Robot Mechanics & Chassis Design: Wheels, Gears, Bearings, Torque & Materials

Robotics software engineers often treat hardware as an idealized, abstract API: call set_velocity(1.5), and the robot moves at 1.5 m/s.

In reality, the physical world does not forgive mechanical mistakes:

• If gear teeth have excessive backlash (mechanical play), a PID position loop will oscillate violently regardless of software tuning.
• If a chassis flexes when turning, wheel encoder odometry becomes mathematically invalid.
• If motors lack sufficient stall torque to climb a 15-degree handicap ramp, the autonomous mobile robot (AMR) becomes stranded.

Mechanical engineering is the physical bridge that allows electrical energy and software algorithms to interact safely with the real world.

To select the correct motor and gearbox reduction ratio, you must calculate the total tractive force ($F_{\text{total}}$) required at the wheel contact patch.

The Three Forces of Mobile Motion

1. 1
   Rolling Resistance ($F_{\text{rr}}$): The force required to deform the tire and ground surface:

*(where $C_{\text{rr}} \approx 0.015$ for hard wheels on smooth concrete, $0.05$ for rubber on asphalt, and $0.15$ for thick carpet).*

1. 2
   Grade Resistance ($F_{\text{grade}}$): The gravitational pull when climbing an incline angle $\alpha$:

1. 3
   Acceleration Force ($F_{\text{acc}}$): The force required to reach target velocity $v$ in time $t_{\text{acc}}$:

Calculating Total Required Motor Torque

The total required linear force is:

For a robot with radius $r$ and $N$ driven wheels sharing load equally, the torque required per wheel shaft is:

Always apply an engineering safety factor of $1.5\times$ to $2.0\times$ to account for gearbox friction, bearing losses, and motor thermal derating.

Choosing the physical wheel configuration dictates the robot's mobility, mechanical complexity, and terrain capability.

Electric motors are naturally high-speed, low-torque devices (e.g., spinning at 6,000 RPM with only $0.05\text{ N}\cdot\text{m}$ of torque). To drive a robot wheel at 150 RPM with $2.0\text{ N}\cdot\text{m}$ of torque, we use a mechanical speed reducer.

1. Planetary Gearboxes (Epicyclic)

• Architecture: A central Sun gear drives three or four Planet gears rotating inside an internal Ring gear.
• Why Roboticists Love Them: The torque load is split across multiple gear teeth simultaneously, giving incredible torque density in a compact coaxial cylindrical package.
• Efficiency: 90-95% per stage. Standard in mobile robot wheels and brushless actuators.

2. Worm Drives (Right-Angle 90°)

• Architecture: A spiral screw (worm) meshes with a spur gear (worm wheel).
• The Self-Locking Property: Because of the shallow lead angle, the worm can turn the wheel, but the wheel *cannot backdrive the worm*.
• Use Case: Elevating scissor lifts, winch cables, and heavy robot arms where a power cut must not drop a suspended payload.
• Downside: High sliding friction yields low efficiency (40-65%), dissipating energy as heat.

3. Harmonic Drives (Strain-Wave Gearing)

• Architecture: An elliptical wave generator rotates inside a flexible, thin-walled toothed cup (Flexspline), engaging with a circular rigid outer spline.
• The Zero-Backlash Miracle: Continuous tooth engagement eliminates mechanical play ($< 1\text{ arcminute}$ backlash).
• Use Case: High-precision industrial robot arm joints (Universal Robots, KUKA).

The number one rookie hardware mistake in robotics is bolting a heavy 150mm wheel directly onto the 6mm output shaft of a DC motor without external support.

The Cantilever Problem (Bending Moments)

When a 20 kg robot hits a floor seam at 1 m/s, the vertical impact force acts at the wheel rim. Because the wheel center is offset from the motor casing, this force creates a massive bending moment ($M = F \cdot L$). Internal motor bushings and miniature gearbox pins are designed purely to transmit *torsional torque*, not bending moments. Over time:

1. 1
   Gearbox shafts bend by a fraction of a millimeter.
2. 2
   Internal spur gear teeth misalign, wear out unevenly, and strip under load.
3. 3
   Shaft seals fail, leaking grease onto electronics.

Proper Mechanical Load Isolation

Industrial mobile bases place the wheel on a dead axle or dedicated live axle supported by two deep-groove ball bearings or flanged bearings pressed into the chassis frame. The motor connects to this axle via:

• A flexible shaft coupling (absorbs axial and angular misalignment)
• Or a timing belt/pulley reduction (isolates shock loads completely from the gearbox).

Selecting the right chassis material determines whether your robot survives a 1-meter drop test or shatters into pieces.

The "Acrylic Trap"

Laser-cut cast acrylic (Plexiglass) looks gorgeous, glossy, and futuristic. However, acrylic is the worst material for functional robotics:

• It is brittle and has virtually zero impact resistance.
• Overtightening a screw or motor mounting bolt introduces microscopic stress concentrations that propagate into catastrophic cracks within days under motor vibration.
• Threading screws directly into acrylic will strip instantly.

Engineering Materials Compared

A robot can have perfect motor torque and rigid aluminum plates, but if its weight is distributed poorly, it will tip over backward whenever it accelerates or brakes hard.

Managing the Center of Gravity (CG)

• Lower is Always Better: Mount heavy components—namely the battery pack (often 30-50% of the robot's total weight) and heavy motor assemblies—as low as physically possible, beneath the chassis floor plate if clearance permits.
• Static Stability Margin: For a 3-wheeled or 4-wheeled robot, the vertical projection of the Center of Gravity must always stay well inside the support polygon formed by the wheel contact points.
• Dynamic Deceleration Tipping: When braking from high speed with a tall sensor mast:

If $m \cdot a \cdot h_{\text{CG}} > m \cdot g \cdot d_{\text{front}}$, the rear wheels lift off the ground, causing the robot to face-plant into the floor.