⚖ PAYLOAD · DESIGN MATH

Designing for the weight of what you carry

Game-object mass feeds five places in your design: grip force, arm and lift torque, drivetrain budget, center of gravity, and structural deflection. This guide shows the math for each, with worked Override 2026-27 examples.

// Section 01
Why payload weight matters
Mass is one of the few inputs that touches almost every subsystem. Get it right early and the rest of the design math falls into place; get it wrong and you re-do work later.

Five places weight feeds your design

Every V5RC robot that picks something up runs into the same five questions. The same payload mass m shows up in all of them.

Design outputWhat weight tells youWhere on this site
Claw grip forceMinimum normal force per gripping surface to hold the object against gravity and dynamic loads.This page § Grip Force, plus mechanism-claw
Arm / lift motor torqueContinuous torque the motor sees at the worst moment-arm position; sets reduction ratio and motor count.This page § Arm Torque, plus mechanism-lifts
Drivetrain wattage budgetWhether payload meaningfully changes acceleration or top speed within the 88W cap (Override R10a).This page § Drivetrain, plus super-clawbot-v2-override
Center of gravity shiftHow much picking up the payload moves the robot's CG horizontally and vertically — tipping risk.This page § Center of Gravity, plus center-of-gravity
Structural deflectionWhether the arm or lift sags under load enough to miss scoring positions; aluminum vs. steel choice.This page § Deflection, plus wheel-and-config-analysis

The honest scale check

For a 5 kg robot lifting an 80 g object, the payload is roughly 1.5% of the total mass. That sounds small enough to ignore — and for some calculations (drivetrain wattage, simple structural deflection) it really is. But for two of the five outputs the payload completely dominates: the grip force is set only by the payload mass (the robot mass is irrelevant), and the worst-case arm torque comes from mgL at the end of the moment arm.

So the right mental model isn't "payload is small compared to robot" — it's "different design questions are sensitive to different masses." Section 7 has a full sensitivity table.

🔎
This guide is general; the worked examples are Override. The math frameworks apply to any V5RC season; the cup and pin examples use Team 2822's measured values for Override 2026-27 (73 g pin, 78 g cup — see Section 1 for source). Substitute your season's masses for any other game.

Related guides on this site

// Section 02
Where the weight number comes from
Three sources, in order of preference. The right answer depends on what stage of the season you're in.

1. Game manual (best, when available)

Every official game manual eventually publishes element masses in the appendix or game-element specifications. This is the only source judges, refs, and other teams will all cite consistently. When you have it, use it; when you don't, document what you used.

2. Direct measurement (good)

Once you have actual elements in hand — from a kit, a competition, or a 3D-print — weigh them. A kitchen-grade digital food scale reads to 1 g resolution with ±1–2 g accuracy at this mass range, which is more than precise enough for V5RC design math. Notebook discipline:

3. Estimate (last resort)

Before any element exists in the wild, estimates are the only option. Sources, in decreasing order of trust:

  1. Reveal video / specifications page from VEX, if dimensions and material are listed.
  2. Comparable element from past seasons. A 6.5″ tall hollow plastic cup is in roughly the same envelope as several historical game pieces; a 3D model + assumed wall thickness gives a usable estimate.
  3. CAD volume × assumed density. Polycarbonate is ~1.2 g/cm³; ABS is ~1.05; HDPE is ~0.95. Compute volume from a parametric model in Onshape, multiply.

Estimates should always be flagged as such in the notebook, and revisited as soon as a real element is available.

Override 2026-27 status

Pin: 73 g. Hex prism, 6.5″ tall, tapered 3.16″ base → 1.40″ neck.
Cup: 78 g. Hourglass profile, 6.5″ tall, transparent + opaque halves.

Source: Measured by Team 2822 on a kitchen-grade digital food scale (1 g resolution), May 2026. Manual v0.1 (April 27, 2026) does not specify masses; v1.1 (expected August 13, 2026) may publish official values for cross-checking. Re-measure after v1.1.

