Swerve System Geometry & Motion Math

Advanced design ties the CAD model to physics. For a swerve drivebase, the geometry you lay out and the gear ratio you pick determine how fast, controllable, and tip-resistant the robot is.

Free speed from a gear ratio. Robot drive free speed = (motor free RPM ÷ gear ratio) × wheel circumference. The MK4i uses a 4 in wheel, so circumference = π × (4/12) ft ≈ 1.047 ft. With the L2 ratio (6.75:1) and a motor near ~6000 RPM free speed: 6000 ÷ 6.75 ≈ 889 wheel RPM → (889/60) × 1.047 ≈ 15.5 ft/s theoretical free speed (real loaded speed is lower). The MK4i's published drive ratios are L1 8.14:1, L2 6.75:1, L3 6.12:1; SDS publishes an official free-speed table per motor, so pull exact ft/s figures from there rather than relying on the back-of-envelope number. A lower ratio number (L3 6.12) is faster but lower-torque; a higher number (L1 8.14) gives more pushing force. Most full-weight robots run L1 or L2; L3 is for lighter robots.

Steering ratio. The MK4i steers at 150/7:1 (≈21.43:1) — that is the module azimuth gearing, relevant when you tune the steering controller and check how fast modules can re-point.

Wheelbase, track, and tipping. Your layout sketch sets the track (#track) and wheelbase. CAD computes center of mass automatically; the design rule is to keep the COM projection inside the wheel contact polygon under acceleration. A taller robot or an extended arm shifts COM toward an edge — read mass properties at the worst-case pose (arm out, full of game pieces) and confirm the COM stays comfortably inboard of the wheels. Lower-mounted batteries and lower overall CG resist tipping.

Current-limited traction. Free speed is only half the story; you also need traction without browning out. Estimate per-module tractive force from motor stall torque, gear ratio, and wheel radius, then compare to the friction limit (wheel coefficient of friction × weight per wheel). If the geared force exceeds available traction, the wheels slip and the extra ratio is wasted — and pulling full stall current on four drive motors can trip breakers, so teams apply motor current limits in firmware. Choosing the ratio is therefore a joint mechanical + electrical decision: enough torque to use available traction, not so much that you waste current.

Putting it together: lay out track/wheelbase in CAD, pick the gear ratio that hits your target speed while staying traction- and current-limited, then validate COM and free speed against the worst-case pose. This is the bridge from a pretty model to a robot that actually drives well.