake — stacks the two heaviest components both at ~3-5″ height. CoG goes way up. Always put battery below brain.

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Battery on the arm or any moving part. Massively destabilizing because dynamic CoG swings as the arm moves. Plus the cable will eventually break from repeated flexing. Always on the chassis.

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Pneumatic tanks both on one side. 250 g of mass concentrated on one side of the chassis throws off left-right CoG balance. Robot turns into a slight curve at full speed. Always symmetric.

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Brain at the highest point of the chassis. "We needed the touchscreen visible" is not a good reason. Use a low brain mount and a periscope mirror, or accept that you'll need to lean over to see the screen during pit work. CoG matters more than convenience.

❌

Manipulator motor at the end of an extended arm. Doubles or triples the dynamic CoG shift when the arm extends. Always mount manipulator motors at the arm base, never at the end.

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3D CoG Calculator

Plug in the height (Z), front-back (Y), and left-right (X) position of each major component. Get total CoG, stability angle, and rating.

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How to use: Reference all positions from the back-left bottom corner of your 18″ × 18″ × 18″ envelope. So 9, 9, 0 is the center of the chassis bottom. 9, 9, 9 is the geometric center. Heights are measured from the ground (top of wheel surface). Estimate to the nearest inch — this is a planning tool, not a precision instrument.

⚙️ ROBOT COG ANALYSIS

V5 Battery

354 g

X (in)

Y (in)

Z height (in)

V5 Brain

285 g

X (in)

Y (in)

Z height (in)

Drivetrain (4 × 11W motors)

620 g

X (in)

Y (in)

Z height (in)

Arm Assembly + 2 Motors

650 g

X (in)

Y (in)

Z height (in)

Manipulator + Motor

280 g

X (in)

Y (in)

Z height (in)

Pneumatic Tanks (optional)

250 g

X (in)

Y (in)

Z height (in)

Chassis Structure (estimated)

2500 g

X (in)

Y (in)

Z height (in)

Wheelbase

Wheelbase width (in)

Wheelbase length (in)

CoG X

—

CoG Y

—

CoG Height (Z)

—

Total Mass

—

Tip Angle (side)

—

Tip Angle (front)

—

Adjust component positions above. Default values are a typical Spartan-style robot.

Reading the Results

Stability Angle	Rating	What to Do
≥ 55°	Excellent	Robot can take heavy contact + arm extension without tipping
50° – 55°	Good	Override-ready; matches normal V5RC build standards
40° – 50°	Marginal	OK for static play but vulnerable when arm extends or under push
30° – 40°	Tippy	Lower the heaviest component; widen wheelbase if possible
< 30°	Critical	Will tip from a bump. Redesign before building.

Tips for Better Numbers

Drop the battery first. If you can move the battery from 4″ to 2″, you typically gain 3-4° of stability angle. Biggest single ROI.
Brain at 4″ is fine. Don't sacrifice usability putting the brain on the floor — the touchscreen needs to be readable. 4-5″ is a good compromise.
Move pneumatic tanks behind the chassis center. If your arm extends forward (Y < 9), put pneumatic tanks at Y > 9 to balance.
X coordinate should always be 9 for everything heavy. Off-center mounting on heavy parts creates left/right imbalance.
Increase wheelbase length. Going from 14″ to 16″ wheelbase length gains you ~3° of front-back stability with no other changes.

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Override Application + Engineering Notebook

How to apply CoG to specific Override mechanics, and how to document CoG analysis on the notebook slides judges actually grade.