If you're another V5RC team and you have your own measurements, they're more authoritative than ours for your robot. The 73 / 78 g numbers are the best-available reference until VEX publishes official values.

// Section 03
Grip force — the only place payload dominates
Static hold sets the floor. Dynamic loads from arm acceleration multiply it. Friction coefficients depend on durometer and surface.

Static hold formula

For two gripping surfaces (wheels, fingers, jaws) compressing the object from opposite sides, each providing normal force N, friction coefficient μ with the object surface:

2 · μ · Nm · g   →   N ≥ (m · g) / (2μ) m = payload mass (kg), g = 9.81 m/s², μ = friction coefficient, N = normal force per side (N).

This is the minimum hold — you'd add a safety factor (typically 5–10×) on top.

Friction coefficients (rubber on plastic game element)

Wheel materialμ (typical)Notes
Black flex (65A) — hard~0.3Most durable, lowest grip; needs more compression to compensate.
Dark gray flex (45A) — medium ← common pick~0.5Goldilocks zone; good grip + acceptable wear.
Light gray flex (35A) — soft~0.8Highest grip; wears faster, may grab too aggressively.
Standard wheel rubber on cup plastic~0.6For reference if not using flex wheels.
3D-printed PLA/PETG — smooth~0.2–0.3Add a TPU pad or rubber strip for grip.

Dynamic load — what static math misses

If the arm holding the payload accelerates — swinging up, slamming to a stop, riding bumps — the effective gravity goes up. The grip has to handle m · (g + a) where a is the linear acceleration of the payload at that moment.

For a payload at the end of a rotating arm:

acentripetal = ω² · L ω = angular velocity (rad/s), L = moment arm length (m). For a 90° sweep in 0.5 s: average ω ≈ (π/2)/0.5 = π rad/s ≈ 3.14 rad/s.

Worked Override example: cup at 17″ reach

// WORKED EXAMPLE

Required grip force: 78 g cup, swung 90° in 0.5 s on a 17″ arm

m = 0.078 kg  |  L = 0.432 m (17 inches)  |  μ = 0.5 (dark-gray flex on plastic)
Static gravity: g = 9.81 m/s²
Centripetal: a = ω²L = (3.14)² × 0.432 = 4.26 m/s²
Effective vertical accel during sweep: g_eff ≈ 9.81 + 4.26 = 14.07 m/s²
Per-side normal force needed (no SF): N = m · g_eff / (2μ) = 0.078 × 14.07 / 1.0 = 1.10 N
With 10× safety factor: N ≥ 11.0 N per side
→ Each gripping surface must provide ~11 N normal force during the worst-case dynamic moment.

For static-only conditions (object held still), this drops to ~7.6 N per side at 10× SF. The mechanism-claw Architecture E delivers ~10 N per side at the recommended 0.125″ compression — covers static fully (13× SF), and dynamic with 9× SF.

Battery sag is the silent grip-force killer. Pneumatic grippers don't care about battery voltage, but motorized grips (claw motors, intake roller grips) deliver less force at lower battery voltage. Test grip force on a fresh battery and a 10.8V depleted battery before declaring a design done.
// Section 04
Arm and lift torque
The motor sees torque equal to weight times moment arm. Worst case is fully-extended horizontal. Add the arm's own weight; reduce by your gear ratio.

Gravitational torque at the joint

For an arm pivoting at one end, holding payload m at distance L from the pivot, the worst-case torque (arm fully horizontal) is:

τpayload = m · g · L Result is in N·m. Multiply by 8.85 to convert to in·lb. Add the arm's own moment τarm = marm · g · Lcg (where Lcg is the distance from pivot to the arm's center of gravity, typically L/2 for a uniform arm).

Reduction trades torque for speed

A motor at 100 RPM with stall torque τstall can drive an arm output through a gear reduction R:

τoutput = R · τstall · η Where R = reduction ratio (5:1 means R = 5), η ≈ 0.85–0.92 efficiency for clean spur gears. Output speed = motor speed / R.

