Often, the role of the motion subsystem on a robot will be to move the robot along the ground. The last step in the drive train, after the motors and gears, is the wheels.
Like motors and gears, different properties of the wheel will affect your robot’s performance. The size of the wheels will be an important factor here, and will affect two distinct and different characteristics of the robot: its acceleration, and its top speed.
Wheel Sizes and Acceleration
The relationship between wheel size and acceleration is simple: bigger tires give you slower acceleration, while smaller tires give you faster acceleration.
This relationship is the product of the physics of converting the spinning motion of a motor into the forward motion of the vehicle.
Motors generate a “spinning” force (torque), which wheels convert into a “pushing” force at the point where they contact the ground. The larger this “pushing” force is, the faster the robot will accelerate.The relationship between torque and force is:
Force = Torque Distance from Center
to Edge of Wheel
A longer distance between the center of the wheel and the ground will produce a smaller force for the same amount of torque, hence the larger wheel (which has the longer distance) has a smaller force, and hence the slower acceleration.
Wheel Sizes and Top Speed
At top speed, robots with the same motor and gear ratio will generally travel with the motor running at the fastest speed it can spin. Robots may take some time to reach this speed, especially if they have high gear ratios (high gear ratio = low torque), but eventually, they tend to reach it, or at least come close.
When a wheel rolls along the ground, it is effectively “unrolling” its circumference onto the surface it is traveling on, every time it goes around. Larger wheels have longer circumferences, and therefore “unroll” farther per rotation.
Putting these two observations together, you can see that a robot with larger wheels will have a higher top speed. The robot with larger wheels goes farther with each turn of the wheels, and at top speed, robots with the same motor and gears will have their wheels turning the same number of times per second. Same number of turns times more distance per turn equals more distance, so the robot with larger wheels goes faster.