Acceleration and braking redistribute an AGV’s or AMR’s vertical wheel loads. For a vehicle supported at two longitudinal support lines on a level floor, the load transferred between them is:
[
\Delta N=W\frac{|a_x|}{g}\frac{h}{L}
]
Here, (W) is the total loaded vehicle weight, (a_x) is longitudinal acceleration, (g) is gravitational acceleration, (h) is the loaded center-of-gravity height, and (L) is the distance between the support lines. This is the axle-group form of the longitudinal load-transfer relationship presented in Matthijs Klomp’s vehicle dynamics research at Chalmers University of Technology, Section 2.1.1, Equations 2.6–2.7.
The transferred load is added to one support group and subtracted from the other—not added to every wheel. During forward acceleration, the rear group gains load; during forward braking, the front group gains load. Start with the actual static reactions, apply this transfer, and only then determine the load on each complete caster assembly.
Determine Whether Two Support Lines Represent the Chassis
The equations below use a rigid-body, quasi-static model: vertical and pitch accelerations are neglected, the payload remains fixed, and the vehicle travels straight on a level floor. Propulsion and braking forces act through the wheel-floor contacts. The calculation estimates vertical support reactions, not stopping distance, impact force, or a complete caster’s combined vertical and horizontal loading.
A front row of two casters and a rear row of two drive wheels can fit this model. “Support line” means a transverse line through the effective floor-contact locations; it does not require a physical axle connecting the wheels.
Other layouts require additional information:
- A central drive axle with casters both ahead of and behind it has three longitudinal support lines. Static equilibrium alone does not determine how all three share the load.
- Spring-loaded drive modules, rocker mechanisms, and equalized caster mounts require their spring characteristics or linkage geometry to establish load sharing.
- Four corner casters plus central drive wheels cannot be reduced to “drive wheels versus casters” merely by entering the two wheel counts.
- A towing force or docking force applied above floor level introduces an additional pitching moment that the basic equation does not include.
For swivel casters, use the actual wheel-floor contact positions when caster orientation changes the effective support spacing materially. Mounting-plate spacing is not necessarily the same as contact-patch spacing.
If the chassis cannot be represented by two support lines, obtain its support-reaction model from the equipment manufacturer or use instrumented wheel-load measurements. Dividing total weight by the installed wheel count does not resolve an unknown load distribution.
Establish Static Loads Before Applying Acceleration
Use the complete operating configuration: chassis, batteries, attachments, lifting equipment, fixtures, and payload. The relevant center of gravity is that of the entire loaded vehicle, not the payload alone.
For the two-support-line model, define:
| Variable | Meaning | U.S. customary units |
|---|---|---|
| (W) | Total loaded vehicle weight, a force | lbf |
| (L) | Longitudinal distance between rear and front support lines | in. |
| (x) | Horizontal distance from the rear support line to the combined center of gravity | in. |
| (h) | Combined center-of-gravity height above the floor | in. |
| (N_{F0}) | Total static reaction at the front support line | lbf |
| (N_{R0}) | Total static reaction at the rear support line | lbf |
On a level floor:
[
N_{F0}=W\frac{x}{L}
]
[
N_{R0}=W\left(1-\frac{x}{L}\right)
]
These are group loads, not individual caster loads.
If component weights and locations are known, calculate the combined center of gravity:
[
x=\frac{\sum W_i x_i}{\sum W_i},
\qquad
h=\frac{\sum W_i h_i}{\sum W_i}
]
Each (W_i) is a component weight; (x_i) and (h_i) are its longitudinal position and height, measured from the same references.
Alternatively, measure static wheel loads with suitable calibrated scales or load cells, keeping all supports at the same elevation and preserving the normal suspension position. Sum the individual readings for each support line. Static reactions establish the longitudinal load split, but do not by themselves establish center-of-gravity height.
A percentage describing how much payload rests on the casters does not fully define the static caster load. The unloaded robot’s contribution must also be known:
[
N_{C0}=N_{C,\text{robot}}+pW_P
]
Here, (N_{C,\text{robot}}) is the unloaded robot weight carried by the caster group, (W_P) is payload weight, and (p) is the payload fraction carried by that group.
Calculate Acceleration and Braking as Separate Cases
Choose a fixed vehicle coordinate system: front remains front even when the robot reverses. Let (a_x) be positive toward the vehicle’s front, and define:
[
k=\frac{a_x}{g}
]
The signed support reactions are:
[
N_F=N_{F0}-Wk\frac{h}{L}
]
[
N_R=N_{R0}+Wk\frac{h}{L}
]
Thus:
- Forward acceleration has (k>0): front load decreases and rear load increases.