Continuous-load convention

Don't size to stall torque — that's the absolute ceiling, not the sustainable rating. A 11W V5 motor stalled draws ~2.5A and overheats in seconds. The conventional rule is:

Design so that your worst-case static torque is ≤ 50% of stall torque at the output. That gives the motor headroom for dynamic loads, friction, voltage sag, and slight overshoots without thermal protection kicking in.

Worked Override example: Super Clawbot V2 shoulder

// WORKED EXAMPLE

Shoulder torque holding 78 g cup at 17″ reach

L = 0.432 m (17 inches, full arm extension)  |  m_payload = 0.078 kg
Estimated arm self-weight: m_arm = 0.45 kg (aluminum upper + steel forearm + claw assembly)
Arm CG distance: L_cg ≈ 0.22 m (slightly past mid-arm; claw mass biases it outward)
τ_payload = 0.078 × 9.81 × 0.432 = 0.330 N·m (= 2.92 in·lb)
τ_arm = 0.45 × 9.81 × 0.22 = 0.971 N·m (= 8.60 in·lb)
Total static: τ_total = 1.30 N·m = 11.5 in·lb
11W Red 100 RPM motor: stall τ = 2.10 N·m at output shaft
With 5:1 reduction (12T → 60T) & η = 0.88: τ_output_stall = 5 × 2.10 × 0.88 = 9.24 N·m
Utilization: 1.30 / 9.24 = 14% of stall
→ Comfortably under the 50% rule. Single Red motor at 5:1 handles the load with ~7× headroom.

Note that the payload contributes only 25% of the total static torque — the arm's own weight dominates. This is true at V5RC scale for almost every sub-100 g payload: the design driver is the arm itself, not what it carries. See super-clawbot-v2-override for the full V2 power-budget calculation.

💡
Counterbalances handle the arm; the motor handles the payload + dynamics. If the arm's own weight is the dominant torque, a rubber-band counterbalance sized to neutralize most of τarm at the most common operating angle leaves the motor responsible only for accelerating the system and lifting the payload. This is how teams run a 4-DOF arm on small motors.
// Section 05
Drivetrain — usually robust to payload
At V5RC scales, an 80 g payload is small relative to robot mass. Acceleration changes are typically below 2%. The exception is stacked / multi-piece carrying.

Acceleration math with payload

F = (Mrobot + mpayload) · a Where F is the net pushing force from your wheels (after friction losses). Adding payload mass reduces the achievable a for the same F.

Single-element case — small effect

For a typical V5RC robot at ~5 kg pushing 1 cup (78 g):

Multi-piece carrying — payload starts to matter

If the game allows stacking or multi-element possession, mass scales linearly. For an Override robot carrying a hypothetical 4-cup stack:

The drivetrain wattage cap is on the robot, not on the payload. Override R10a caps total motor power at 88 W and R11a caps drivetrain at 55 W — both regardless of what the robot is carrying. Payload mass shows up in the physics, not in the rules.

When to actually run this calc

For most V5RC designs, you can skip drivetrain re-sizing for payload. The robot dominates the mass. The exceptions:

// Section 06
Center of gravity shift
Holding a payload moves the robot's CG. Lifting it adds a vertical shift. Tipping happens when CG projects outside the wheelbase.

CG combination formula

For a robot of mass M with CG at (xR, yR) holding payload m at (xP, yP), the combined CG is the mass-weighted average:

xcombined = (M · xR + m · xP) / (M + m) Same formula for vertical (y). Compute both. Both matter for tipping — horizontal moves the projection, vertical raises the moment arm.

Tipping criterion

The robot tips when the combined CG, projected straight down, falls outside the polygon defined by the wheel contact points (the "support polygon"). For a square holonomic drive, that's the square of the wheelbase. For a long, narrow chassis, the short side is the failure direction.