Override-Specific CoG Targets

Override Mechanic	Recommended CoG Behavior	Why
Toggle pushing (R3, midfield)	CoG height ≤ 5″, wheelbase ≥ 15″	Stability angle ≥ 56° resists sideways push
King-of-hill endgame (18″ height)	CoG height ≤ 7″ with arm down	Robots pushing for hill control will bump you
Cup placement on tall goals (8.7″)	Front CoG margin ≥ 4″ during arm extension	Arm reaching forward shifts CoG forward; you can't tip into the goal
Pin loading from match loaders	CoG centered or slightly back when manipulator engages	Pin pickup mechanics shift forces forward; back-balanced CoG counters
Auton routine planning	Plan so robot is never "extended" on accelerations	Sudden stops with extended arm = tipping risk

How to Measure CoG on the Real Robot

Once your robot is built, you can measure actual CoG (not just CAD-estimated) with simple tools:

Measure total weight. Use a kitchen scale or postal scale. Record in grams or pounds.
Find front-back CoG. Place a thin dowel under the chassis perpendicular to the front-back axis. Slide it until the robot balances. Distance from front wheels = front-back CoG offset.
Find left-right CoG. Same procedure, dowel oriented front-to-back.
Estimate height CoG. Tilt the robot on a ramp until it just starts to tip. Record the angle. Apply: CoG_height = (½ × wheelbase_width) ÷ tan(tip_angle).
Photograph each measurement for the engineering notebook.

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Calibration tip: compare your measured CoG to your CAD-estimated CoG (from Onshape's mass properties tool, or from this calculator). They should agree within 0.5″. If they don't, the heaviest component is mis-modeled in CAD or mis-placed in the build. Either way, it's a useful catch.

Engineering Notebook Documentation

CoG analysis goes on multiple slides — judges look for it explicitly:

Slide 17 — Criteria & Constraints

Add a stability target: "Robot must maintain stability angle ≥ 50° with arm at full extension."
Cite this as a measurable design criterion in the criteria column.

Slide 28-29 — Decision Matrix (Drivetrain Selection)

Include "Stability with arm extended" as one of the matrix scoring rows.
Score each drivetrain candidate (4WD, 6WD, X-drive) against this criterion.
Wider wheelbase patterns (6WD) score higher; X-drive's smaller effective base scores lower.

Slide 38 — Manipulator/Intake CAD

In your CAD specification table, note the manipulator's height and how it shifts dynamic CoG.
Include a calculation: "Manipulator at 8″ height + 0.3 lb game piece shifts robot CoG by X inches when arm extends to 14″."

Slide 47 — Electronics & Wiring

Include a top-down diagram showing battery + brain + tanks + motor placement.
Annotate the diagram with mass values and the calculated CoG location (X, Y, Z).
This is where judges look for "did you actually think about CoG, or just put the battery wherever it fit?"

Slide 49+ — Test & Evaluate (EDP Step 5)

Document your CoG measurement procedure (the 5-step process above).
Include the measured CoG values vs CAD-predicted values.
If the measured stability angle is < 50°, document what you changed and re-measured.

Team Discussion Questions

Q1Where is our battery right now? Measure the height. Is it the lowest mounting point we could achieve?

Q2If our arm is fully extended carrying a cup, where is dynamic CoG? Use the calculator with arm Y = 1 (fully forward) and an extra 30 g for the cup at the manipulator location.

Q3Can our robot survive a side-bump from another robot during king-of-hill? If stability angle < 45° with arm down, the answer is probably no.

Q4If we use pneumatic tanks, are they symmetric L/R? If not, the robot will pull to one side at full speed.

Q5Have we considered widening the wheelbase? Going from 14″ to 16″ wheelbase length gains about 3° of stability without changing any component locations.

Cross-Reference Guides

"How do I model this in CAD?" → /onshape-robot-layout (top-down packaging + 1D CoG estimator)
"What are my drivetrain options for stability?" → /drivetrain-architectures (4WD vs 6WD vs X-drive footprint comparison)
"How heavy should our robot be?" → /drivetrain-101 Section 2 (Speeds + Weight)
"What about lift mechanisms specifically?" → /mechanism-cascade (cascade-lift CoG analysis)
"Where's the canonical robot example?" → /spartan-hero-bot (V1.5 component placement)