- Forward braking has (k<0): front load increases and rear load decreases.
- Acceleration into reverse also has (k<0).
- Braking while traveling in reverse has (k>0).
For every case, the reactions must satisfy:
[
N_F+N_R=W
]
That equality applies because the model neglects vertical acceleration. A calculation that increases both group loads without another vertical force is not this load-transfer model.
Keep Mass, Force, and Acceleration Units Distinct
In the customary-unit equations, use (W) in lbf and enter acceleration as the dimensionless ratio (a_x/g). For example, 0.20 g means (k=0.20), not 20.
If acceleration is measured in ft/s²:
[
k=\frac{a_x}{32.174\ \text{ft/s}^2}
]
Keep (h) and (L) in the same length units.
In SI units, use total mass (m) in kg:
[
W=mg,
\qquad
\Delta N=\frac{m|a_x|h}{L}
]
With acceleration in m/s² and both lengths in meters, the transferred load is in newtons. A catalog rating labeled “lb” needs confirmation that it represents supported load; do not insert a force value into an equation that expects mass.
Use Acceleration Data That Represent the Stop Being Evaluated
Evaluate normal starts, service stops, applicable emergency stops, and both travel directions. Use documented limits and measured behavior for the relevant payload configuration rather than a generic assumed braking rate.
For a constant-deceleration approximation:
[
|a_x|=\frac{v_0}{t}
]
or:
[
|a_x|=\frac{v_0^2}{2s}
]
Here, (v_0) is speed when deceleration begins, (t) is deceleration time, and (s) is distance traveled during deceleration. Total protective stopping distance may include detection and controller delays, so it cannot automatically be substituted for (s).
These equations produce average deceleration. A stop with a sharper peak can produce a higher instantaneous load transfer. Where abrupt stops excite chassis pitch or payload motion, this quasi-static calculation does not establish the peak caster load; dynamic analysis or instrumented testing is needed.
Worked Example: Front Casters and Rear Drive Wheels
Consider a hypothetical robot with two front support casters and two rear drive wheels:
| Input | Assumed value |
|---|---|
| Robot weight without payload | 1,000 lbf |
| Payload weight | 600 lbf |
| Total loaded weight, (W) | 1,600 lbf |
| Support-line spacing, (L) | 48 in. |
| Combined center-of-gravity height, (h) | 24 in. |
| Combined center of gravity ahead of rear support line, (x) | 19.2 in. |
| Forward acceleration | 0.20 g |
| Forward braking deceleration | 0.35 g |
Assume a laterally centered load and equal left-right sharing within each support group. All four wheels remain in contact, and there are no impacts, slopes, or external pitching moments. These are example assumptions, not recommended operating limits.
The static group loads are:
[
N_{F0}=1{,}600\frac{19.2}{48}=640\ \text{lbf}
]
[
N_{R0}=1{,}600-640=960\ \text{lbf}
]
During forward acceleration, the load transferred to the rear is:
[
\Delta N_a=1{,}600(0.20)\frac{24}{48}
=160\ \text{lbf}
]
During forward braking, the load transferred to the front is:
[
\Delta N_b=1{,}600(0.35)\frac{24}{48}
=280\ \text{lbf}
]
The resulting reactions are:
| Operating case | Front caster group | Rear drive group | Per front caster | Per drive wheel |
|---|---|---|---|---|
| Parked | 640 lbf | 960 lbf | 320 lbf | 480 lbf |
| Forward acceleration, 0.20 g | 480 lbf | 1,120 lbf | 240 lbf | 560 lbf |
| Forward braking, 0.35 g | 920 lbf | 680 lbf | 460 lbf | 340 lbf |
The highest calculated caster load is 460 lbf per assembly during braking. The highest calculated drive-wheel load is 560 lbf during acceleration. Those peaks occur in different operating cases.
The braking transfer can also be checked in SI units. The total mass is approximately 725.75 kg, braking deceleration is 3.432 m/s², height is 0.6096 m, and support spacing is 1.2192 m:
[
\Delta N_b=
\frac{725.75(3.432)(0.6096)}{1.2192}
\approx1{,}246\ \text{N}
\approx280\ \text{lbf}
]
Results are rounded to the nearest pound-force or newton; this rounding does not imply equivalent measurement accuracy.
Convert Group Reactions to Individual Caster Loads Carefully
Dividing a group reaction by its caster count is justified only when the group shares that reaction equally:
[
P_C=\frac{N_C}{n_C}
]
A centered payload alone does not prove equal sharing. Floor unevenness, mounting-height differences, chassis twist, suspension preload, and tread deflection can produce unequal individual loads. Blickle’s load-capacity guidance specifically notes that individual wheel or caster loads can vary when four or more supports are used.