Worked Override example: arm extended forward, raised high

// WORKED EXAMPLE

5 kg robot, 18″ square wheelbase, holding 78 g cup at full reach + lift

M = 5.0 kg, robot CG at chassis center: (x_R = 0, y_R = 0.10 m above the wheel axles)
m = 0.078 kg, cup at end of 17″ arm extended forward, raised 16″ above pivot
Pivot location relative to chassis center: x = 0.10 m forward, y = 0.13 m above wheel axles
Cup position: (x_P = 0.10 + 0.43 = 0.53 m forward, y_P = 0.13 + 0.41 = 0.54 m above axles)
x_combined = (5.0 × 0 + 0.078 × 0.53) / 5.078 = 0.0081 m forward (0.32 inches)
y_combined = (5.0 × 0.10 + 0.078 × 0.54) / 5.078 = 0.107 m above axles (raised 0.7 cm)
Distance from CG-projection to nearest wheelbase edge: 0.229 - 0.008 = 0.221 m (8.7 inches)
→ CG shift is small. Tipping margin remains ample (8.7″) even with arm fully extended high.

The 18″ square chassis is forgiving. Narrower chassis (12″ wide rear-mounted lifts) or larger payloads (multi-piece carries, heavier objects) can change this materially. See center-of-gravity for an interactive calculator with multiple wheelbase options.

The dynamic-tipping case is harder than the static one. A robot that's stable when stationary can still tip if it accelerates while the arm is high — the robot's own deceleration creates a forward torque on the elevated payload. If your arm reaches near full height during driving, simulate a hard stop (or just drive the robot into a wall and watch).
// Section 07
Structural deflection
For most V5RC payloads, the arm's own weight deflects the structure more than the payload does. Worth checking, rarely the design driver.

Cantilever deflection formula

For an arm of length L, modulus E, second moment of area I, with a tip load F = m · g:

δtip = F · L³ / (3 · E · I) For VEX C-channel at typical 1×5×1 cross-section: I ≈ 0.0066 in⁴ (steel) or same for aluminum (geometry, not material). Esteel = 29×10⁶ psi. Ealuminum = 10×10⁶ psi. Self-weight contribution: δself = w · L⁴ / (8EI) where w is weight per unit length.

Worked Override example: 78 g cup at 17″ on a steel C-channel

// WORKED EXAMPLE

Tip deflection from payload alone vs. from arm self-weight

L = 17″  |  F = 0.078 × 9.81 = 0.765 N = 0.172 lbf  |  I = 0.0066 in⁴
Steel: δ_payload = (0.172 × 17³) / (3 × 29×10⁶ × 0.0066) = 0.0015 in (negligible)
Aluminum: δ_payload = (0.172 × 17³) / (3 × 10×10⁶ × 0.0066) = 0.0043 in (still negligible)
Steel C-channel weight: ~5 oz/foot = 0.026 lbf/in. Self-weight deflection at 17″: δ_self = 0.026 × 17⁴ / (8 × 29×10⁶ × 0.0066) ≈ 0.18 in
Aluminum C-channel: ~1.8 oz/foot. δ_self ≈ 0.18 in × 0.36 (lighter) × 2.9 (lower E) ≈ 0.19 in — comparable.
→ The 78 g cup deflects the arm 0.001–0.004″; the arm's own weight deflects it 100× more.

For payload masses below ~500 g, structural deflection is dominated by the arm itself. Material choice matters — see wheel-and-config-analysis for the steel-vs-aluminum tradeoff — but for payload-driven deflection at V5RC scale, the answer is "no, you don't have to worry."

When deflection becomes the design driver

// Section 08
Sensitivity — which decisions hinge on payload mass
Not every calculation is equally sensitive to a ±5 g error. Knowing which is which tells you where to spend measurement effort and where a placeholder is fine.

The sensitivity table

"Sensitivity" here means: if your payload mass estimate is off by 10%, by how much does the design output change? The closer to 1:1, the more important accurate measurement is.

