So imagine you have a robot with two wheels, each with a diameter of 1cm. The distance between the wheels (length of axle) is 2cm.
If you move each wheel at a different speed, how would you be able to predict the exact movement of the wheel?
For example: I move the left wheel at 2rev/sec and the right at 1rev/sec for 5 seconds. I know the robot will turn right, but how would I model it mathematically?
The path of travel will be a circle with center to the right of the moving robot. You can measure radii from that center to each wheel, thus obtaining circles with two different circumferences to be traversed in equal time.
If the speed of the outer wheel is twice the speed of the inner wheel, then the circumference of the outer circle must be twice the circumference of the inner circle. Therefore also, the outer radius is twice the inner radius.
Since the distance between the wheels is 2cm, the center of the robot's circle should be another 2cm to its right.
Since the outer wheel has diameter 1cm, it rolls a distance of $\pi$cm with each revolution. We then calculate: $\pi$ cm/rev * 2 rev/sec * 5 sec = 10$\pi$ cm. Since the outer wheel is traversing a circle with radius 4cm, thus with circumference 8$\pi$cm, the robot ought to complete $1.25$ circles in $5$ seconds.