Use individual reaction measurements or an appropriate structural and suspension model when unequal sharing is material. Do not apply “total wheels minus one” as a universal replacement for that analysis.
Also examine unloading. If a calculated group reaction reaches zero, the assumed two-line support condition has reached its contact boundary. A negative reaction would require the floor to pull downward on the wheel, which ordinary wheel contact cannot do. Stop using the equal-sharing calculation at that point and evaluate loss of contact and stability.
A positive group reaction does not prove that every wheel in the group remains loaded, nor does it establish adequate drive-wheel traction.
Compare Loads With Applicable Assembly Ratings
Compare the highest supported load on each caster with the rating of the exact complete assembly—not just its wheel. The bracket, swivel bearing, axle, mounting arrangement, and any suspension must also suit the application.
Use the manufacturer’s applicable dynamic rating for moving service. Static capacity is not a substitute. Blickle distinguishes dynamic and static ratings and identifies speed, floor conditions, obstacles, temperature, and load distribution as relevant departures from its reference application conditions. Its guidance does not establish a universal rating or allowance for every AGV caster.
Confirm with the supplier:
- The exact wheel, tread, bearing, bracket, and mounting configuration.
- Permitted speed at the calculated load.
- Continuous-duty and start-stop operating conditions.
- Applicable temperature, floor-joint, and obstacle conditions.
- Any required application allowance or derating.
- Suitability for horizontal forces, reversing, swivel motion, and braking-related duty.
Do not automatically add a fixed “dynamic factor” to a load-transfer result. Identify whether an allowance covers uneven sharing, impacts, speed, or another condition, and how the manufacturer requires it to be applied.
The group with the higher per-wheel load is not necessarily the capacity-limiting group. Compare load with applicable capacity:
[
U_C=\frac{P_{C,\max}}{C_C},
\qquad
U_D=\frac{P_{D,\max}}{C_D}
]
Here, (C_C) and (C_D) are the applicable caster-assembly and drive-wheel/module capacities.
For illustration only, suppose the example’s applicable capacities were 500 lbf per caster and 800 lbf per drive wheel:
[
U_C=\frac{460}{500}=92%,
\qquad
U_D=\frac{560}{800}=70%
]
The casters would be closer to their capacity despite carrying less absolute load. These percentages express vertical-load utilization only; they do not establish braking performance, traction, structural adequacy, or an approved payload.
Use the AGV Caster Load Calculator Without Assuming Missing Geometry
The AGV and AMR Caster Load Calculator presents static load per caster, worst-case load per caster, worst-case load per drive wheel, and a limiting-axle result. Its published description identifies it as an early-sizing tool rather than a dynamics simulation.
An equipment-specific longitudinal load-transfer calculation requires both (h) and (L), as well as a defensible static load split. The calculator’s displayed input list does not expose the center-of-gravity height and wheelbase needed to reproduce the equations above, even though its introduction refers to those quantities. Do not assume that an output incorporates your chassis geometry when you cannot enter or confirm it.
Use the explicit calculation above when the tool’s geometry and unloaded-robot load split cannot be established. A label identifying the group with the higher load also needs comparison with actual component capacities before it can identify a capacity limit.
Confirm Conditions That the Straight-Line Model Leaves Out
Several operating conditions require a separate calculation or equipment-specific evidence:
| Condition | What needs to be established |
|---|---|
| Raised, offset, or changing payload | Combined center of gravity and static reactions for each permitted configuration |
| Cornering, spinning, or braking in a turn | Lateral transfer, individual support reactions, and horizontal caster loads |
| Ramps and transitions | Grade-specific force balance and actual wheel contact conditions |
| Floor joints, thresholds, or debris | Transient impact loads and manufacturer approval for the obstacle duty |
| Compliant mounts or spring-loaded drives | Suspension preload, travel, stiffness, damping, and resulting load sharing |
| Towing or docking forces | Force magnitude, application height, and the additional pitching moment |
For a robot that changes payload height or position, calculate an operating envelope rather than one nominal result. Include configurations that maximize caster load and those that unload the drive wheels; they may not be the same configuration.
To confirm the estimate on equipment, record individual static support loads, payload position, and acceleration histories. Where predicted loads approach applicable component limits or contact loss, use appropriately instrumented dynamic support-load measurements under a controlled test plan. Static scales establish parked reactions; acceleration measurements establish motion; neither alone measures transient caster loads.
The resulting load envelope supports preliminary caster sizing and comparison. Acceptance still depends on the exact assembly ratings, mounting structure, operating conditions, and equipment-level validation—not a single calculated load.