Design outputSensitivity to payload massRobustness
Claw grip force (required N)1:1 (linear)Low — measure carefully
Arm payload torque alone1:1 (linear)Low
Arm total torque (with self-weight)~0.25:1 (payload is ~25% of total)Medium — estimates often fine
Drivetrain acceleration~0.015:1 (payload is ~1.5% of mass)High — ignore differences below ~50 g
CG horizontal shift~0.015:1 (linear in m/M ratio)High
Payload-only deflection1:1 (linear)High — absolute value tiny
Arm total deflection~0.01:1 (self-weight dominates)Very high

What this means in practice

If you only measure one thing: measure for grip force. A 10% error in payload mass directly causes 10% error in required grip. That can be the difference between "secure" and "drops the cup at the worst moment."

If your payload is < 200 g (most V5RC game elements), drivetrain and CG calculations are robust to even rough estimates. Use a placeholder; refine when you have time.

The arm-torque case is the interesting middle: payload contributes only ~25% of the total joint torque, but that 25% can be the difference between staying under the 50%-of-stall design rule and not. Measure when you can; estimate ±20% if you can't.

💡
Re-measure when: the official manual publishes (cross-check), the kit changes mid-season (rare but happens), you switch to a new vendor's element for practice, you start carrying multi-piece stacks, or you observe a grip-force or torque problem that doesn't match your math.
// Section 09
Writing the payload analysis in your notebook
An EN-compliant entry pattern that makes the design math visible to judges. Pick the calculation that drove your decision and show your work.

What judges want to see

The RECF Engineering Notebook rubric (EN1–EN5) rewards entries where the engineering process is visible. For a payload-driven decision, that means showing:

  1. The number — what is the payload mass and where did it come from?
  2. The math — what calculation did you run with that number?
  3. The decision — what did the math tell you to choose, and why?
  4. The verification — how did you test that the math matched reality?

Example notebook entry — choosing arm reduction ratio

// SAMPLE NOTEBOOK ENTRY

Decision: Arm reduction ratio — 5:1 vs 7:1

Payload mass. Override cup mass measured 78 g (mean of n=3 cups, range 76–79 g) on a kitchen-grade digital food scale, May 2026. Pin mass measured 73 g (mean of n=3, range 72–74 g). Awaiting confirmation against game manual v1.1 (August 2026).

Constraint. Arm must reach the 8.77″ tall center goal from the back-loader position. Reach calculation in [previous entry] sets arm length at 17″. Per V5RC R10a/R11a (Override), our 88 W budget allocates 11 W to the shoulder.

Math. Worst-case static torque at horizontal extension: payload contributes 0.078 × 9.81 × 0.432 = 0.330 N·m. Arm self-weight (0.45 kg, CG at 0.22 m): 0.971 N·m. Total: 1.30 N·m. Red 100 RPM stall = 2.10 N·m at the motor. Required output torque to stay under 50% of stall (the design rule from payload-design): need at least 2 × 1.30 = 2.60 N·m at the output.

Decision. 5:1 reduction gives 2.10 × 5 × 0.88 = 9.24 N·m at the output (3.6× the requirement). 7:1 would give 12.93 N·m but slows the arm from 20 RPM to 14.3 RPM, lengthening cycle time. We chose 5:1 to preserve cycle time at acceptable safety margin.

Verification. Built and tested: arm holds 78 g cup at full extension without motor stall warnings on a 12.8 V battery. Cycled 50 lifts on a depleted (10.8 V) battery — no thermal protection triggered. Test data in [later entry].

📖
EN4 reminder. The numbers in your notebook must be your team's actual measurements and reasoning. The frameworks on this page are reference material; the values, the calculation, and the decision must come from your team's own work. Cite this guide as a reference; the conclusion is yours.

Where this entry fits in the EDP

The example above is a purple-slide entry in the standard notebook color scheme — it's a "select best solution" decision backed by analysis. Place it after your gold-slide brainstorm (where you considered 3:1, 5:1, and 7:1 as candidates) and before the orange-slide build log. See notebook-template for the full slide-color scheme and how this fits into a complete EDP cycle.